A manifold means “1. Having many forms, parts, etc.” [1] Manifolds which have many parts, forms are not
necessarily one to one to 3 spheres. Poincare conjecture can be proven and disproven based on the case study of
imaginary manifolds, imaginary numbers, ellipses, rhombus, trapezoids, parallelograms, triangles, squares,
always changing manifolds and the Sun or stars. Proof and disproof are reasonable for the Poincare Conjecture.
Homeomorphic has 2 meanings. One meaning of homeomorphic is similar in form and one meaning of
homeomorphic is deformable. [2] Proof and disproof of Poincare Conjecture are supported by the 2 definitions of
homeomorphic and the definitions of manifold. Dr. Grigori Perelman’s proof of the Poincare Conjecture does not
place enough emphasis on the meaning of homeomorphic as having similarity of form or the definition of manifold
as many, diverse or varied.
Graphs consist of vertices connected by edges. Large graphs with billions of vertices are studied theoretically to understand their properties regardless of small changes in definition. There are different types of graphs including weighted, undirected, directed, connected, and complete graphs. Graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS) are used to search graphs, with DFS using a stack and BFS using a queue. Graph theory has applications in modeling networks, computer architectures, and optimization problems.
The document defines key terms in geometry such as undefined terms, definitions, postulates, and theorems. It explains that undefined terms like point, line, and plane cannot be defined precisely but can be described. Definitions use words to precisely define a term. Postulates are accepted as true without proof, while theorems can be proven. It provides examples of geometry postulates and theorems.
The document is a student's geometry PowerPoint presentation showing examples of geometry found in everyday life. It contains 14 slides with pictures demonstrating various geometric shapes found in objects around the student's home and explanations of the shapes. The shapes include circles, decagons, frustums, perimeters, rhombi, tangents, planes, chords, parallel and perpendicular lines, rectangles, nets, cylinders, kites, regular polygons, special right triangles, tessellations, triangles, spheres, and decagons. Each slide contains a picture example, labeling of relevant geometric aspects, and definitions of key terms.
Mathematics is evident everywhere in nature and is an integral part of our lives. It is the science of patterns, quantities and relationships. The document discusses several examples of patterns in nature like geometric shapes, symmetry, the Fibonacci sequence and golden ratio that are all deeply rooted in mathematics. It also elaborates on the importance and applications of mathematics in fields like science, technology, medicine and more, establishing it as an indispensable and universal language.
This document discusses the nature and scope of mathematics. It begins by examining different views on what mathematics is, from counting to abstract structures and patterns. It also looks at pure versus applied mathematics. Pure mathematics solves problems internal to mathematics, while applied mathematics solves real-world problems. Number theory is used as an example of pure mathematics exploring questions like prime number distribution. Applied mathematics is illustrated through calculating the time for an object to fall down a well, showing how mathematics can model physical situations. The distinction between pure and applied is blurred, as work in one area can lead to applications in another.
Fractals are the mathematical explanation of our world. Knowledge of fractals is essential to everyone's experience of their world. Here, I have explained the concept of fractals.
This document discusses three-dimensional space and geometry. It begins by defining dimension and explaining that a point in 3D space is defined by three coordinates: x, y, and z. Different coordinate systems for 3D space are presented, including Cartesian and cylindrical/spherical coordinates. Common 3D shapes are described such as polyhedrons, prisms, cylinders, cones, and spheres. Higher dimensions beyond 3D are briefly touched on. The document also discusses visualizing 3D space through graphs of functions with multiple variables.
Benedetto Scoppola: From Euclid to Montessori, the construction of rational g...Jirka Pelc
- Montessori was influenced by the Greek origins of mathematics from figures like Plato and Euclid
- She understood the difference between the Platonic view of "evident truths" vs the Euclidean view of starting from defined postulates and deducing theorems
- In her work, she adopted a Platonic approach to engage children's interest, but recognized the need to later introduce the rational, deductive method of Euclid
- Her goal was to educate children to be skeptical and convince themselves through work, preparing their minds for rigorous logical thought which can discourage irrationality and violence
Graphs consist of vertices connected by edges. Large graphs with billions of vertices are studied theoretically to understand their properties regardless of small changes in definition. There are different types of graphs including weighted, undirected, directed, connected, and complete graphs. Graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS) are used to search graphs, with DFS using a stack and BFS using a queue. Graph theory has applications in modeling networks, computer architectures, and optimization problems.
The document defines key terms in geometry such as undefined terms, definitions, postulates, and theorems. It explains that undefined terms like point, line, and plane cannot be defined precisely but can be described. Definitions use words to precisely define a term. Postulates are accepted as true without proof, while theorems can be proven. It provides examples of geometry postulates and theorems.
The document is a student's geometry PowerPoint presentation showing examples of geometry found in everyday life. It contains 14 slides with pictures demonstrating various geometric shapes found in objects around the student's home and explanations of the shapes. The shapes include circles, decagons, frustums, perimeters, rhombi, tangents, planes, chords, parallel and perpendicular lines, rectangles, nets, cylinders, kites, regular polygons, special right triangles, tessellations, triangles, spheres, and decagons. Each slide contains a picture example, labeling of relevant geometric aspects, and definitions of key terms.
Mathematics is evident everywhere in nature and is an integral part of our lives. It is the science of patterns, quantities and relationships. The document discusses several examples of patterns in nature like geometric shapes, symmetry, the Fibonacci sequence and golden ratio that are all deeply rooted in mathematics. It also elaborates on the importance and applications of mathematics in fields like science, technology, medicine and more, establishing it as an indispensable and universal language.
This document discusses the nature and scope of mathematics. It begins by examining different views on what mathematics is, from counting to abstract structures and patterns. It also looks at pure versus applied mathematics. Pure mathematics solves problems internal to mathematics, while applied mathematics solves real-world problems. Number theory is used as an example of pure mathematics exploring questions like prime number distribution. Applied mathematics is illustrated through calculating the time for an object to fall down a well, showing how mathematics can model physical situations. The distinction between pure and applied is blurred, as work in one area can lead to applications in another.
Fractals are the mathematical explanation of our world. Knowledge of fractals is essential to everyone's experience of their world. Here, I have explained the concept of fractals.
This document discusses three-dimensional space and geometry. It begins by defining dimension and explaining that a point in 3D space is defined by three coordinates: x, y, and z. Different coordinate systems for 3D space are presented, including Cartesian and cylindrical/spherical coordinates. Common 3D shapes are described such as polyhedrons, prisms, cylinders, cones, and spheres. Higher dimensions beyond 3D are briefly touched on. The document also discusses visualizing 3D space through graphs of functions with multiple variables.
Benedetto Scoppola: From Euclid to Montessori, the construction of rational g...Jirka Pelc
- Montessori was influenced by the Greek origins of mathematics from figures like Plato and Euclid
- She understood the difference between the Platonic view of "evident truths" vs the Euclidean view of starting from defined postulates and deducing theorems
- In her work, she adopted a Platonic approach to engage children's interest, but recognized the need to later introduce the rational, deductive method of Euclid
- Her goal was to educate children to be skeptical and convince themselves through work, preparing their minds for rigorous logical thought which can discourage irrationality and violence
This document discusses different definitions of dimension, focusing on topological dimension and Hausdorff dimension. It provides examples of fractals like the Sierpinski triangle and Koch curve that challenge classical dimension definitions. While topological dimension aligns with intuition, the Hausdorff dimension considers how content scales with measurement. The document explains how fractals like the Sierpinski triangle have topological dimension of 1 but area of 0, requiring a fractional Hausdorff dimension to adequately measure their content. This provides the conceptual basis for Mandelbrot's definition of fractals as sets where the Hausdorff dimension exceeds the topological dimension.
Mathematics was invented by humans to describe patterns and quantities in the real world. Some key points:
- Early humans developed counting as a practical tool for tasks like tracking food supplies and trade goods. Counting led to the development of basic arithmetic operations and the first written number systems.
- Properties of numbers, geometry, algebra, calculus, etc. were conceptualized by mathematicians over thousands of years through observing patterns and designing logical systems to model physical phenomena. Different cultures developed unique systems for writing and representing numbers.
- While mathematics describes inherent patterns in nature, the specific symbols, notations, definitions, and branches we use today are all human constructs. The rules and structures of mathematics have evolved significantly over the course of history
Add math project 2018 kuala lumpur (simultaneous and swing)Anandraka
This document is a student's additional mathematics project work. It includes an introduction on the history of equations and their applications. It discusses how ancient Babylonians, Arabs, and Europeans contributed to solving quadratic equations over time. It also provides examples of how quadratic equations are used in various areas like determining the length of the hypotenuse and establishing the proportions of paper sizes. The student expresses frustration with lack of help from their teacher and tuition teacher in completing the project, but was able to finish it through their own research and discussion with friends.
Algebraic topology uses algebra to study topological spaces. It translates questions about spaces into equivalent algebraic questions that are often easier to answer. For example, it uses the fundamental group to distinguish between a sphere and donut by showing they have different fundamental groups. Modern algebraic topology generalizes the concept of a topological space to spectra, which allows consideration of "negative-dimensional space" analogous to negative numbers extending integers.
Writing A Hypothesis Worksheet - EscolagersonalKathryn Patel
Cluniac monasticism had both strengths and weaknesses between the 10th and 12th centuries. A key strength was its independence from local control, allowing it to elect its own abbot and expand. This expansion occurred as other monasteries were reformed under Cluniac rule. However, maintaining control over a widespread network of dependencies was challenging. While Cluniac monks observed a strict Benedictine rule and engaged in charity, critics argued this resulted in worldly corruption over time.
The document defines linear equations in two variables as equations that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It provides an example linear equation as 2x + 3y = 18 and explains how to determine if a given ordered pair (3, 4) is a solution by substituting the values into the equation.
Crop circles first appeared over 300 years ago in England. Over time, they grew in size and complexity, evolving from simple circles to intricate geometric patterns. Mathematicians have studied crop circles and discovered that many follow precise geometric rules and relationships. Some mathematicians even proposed new theorems based on analyses of crop circle patterns. While the origins of crop circles remain mysterious, they have inspired new mathematical discoveries and interest in geometry.
Form and shape can be described in two or three dimensions. Two-dimensional forms have width and height, while three-dimensional shapes also have depth. Forms can also be categorized as organic or geometric. Organic forms are irregular and asymmetrical, often occurring naturally, while geometric forms correspond to regular shapes like squares and circles. Two-dimensional forms use techniques like line, value, hue, texture, and negative space to create the illusion of three-dimensional shapes and spaces.
Fractals and symmetry are closely related concepts in mathematics. Fractals exhibit a repeating pattern that displays at every scale and often have non-integer fractal dimensions. Some key fractals include the Mandelbrot set, Julia set, and Koch snowflake. Symmetry refers to an object having identical corresponding parts on opposite sides of a dividing line or plane. There are several types of symmetry such as reflection, rotation, translation, and scale symmetry which fractals demonstrate. Benoit Mandelbrot coined the term "fractal" and studied their properties, finding their applications in fields like art, geography, and physics.
20130523 06 - The mathematics the way algorithms think / the mathematics the ...LeClubQualiteLogicielle
This document summarizes Thomas McCabe's presentation on quantifying shifts in consciousness mathematically. McCabe introduces the Dihedral complexity, which quantifies perspectives inherent to thoughts in the same way the McCabe complexity quantifies algorithm paths. He discusses how algorithm complexity impacts software and how consciousness complexity could have emerging computer science applications. The talk traces the mathematical derivation of algorithmic and consciousness complexity and discusses increasing complexity of consciousness.
Supersize Me essay. Supersize me essay. Super Size Me - Textual Analysis. Supersize Me Essay. Supersize Me Worksheet Free Yeah in 2020 | Super teacher worksheets .... Super Size Me by Morgan Superlock Essay Example | Topics and Well .... 004 Supersize Me Essay Example 008016034 1 ~ Thatsnotus. Descriptive Essay: Super size me essay.
This document is the preface to "The History of Mathematics: A Brief Course Answers to Questions and Problems" by Roger Cooke. It explains that the solutions manual is intended for instructors and not students directly, and contains the author's personal views in response to questions from the textbook. The preface notes that references and citations from the textbook are included for context but the literature list is not. It aims to promote discussion and critical thinking rather than provide definitive answers.
FRACTAL GEOMETRY AND ITS APPLICATIONS BY MILAN A JOSHIMILANJOSHIJI
This document provides an introduction to fractal geometry and its applications. It discusses how fractals were discovered by Mandelbrot as a way to describe irregular patterns in nature. Some key areas where fractals are applied that are mentioned include astronomy (galaxies and Saturn's rings), biology (bacteria cultures, plants), data compression, diffusion, economy, special effects in movies like Star Trek, weather patterns, antennas, and understanding global warming. The document also provides mathematical definitions of fractals and the Mandelbrot set, and describes how to graph the Mandelbrot set. Examples of fractals discussed in more depth include the Sierpinski triangle, Koch curve, broccoli, veins, and the Lorenz
This document provides an introduction to fractal geometry and its applications. It discusses how fractals were discovered by Mandelbrot as a way to describe irregular patterns in nature. Some key areas where fractals are applied that are mentioned include astronomy (galaxies and Saturn's rings), biology (bacteria cultures, plants), data compression, special effects in movies like Star Trek, weather patterns, heartbeats, antennas, and modeling global warming. The document also provides mathematical definitions of fractals and the Mandelbrot set, and describes how to generate fractal landscapes and the Mandelbrot set using iterated functions.
Anti-Smog Radar Application for VehiclesIJMREMJournal
Smog is regarded as a dangerous situation for vehicles as the visibility of human fails and a person cannot
drive smoothly and safely which can lead to severe accidents and routine disturbances. Hence, “Anti-Smog
Radar Application for Vehicles” is proposed using Internet of Things technology which ensures the smooth flow
of vehicles in smog and prevents accidents in time and cost-efficient manner by detecting and displaying the
front objects with their important information (distance, position, velocity and size) on smart phone used by
authenticated drivers. The radar application controls the hardware system to be deployed on vehicles through
which the user can start, stop and set the hardware in particular direction. The hardware contains NodeMcu
(Microcontroller with built-in Wi-Fi), Ultrasonic sensor and servo motor. The servo is used to detect the
position of front objects and ultrasonic sensor is clipped on servo to detect the objects. For alerts, the objects
are drawn with different colors on application i.e. the red colored objects will be near to the vehicle, the yellow
colored objects will be at some distance from the vehicle and the green colored objects will be far from the
vehicle. Kalman algorithm is used to filter the ultrasonic readings to eliminate the noise. The proposed system
can work in every condition i.e. in day and night.
IoT based Environmental Monitoring and Control SystemIJMREMJournal
IoT plays a major role in collecting the information from the sensing unit enclosing our environment due to
alterations in the climate which led to the significance of environmental monitoring. This Paper presents a
development of real time environmental monitoring and control system by utilizing Node MCU, DHT11 sensor,
ACS712 current sensor, Thing Speak (Open IoT analytics service) and Blynk application. The main task of
monitoring parameters (Humidity, temperature and power consumption) with real time sensors is done by Thing
Speak continuously which has API (Application programming Interface) for gathering sensed data and enabling
users to observe the monitored data in graphs for an interval of every 15 seconds.
This project is also designed to control home devices sitting at any place in the world by utilizing power
efficiently through Blynk application which is used to read data from sensors located in home environment using
smart phone and to turn on/off heating and cooling appliances automatically with respect to room temperature
values.
Analysis and Implementation of Solid-State Relays in Industrial application F...IJMREMJournal
There are many applications and circumstances where switching devices are required for proper operation,
controlling and isolating the high power and low power systems. The most widely used switching devices are
electromechanical relays and solid state relays. In this work, analysis and implementation of solid state relays over
electromechanical relays with respect to instantaneous current supply inindustrial application is conducted and
compared. For this purpose, an experimental setup is arranged for switching operation of electromechanical relays
and solid-state relays.The results of voltage and the current transients are analyzed and compared. It was observed
that there are no transients occurred during switching of solid state relays where as during switching of
electromechanical relay transients observed in volatge and current waveforms. So, it is advisable to use the solid
state relays over electromagnetic relay for safe and smooth operation of the system.
MIM (Mobile Instant Messaging) Classification using Term Frequency-Inverse Do...IJMREMJournal
This document presents a study that aims to classify Mobile Instant Messages (MIMs) from WhatsApp using a Term Frequency-Inverse Document Frequency (TF-IDF) model and Bayesian algorithm. The study collected 417 WhatsApp messages labeled as positive or negative, then preprocessed the data through tokenization, stopword removal, normalization, punctuation removal and stemming. A Bernoulli Naive Bayesian classifier was trained on 75% of the data and tested on the remaining 25%, achieving an accuracy of 81.73% compared to the baseline of 69.23%. The study demonstrated that the proposed hybrid classification approach with preprocessing achieved satisfactory results for sentiment analysis of WhatsApp messages.
Is Lean Management applicable to the hospital and for which results?IJMREMJournal
lean management is a mode of organism inspired by Toyotism; His practice is evident throughout the world and
is one of the most affected institutions, except that the latter is a different profession. There is no shared vision
among the different actors on measuring the performance of the hospital. The activity of the hospital applies to
unique "products": each patient, with its peculiar specificity. The relationship of the workers with the patient is
radically different from the relationship of the worker with his product. That is why the practice of Lean has a
certain specificity in the health field.
Fabrication and Performance Analysis of Solar Tracking System by Using By-Pas...IJMREMJournal
Energy is a burning issue that almost every person experience now a days. Energy demand increases exponentially
since a decade. Due to the global warming and it’s threatening impacts on human life. Therefore, to overcome
such disastrous impacts on the planet, renewable energy resources play vital role now a days. Solar energy is one
of the vastest available renewable energy resources around the globe, but the main issue is its poor efficiency.
Pakistan is facing energy shortage that can be compensated through solar power and the need is to design a project
that maximizes its efficiency. So, the research is mainly focused on improving efficiency of solar panels against
shading loss by using different techniques. In this research, different results will be obtained and compared with
different techniques which are LDR based solar tracking system, by-pass diodes technology and super capacitors.
Fabrication of solar tracker is based on Microcontroller that drives L298N driver to operate stepper motor.
Reactivity Feedback Effect on the Reactor Behaviour during SBLOCA in a 4-loop...IJMREMJournal
The reactivity coefficient is a very important parameter for safety and Stability of reactors operation. To provide
the safety analysis of the reactor, the calculation of changes in reactivity caused by temperature is necessary
because it is related to the reactor operation. The objective is to study the effect of the temperature reactivity
coefficients of fuel and moderator of the PWR core, as well as the moderator density and boron concentration on
fluid density, reactivity, void fraction. peak fuel clad temperature and time to core uncover were found for two
feedback cases. This paper focuses on the effect of the Reactivity feedback, of the 6" (6-inch) Cold Leg
SBLOCA sequences in a 4-loop PWR Westinghouse nuclear power plant with a scram for various feedback,
moderator density coefficient, MDC, moderator temperature coefficient, MTC, the fuel temperature coefficient,
FTC, and boron concentrations. Dragon neutronic code is used for calculating reactivity's coefficient which is
used in RELAP5 thermal hydraulic computer code to simulate the effect of Reactivity feedback during Cold
Leg SBLOCA. The plant nodalization consists of two loops; the first one represents the broken loop and the
second one represents the other three intact loops. In the present analysis two models in RELAP5 code for
computation of the reactivity feedback, separable and tabular models are used. The 6-inch break size was chosen
because the previous work [1], showed that it was the worst size break in a 4-loop PWR Westinghouse. The
results show that the neglecting of the reactivity feed-back effect causes overheating of the clad and that the
importance of the reactivity feed-back on calculating the power (reactivity) which the key parameter that
controls the clad and fuel temperatures to maintain them below their melting point and therefore prevent core
uncover and fuel damage where the fuel temperature, clad temperature and core water level are in the range.
Lyapunov-type inequalities for a fractional q, -difference equation involvin...IJMREMJournal
The document summarizes a research paper that presents new Lyapunov-type inequalities for a fractional boundary value problem involving a fractional difference equation with a p-Laplacian operator. The paper obtains necessary conditions for the existence of nontrivial solutions to the equation. It also presents some applications to eigenvalue problems. Key concepts from fractional calculus such as fractional derivatives and integrals are reviewed. Lemmas establishing uniqueness of solutions to related problems are also presented.
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This document discusses different definitions of dimension, focusing on topological dimension and Hausdorff dimension. It provides examples of fractals like the Sierpinski triangle and Koch curve that challenge classical dimension definitions. While topological dimension aligns with intuition, the Hausdorff dimension considers how content scales with measurement. The document explains how fractals like the Sierpinski triangle have topological dimension of 1 but area of 0, requiring a fractional Hausdorff dimension to adequately measure their content. This provides the conceptual basis for Mandelbrot's definition of fractals as sets where the Hausdorff dimension exceeds the topological dimension.
Mathematics was invented by humans to describe patterns and quantities in the real world. Some key points:
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Add math project 2018 kuala lumpur (simultaneous and swing)Anandraka
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Writing A Hypothesis Worksheet - EscolagersonalKathryn Patel
Cluniac monasticism had both strengths and weaknesses between the 10th and 12th centuries. A key strength was its independence from local control, allowing it to elect its own abbot and expand. This expansion occurred as other monasteries were reformed under Cluniac rule. However, maintaining control over a widespread network of dependencies was challenging. While Cluniac monks observed a strict Benedictine rule and engaged in charity, critics argued this resulted in worldly corruption over time.
The document defines linear equations in two variables as equations that can be written in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not equal to 0. It provides an example linear equation as 2x + 3y = 18 and explains how to determine if a given ordered pair (3, 4) is a solution by substituting the values into the equation.
Crop circles first appeared over 300 years ago in England. Over time, they grew in size and complexity, evolving from simple circles to intricate geometric patterns. Mathematicians have studied crop circles and discovered that many follow precise geometric rules and relationships. Some mathematicians even proposed new theorems based on analyses of crop circle patterns. While the origins of crop circles remain mysterious, they have inspired new mathematical discoveries and interest in geometry.
Form and shape can be described in two or three dimensions. Two-dimensional forms have width and height, while three-dimensional shapes also have depth. Forms can also be categorized as organic or geometric. Organic forms are irregular and asymmetrical, often occurring naturally, while geometric forms correspond to regular shapes like squares and circles. Two-dimensional forms use techniques like line, value, hue, texture, and negative space to create the illusion of three-dimensional shapes and spaces.
Fractals and symmetry are closely related concepts in mathematics. Fractals exhibit a repeating pattern that displays at every scale and often have non-integer fractal dimensions. Some key fractals include the Mandelbrot set, Julia set, and Koch snowflake. Symmetry refers to an object having identical corresponding parts on opposite sides of a dividing line or plane. There are several types of symmetry such as reflection, rotation, translation, and scale symmetry which fractals demonstrate. Benoit Mandelbrot coined the term "fractal" and studied their properties, finding their applications in fields like art, geography, and physics.
20130523 06 - The mathematics the way algorithms think / the mathematics the ...LeClubQualiteLogicielle
This document summarizes Thomas McCabe's presentation on quantifying shifts in consciousness mathematically. McCabe introduces the Dihedral complexity, which quantifies perspectives inherent to thoughts in the same way the McCabe complexity quantifies algorithm paths. He discusses how algorithm complexity impacts software and how consciousness complexity could have emerging computer science applications. The talk traces the mathematical derivation of algorithmic and consciousness complexity and discusses increasing complexity of consciousness.
Supersize Me essay. Supersize me essay. Super Size Me - Textual Analysis. Supersize Me Essay. Supersize Me Worksheet Free Yeah in 2020 | Super teacher worksheets .... Super Size Me by Morgan Superlock Essay Example | Topics and Well .... 004 Supersize Me Essay Example 008016034 1 ~ Thatsnotus. Descriptive Essay: Super size me essay.
This document is the preface to "The History of Mathematics: A Brief Course Answers to Questions and Problems" by Roger Cooke. It explains that the solutions manual is intended for instructors and not students directly, and contains the author's personal views in response to questions from the textbook. The preface notes that references and citations from the textbook are included for context but the literature list is not. It aims to promote discussion and critical thinking rather than provide definitive answers.
FRACTAL GEOMETRY AND ITS APPLICATIONS BY MILAN A JOSHIMILANJOSHIJI
This document provides an introduction to fractal geometry and its applications. It discusses how fractals were discovered by Mandelbrot as a way to describe irregular patterns in nature. Some key areas where fractals are applied that are mentioned include astronomy (galaxies and Saturn's rings), biology (bacteria cultures, plants), data compression, diffusion, economy, special effects in movies like Star Trek, weather patterns, antennas, and understanding global warming. The document also provides mathematical definitions of fractals and the Mandelbrot set, and describes how to graph the Mandelbrot set. Examples of fractals discussed in more depth include the Sierpinski triangle, Koch curve, broccoli, veins, and the Lorenz
This document provides an introduction to fractal geometry and its applications. It discusses how fractals were discovered by Mandelbrot as a way to describe irregular patterns in nature. Some key areas where fractals are applied that are mentioned include astronomy (galaxies and Saturn's rings), biology (bacteria cultures, plants), data compression, special effects in movies like Star Trek, weather patterns, heartbeats, antennas, and modeling global warming. The document also provides mathematical definitions of fractals and the Mandelbrot set, and describes how to generate fractal landscapes and the Mandelbrot set using iterated functions.
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Anti-Smog Radar Application for VehiclesIJMREMJournal
Smog is regarded as a dangerous situation for vehicles as the visibility of human fails and a person cannot
drive smoothly and safely which can lead to severe accidents and routine disturbances. Hence, “Anti-Smog
Radar Application for Vehicles” is proposed using Internet of Things technology which ensures the smooth flow
of vehicles in smog and prevents accidents in time and cost-efficient manner by detecting and displaying the
front objects with their important information (distance, position, velocity and size) on smart phone used by
authenticated drivers. The radar application controls the hardware system to be deployed on vehicles through
which the user can start, stop and set the hardware in particular direction. The hardware contains NodeMcu
(Microcontroller with built-in Wi-Fi), Ultrasonic sensor and servo motor. The servo is used to detect the
position of front objects and ultrasonic sensor is clipped on servo to detect the objects. For alerts, the objects
are drawn with different colors on application i.e. the red colored objects will be near to the vehicle, the yellow
colored objects will be at some distance from the vehicle and the green colored objects will be far from the
vehicle. Kalman algorithm is used to filter the ultrasonic readings to eliminate the noise. The proposed system
can work in every condition i.e. in day and night.
IoT based Environmental Monitoring and Control SystemIJMREMJournal
IoT plays a major role in collecting the information from the sensing unit enclosing our environment due to
alterations in the climate which led to the significance of environmental monitoring. This Paper presents a
development of real time environmental monitoring and control system by utilizing Node MCU, DHT11 sensor,
ACS712 current sensor, Thing Speak (Open IoT analytics service) and Blynk application. The main task of
monitoring parameters (Humidity, temperature and power consumption) with real time sensors is done by Thing
Speak continuously which has API (Application programming Interface) for gathering sensed data and enabling
users to observe the monitored data in graphs for an interval of every 15 seconds.
This project is also designed to control home devices sitting at any place in the world by utilizing power
efficiently through Blynk application which is used to read data from sensors located in home environment using
smart phone and to turn on/off heating and cooling appliances automatically with respect to room temperature
values.
Analysis and Implementation of Solid-State Relays in Industrial application F...IJMREMJournal
There are many applications and circumstances where switching devices are required for proper operation,
controlling and isolating the high power and low power systems. The most widely used switching devices are
electromechanical relays and solid state relays. In this work, analysis and implementation of solid state relays over
electromechanical relays with respect to instantaneous current supply inindustrial application is conducted and
compared. For this purpose, an experimental setup is arranged for switching operation of electromechanical relays
and solid-state relays.The results of voltage and the current transients are analyzed and compared. It was observed
that there are no transients occurred during switching of solid state relays where as during switching of
electromechanical relay transients observed in volatge and current waveforms. So, it is advisable to use the solid
state relays over electromagnetic relay for safe and smooth operation of the system.
MIM (Mobile Instant Messaging) Classification using Term Frequency-Inverse Do...IJMREMJournal
This document presents a study that aims to classify Mobile Instant Messages (MIMs) from WhatsApp using a Term Frequency-Inverse Document Frequency (TF-IDF) model and Bayesian algorithm. The study collected 417 WhatsApp messages labeled as positive or negative, then preprocessed the data through tokenization, stopword removal, normalization, punctuation removal and stemming. A Bernoulli Naive Bayesian classifier was trained on 75% of the data and tested on the remaining 25%, achieving an accuracy of 81.73% compared to the baseline of 69.23%. The study demonstrated that the proposed hybrid classification approach with preprocessing achieved satisfactory results for sentiment analysis of WhatsApp messages.
Is Lean Management applicable to the hospital and for which results?IJMREMJournal
lean management is a mode of organism inspired by Toyotism; His practice is evident throughout the world and
is one of the most affected institutions, except that the latter is a different profession. There is no shared vision
among the different actors on measuring the performance of the hospital. The activity of the hospital applies to
unique "products": each patient, with its peculiar specificity. The relationship of the workers with the patient is
radically different from the relationship of the worker with his product. That is why the practice of Lean has a
certain specificity in the health field.
Fabrication and Performance Analysis of Solar Tracking System by Using By-Pas...IJMREMJournal
Energy is a burning issue that almost every person experience now a days. Energy demand increases exponentially
since a decade. Due to the global warming and it’s threatening impacts on human life. Therefore, to overcome
such disastrous impacts on the planet, renewable energy resources play vital role now a days. Solar energy is one
of the vastest available renewable energy resources around the globe, but the main issue is its poor efficiency.
Pakistan is facing energy shortage that can be compensated through solar power and the need is to design a project
that maximizes its efficiency. So, the research is mainly focused on improving efficiency of solar panels against
shading loss by using different techniques. In this research, different results will be obtained and compared with
different techniques which are LDR based solar tracking system, by-pass diodes technology and super capacitors.
Fabrication of solar tracker is based on Microcontroller that drives L298N driver to operate stepper motor.
Reactivity Feedback Effect on the Reactor Behaviour during SBLOCA in a 4-loop...IJMREMJournal
The reactivity coefficient is a very important parameter for safety and Stability of reactors operation. To provide
the safety analysis of the reactor, the calculation of changes in reactivity caused by temperature is necessary
because it is related to the reactor operation. The objective is to study the effect of the temperature reactivity
coefficients of fuel and moderator of the PWR core, as well as the moderator density and boron concentration on
fluid density, reactivity, void fraction. peak fuel clad temperature and time to core uncover were found for two
feedback cases. This paper focuses on the effect of the Reactivity feedback, of the 6" (6-inch) Cold Leg
SBLOCA sequences in a 4-loop PWR Westinghouse nuclear power plant with a scram for various feedback,
moderator density coefficient, MDC, moderator temperature coefficient, MTC, the fuel temperature coefficient,
FTC, and boron concentrations. Dragon neutronic code is used for calculating reactivity's coefficient which is
used in RELAP5 thermal hydraulic computer code to simulate the effect of Reactivity feedback during Cold
Leg SBLOCA. The plant nodalization consists of two loops; the first one represents the broken loop and the
second one represents the other three intact loops. In the present analysis two models in RELAP5 code for
computation of the reactivity feedback, separable and tabular models are used. The 6-inch break size was chosen
because the previous work [1], showed that it was the worst size break in a 4-loop PWR Westinghouse. The
results show that the neglecting of the reactivity feed-back effect causes overheating of the clad and that the
importance of the reactivity feed-back on calculating the power (reactivity) which the key parameter that
controls the clad and fuel temperatures to maintain them below their melting point and therefore prevent core
uncover and fuel damage where the fuel temperature, clad temperature and core water level are in the range.
Lyapunov-type inequalities for a fractional q, -difference equation involvin...IJMREMJournal
The document summarizes a research paper that presents new Lyapunov-type inequalities for a fractional boundary value problem involving a fractional difference equation with a p-Laplacian operator. The paper obtains necessary conditions for the existence of nontrivial solutions to the equation. It also presents some applications to eigenvalue problems. Key concepts from fractional calculus such as fractional derivatives and integrals are reviewed. Lemmas establishing uniqueness of solutions to related problems are also presented.
The Policies of Government Intervention as Third-Party for Conflict in Bike-S...IJMREMJournal
This research accesses to the unbalance phenomenon between the rapid development of Sharing bicycle industry
and the good public order. Taking into account the inconsistent goals of bicycle companies and users, the local
government is employed as a third party to mediate the conflict. We establish the conflict model including three
decision makers - Enterprises, Citizens and Government - based on GMCR (Graph Model for Conflict Resolution)
theory, and then find out the equilibrium by means of the decision support system GMCR II. The results show that
the sustainable development of the Sharing bicycle market requires the cooperation and efforts of all the three
parties, the government plays a necessary role to guide the enterprises and the users. We also propose some
management insights on how to provide suggestions for the sharing bicycle companies to improve their
dispatching services, and how to establish and improve relevant laws and regulations to guide citizens to use
shared bicycles in order to achieve mutual benefits
Epidemiological study for Trichomonas Vaginalis for Discrete time model and C...IJMREMJournal
During the period of July until December 2017 Conduct an epidemiological study to investigate the prevalence
of Trichomonas Vaginalis among women who have been consulted for the consultation and emergency of the
maternity and child hospital in Diwaniyah city in Iraq. The number of specimens examined was 857 samples
and the ages ranged between 15-60 years. After the swabs were taken, the direct examination and coloring and
planting on the different food communities to diagnose parasitic Trichomonas vaginalis the incidence of
Trichomonas vaginalis was 129 (17%). Using the mathematical model discrete time model and continuous time
model, it was observed that the highest percentage of infection was in July and the disease began to fade until it
reached the lowest rate in December. Using the mathematical model mentioned above, it was noted that
teaching a significant role in curbing the spread of the disease.
Energy Conservation through Smart Building and Smart Lighting SystemIJMREMJournal
Energy conservation is an extensive topic due to the propagation of electricity demand and challenges globally
and is regarded as one of the most significant issues affects the power system quality, global environment and
consumers. Smart building is a technology that can connect everything to networks or systems to monitor and
control them in various areas such as offices, energy-consuming devices especially in laboratories, security
devices etc. Nevertheless, people's perception about using smart technology for energy saving is still in the mind’s
eye. This means that people discuss about environmental awareness readily. Due to the availability of electricity
and its elemental role, regulating consumers’ behaviours towards power savings can be a challenge. Remarkably,
the gap in today's smart technology design in smart buildings is the compassionate of consumers’ attitudes and
the merging of this perspective into the smart technology. Implementation of PLC based controlling system is a
convenient method to save the power and energy strategy for whole building. Furthermore, prepare a lighting
scheme can results a rapid response in energy conservation. Consequently, PLC Automatic system removes the
human intervention which makes the process smart and energy reduction will gives benefits to the consumers in
terms of reducing the cost of electricity bills. Nonetheless, contemporary buildings’ energy conservation has been
significant solution to cope with the rising electricity necessity.
The Effect of Workplace Relationship toward Job Satisfaction of Divine Word C...IJMREMJournal
The study was conducted to determine workplace relationship between employer and employees and among employees of Divine Word Colleges in Ilocos Sur, Philippines and its effect on the job satisfaction. Literatures and studies were reviewed, and questionnaires were used to gather the data related to workplace relationship and job satisfaction. The respondents of the study are employees of the colleges of Ilocos region which include Ilocos Sur and Ilocos Norte. The study is a descriptive study involving survey and fact-finding inquiry. Weighted mean and Pearson r were used to determine the workplace relationship and its correlation with job satisfaction. The study found that there is a significant correlation between workplace relationship and job satisfaction. Therefore, the study recommends that management need to monitor and improve workplace relationship between employer and employees and among employees and also improve and monitor factors that affect job satisfaction.
Semi-automatic Picture Book Generation based on Story Model and Agent-based S...IJMREMJournal
In the fields of artificial intelligence, automatic narrative generation has attracted considerable interest. Lots of studies on narrative generation have been reported such as novel, comic, and picture book. However, most of those reuse original stories, pictures, and sentences. As a result, there is a problem that generated narratives infringe on copyright. In this paper, we focus on the picture book as the narrative because picture book is a mix of images and language. As a first step of automatic story generation without representation mediums, we propose a novel semi-automatic picture book generation method based on story model and agent-based simulation. The computational experiments are carried out to confirm the effectiveness of the proposed method
Efficiency Evaluation of Thailand Gross Domestic Product Using DEAIJMREMJournal
The goal of this research is to evaluate the efficiency of GDP in Thailand from the past years and provide suggestions for government and policy-makers on ways to manage inputs and improve outputs in the future while enhancing the GDP of Thailand. The paper analyzed the data collected from Office of the National Economic and Social Development of Thailand through a period of 25 years ranging from 1993 to 2017. The results show that the year 2017 was the worst years in terms of efficiency. In order to achieve the research goal, data envelopment analysis (DEA) was used. Theoretically, research has found that evaluation of GDP can be improved by eradicating the negative values of slack movement. In economic terms, the research proposed the promotion of export-led growth, business incubators, and entrepreneurship to boost not only the inputs but also the GPD of the country. In general, the GDP of Thailand is quite efficient. This research can provide strategic advice for Thai Government to improve the Gross Domestic Product thoroughly
Predicting Trade Conflict Outcomes using a Third-Party Intervention ModelIJMREMJournal
As anti-import sentiment and protectionism have been increasing, more papers have focused on using theories to explain or resolve them. However, most research has focused on disputes involving larger nations such that there is not much relatable information for disputes such as the one between South Africa and Zimbabwe. The aim of this paper was to bridge the knowledge gap by using the graph model for conflict resolution and the decision support software GMCRII to simulate possible responses to this regional trade conflict. This thirdparty intervention model will assist in investigating and prescribing a diplomatic solution with fair compromise to resolve the unequal trade problem between Zimbabwe and South Africa without harming the economies of both the countries. This research found that a peaceful resolution of the disagreement could be found by the addition of a third-party to help in the conflict resolution thereby ending the prolonged trade conflict. This undertaking will serve as a template for modelling and predicting an outcome in the event of third-party intervention for future trade disputes involving regional trade partners with emerging or developing economies such as those that exist in Africa
Proposed Framework for Effective Management of End-User Stakeholders’ in Publ...IJMREMJournal
Significant infrastructure such as roads, prisons, schools, rail tracks and train systems, among others are currently developed through the involvement of Public Private Partnership (PPP) arrangements which have been acknowledged internationally in recent time. The poor management of end-user stakeholder during PPP projects in developing nation like Nigeria has been established as one of the major factor affecting the successful growth and development of PPP projects. Due to the paucity in research on end-user stakeholder management on PPP projects in Nigeria, informs this study aim to expose the main strategic factors that can accommodate end-user stakeholder’s management in any PPP road project in Nigeria. The professionals that have worked on the project cum the end-user of the project area were used as targeted respondents for the adopted case study and survey strategies method approach. Thematic analysis was used to analyse the eighteen (18) interviews that were conducted having completed and analysed total number of 282 questionnaires using reliability and factor analysis approach. Seven valid underlying factors were revealed from 28 variables that were left on the questionnaire data with the aid of factor analysis which were used later as factors affecting end-user stakeholders’ management in PPP road project in Nigeria. A proposed framework was created with the seven underlying factors as a template for any successful PPP road project in developing country like Nigeria. These will quench the agitation of enduser stakeholders’ quarrels on PPP toll road projects
Fresh and Hardened Properties of Ground Granulated Blast Furnace Slag Made Co...IJMREMJournal
This research work was carried out on concrete specimens made with different proportion of Ground Granulated Blast Furnace Slag (GGBFS) as a cement substitution in concrete. To accomplish the goal of the research work, overall 75 cubes and 60 cylinders were made. Out of 75 cubes and 60 cylinders, 15 cubes and 12 cylinders were cast for control concrete, and 60 cubes and 48 cylinders were cast by replacing 5,10,15 and 20% of cement with GGBFS. The cubes and cylinder specimens were 100x100x100 mm and 100x200 mm respectively, and mix design was done for 28 Mpa. All specimens were tested at 3. 7, 28 and 90 days of curing ages. The fresh properties such as workability and hardened properties such as compressive and tensile strength of all mixes were determined. Tests results showed that the workability of the concrete mixes made with GGBFS was higher than control mix. As the percentage of GGBFS increased the workability also increased. Hardened properties of concrete mixes made with GGBFS was lower than control concrete at early ages of curing. At the later age, hardened properties of GGBFS made concrete was more than control concrete. Furthermore, water absorption and density of GGBFS made concrete was lower than control concrete.
Design and Evaluation of Open Graded Hot Mix Asphalt Using Cement as A Grout...IJMREMJournal
Road networks ought to be efficiently designed to be safe, speedy and loading sustaining as it has a significant importance in country’s development. For that, pavement should be designed efficiently to exhibit better strength, durability and economical at the same time. Generally, a pavement is classified as Flexible or Rigid. Flexible pavement is opened early to traffic, has good riding quality and ease of maintenance but owing to heavy loading conditions these pavements are more susceptible to wear and tear. On the contrary rigid pavement is load sustaining, durable but having higher construction cost and poor riding quality. World is heading to semirigid pavement which exhibits characteristics of both these pavements. It is the combination of cement concrete and porous asphalt concrete which is achieved by leaving 25% to 30% air voids infused by cement grouts and is known as Semi-rigid pavement.In this research, semi-rigid pavement was designed using ratio of grout of optimum mix was 1:0.55 at water cement ratio by 2% of cement dosage with SP. Study concludes that, Semirigid pavement’s Marshall stability of 7 days was almost 85% of rigid pavement and 28 days compressive strength of semi-rigid pavement was almost 30.5% that of rigid pavement. Besides, it has been ensured that 7 days strength is comparable to 28 days strength of Semi-rigid pavement.
Design of Cold Recycled Emulsified Asphalt Mixtures Using Portland Cement as ...IJMREMJournal
Cold Recycling is getting popularity in research sector and construction industries because it overcomes all the issues of Hot Mix Asphalt of more consumption of natural resources, high production energy, central plant recycling, effect of greenhouse gases and non-feasibility in colder regions. In this research study, a cold recycled mixture is designed and compared in terms of mechanical and volumetric properties with control hot mix asphalt mixture, using 60% RAP (reclaimed asphalt pavement) aggregates and 40 % virgin aggregates to fulfill gradation requirements. Asphalt emulsion for cold recycled mixtures is used as a binder with varying five contents (4.3%, 4.8%, 5.3%, 5.8% and 6.3%). Also, a modified cold recycled mixture is prepared at optimum emulsion content of control cold recycled mixture by partially replacing conventional aggregate mineral filler with three different contents of Portland cement (2%, 3% and 4%) of total dry mass of aggregates. Marshall mix design procedure was adopted to calculate the optimum (bitumen, emulsion and filler content) for control hot mix asphalt, control cold recycled mixture and modified cold recycled mixtures respectively. Mechanical properties of each of these mixtures were compared with each other and it was found that modified cold recycled mixtures were better than controlled cold recycled mixture and comparable in properties to hot mix asphalt mixtures and Optimum filler content of Portland cement for modified cold recycled mixture was found to be at 4%.
Thermodynamic Analysis of Cooling Tower with Air to Air Heat Exchanger for Re...IJMREMJournal
In this paper a thermodynamic analysis of cooling tower with air-to-air heat exchanger is presented. During manual operation of conventional cooling tower, a good quantity of water is evaporated which requires equivalent amount of makeup water for their condensers. So, in this regard, the thermodynamic model of a cooling with an air to air heat exchanger is developed using engineering equation solver (EES) software and then simulated in different climatic conditions of two major cities of Pakistan namely Karachi and Jamshoro through the period of June & December 2017. The results show a significant variation in water vapor recovery with respect to atmospheric conditions mainly humidity and ambient air temperature. Results reveal that the when a cooling tower coupled with air to air heat exchanger maximum amount of water vapors are recovered at Karachi and ranges up to 67% and 62% in Jamshoro during the month of December.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
This study Examines the Effectiveness of Talent Procurement through the Imple...DharmaBanothu
In the world with high technology and fast
forward mindset recruiters are walking/showing interest
towards E-Recruitment. Present most of the HRs of
many companies are choosing E-Recruitment as the best
choice for recruitment. E-Recruitment is being done
through many online platforms like Linkedin, Naukri,
Instagram , Facebook etc. Now with high technology E-
Recruitment has gone through next level by using
Artificial Intelligence too.
Key Words : Talent Management, Talent Acquisition , E-
Recruitment , Artificial Intelligence Introduction
Effectiveness of Talent Acquisition through E-
Recruitment in this topic we will discuss about 4important
and interlinked topics which are
Generative AI Use cases applications solutions and implementation.pdfmahaffeycheryld
Generative AI solutions encompass a range of capabilities from content creation to complex problem-solving across industries. Implementing generative AI involves identifying specific business needs, developing tailored AI models using techniques like GANs and VAEs, and integrating these models into existing workflows. Data quality and continuous model refinement are crucial for effective implementation. Businesses must also consider ethical implications and ensure transparency in AI decision-making. Generative AI's implementation aims to enhance efficiency, creativity, and innovation by leveraging autonomous generation and sophisticated learning algorithms to meet diverse business challenges.
https://www.leewayhertz.com/generative-ai-use-cases-and-applications/
Accident detection system project report.pdfKamal Acharya
The Rapid growth of technology and infrastructure has made our lives easier. The
advent of technology has also increased the traffic hazards and the road accidents take place
frequently which causes huge loss of life and property because of the poor emergency facilities.
Many lives could have been saved if emergency service could get accident information and
reach in time. Our project will provide an optimum solution to this draw back. A piezo electric
sensor can be used as a crash or rollover detector of the vehicle during and after a crash. With
signals from a piezo electric sensor, a severe accident can be recognized. According to this
project when a vehicle meets with an accident immediately piezo electric sensor will detect the
signal or if a car rolls over. Then with the help of GSM module and GPS module, the location
will be sent to the emergency contact. Then after conforming the location necessary action will
be taken. If the person meets with a small accident or if there is no serious threat to anyone’s
life, then the alert message can be terminated by the driver by a switch provided in order to
avoid wasting the valuable time of the medical rescue team.
Supermarket Management System Project Report.pdfKamal Acharya
Supermarket management is a stand-alone J2EE using Eclipse Juno program.
This project contains all the necessary required information about maintaining
the supermarket billing system.
The core idea of this project to minimize the paper work and centralize the
data. Here all the communication is taken in secure manner. That is, in this
application the information will be stored in client itself. For further security the
data base is stored in the back-end oracle and so no intruders can access it.
Open Channel Flow: fluid flow with a free surfaceIndrajeet sahu
Open Channel Flow: This topic focuses on fluid flow with a free surface, such as in rivers, canals, and drainage ditches. Key concepts include the classification of flow types (steady vs. unsteady, uniform vs. non-uniform), hydraulic radius, flow resistance, Manning's equation, critical flow conditions, and energy and momentum principles. It also covers flow measurement techniques, gradually varied flow analysis, and the design of open channels. Understanding these principles is vital for effective water resource management and engineering applications.
Road construction is not as easy as it seems to be, it includes various steps and it starts with its designing and
structure including the traffic volume consideration. Then base layer is done by bulldozers and levelers and after
base surface coating has to be done. For giving road a smooth surface with flexibility, Asphalt concrete is used.
Asphalt requires an aggregate sub base material layer, and then a base layer to be put into first place. Asphalt road
construction is formulated to support the heavy traffic load and climatic conditions. It is 100% recyclable and
saving non renewable natural resources.
With the advancement of technology, Asphalt technology gives assurance about the good drainage system and with
skid resistance it can be used where safety is necessary such as outsidethe schools.
The largest use of Asphalt is for making asphalt concrete for road surfaces. It is widely used in airports around the
world due to the sturdiness and ability to be repaired quickly, it is widely used for runways dedicated to aircraft
landing and taking off. Asphalt is normally stored and transported at 150’C or 300’F temperature
SENTIMENT ANALYSIS ON PPT AND Project template_.pptx
Poincare Conjecture Proven and Disproved Using Imaginary
1. International Journal of Modern Research in Engineering & Management (IJMREM)
||Volume|| 1||Issue|| 3 ||Pages|| 43-51 ||March 2018|| ISSN: 2581-4540
www.ijmrem.com IJMREM Page 43
Poincare Conjecture Proven and Disproved Using Imaginary
Numbers, Imaginary Manifolds, Always Changing Manifolds,
Suns or Stars, Rhombus, Trapezoids, Ellipses, Triangles,
Parallelograms, Squares and Word Meanings
Mathematical Classifications 03Fxx 01Axx 51Nxx
1,
James T. Struck BA, BS, AA, and MLIS
Affiliation- President A French American Museum of Chicago, President Dinosaurs Trees Religion and
Galaxies, Researcher NASA, Assistant Midwest Benefits Group
Address- PO BOX 61 Evanston IL 60204
-------------------------------------------------------ABSTRACT---------------------------------------------------
A manifold means “1. Having many forms, parts, etc.” [1] Manifolds which have many parts, forms are not
necessarily one to one to 3 spheres. Poincare conjecture can be proven and disproven based on the case study of
imaginary manifolds, imaginary numbers, ellipses, rhombus, trapezoids, parallelograms, triangles, squares,
always changing manifolds and the Sun or stars. Proof and disproof are reasonable for the Poincare Conjecture.
Homeomorphic has 2 meanings. One meaning of homeomorphic is similar in form and one meaning of
homeomorphic is deformable. [2] Proof and disproof of Poincare Conjecture are supported by the 2 definitions of
homeomorphic and the definitions of manifold. Dr. Grigori Perelman’s proof of the Poincare Conjecture does not
place enough emphasis on the meaning of homeomorphic as having similarity of form or the definition of manifold
as many, diverse or varied.
---------------------------------------------------------------------------------------------------------------------------------------
Date of Submission: Date, 18 March 2018 Date of Accepted: 27 March 2018
---------------------------------------------------------------------------------------------------------------------------------------
I. METHODOLOGY
I rely primarily on meanings of homeomorphic and manifolds or linguistic discussion. I also use case study or
examples of imaginary numbers, always changing manifolds, imaginary manifolds, rhombus, trapezoids, ellipse
and Sun and stars to discuss the Poincare Conjecture. Another type of disproof is that we are not completely sure
what Henry Poincare actually saw as the Poincare conjecture as we cannot speak to him directly in 1900 and 1904.
The Meaning of Homeomorphic: Discussion of the Poincare Conjecture can be seen as related to the Meaning
of homeomorphic. I use a math resource Wolfram Math World to define homeomorphic. Here is Wolfram Math
world’s definition accessed on 12/31/2017.
“There are two possible definitions:
1. Possessing similarity of form,
2. Continuous, one-to-one, in surjection, and having a continuous inverse.”
The most common meaning is possessing intrinsic topological equivalence. Two objects are homeomorphic if
they can be deformed into each other by a continuous, invertible mapping. Such a homeomorphism ignores the
space in which surfaces are embedded, so the deformation can be completed in a higher dimensional space than
the surface was originally embedded. Mirror images are homeomorphic, as are Möbius strip with an even number
of half-twists, and Möbius strip with an odd number of half-twists.
In category theory terms, homeomorphisms are isomorphisms in the category of topological spaces and continuous
maps. [3]
Here I rely on both meanings. I use similarity of form and deformable as the definitions of the word homeomorphic
in order to show that there can be both proof and disproof of the Poincare conjecture related to those definitions.
The Meaning of Manifold: For the meaning of manifold, I rely on the Merriam Webster definition as the common
word use or everyday use of manifold is arguably more linked to the meaning used by Henri Poincare at the turn
of the 20th
century in 1900 and 1904. Here is a meaning of manifold according to the online Merriam Webster
dictionary accessed on 12/31/2017.
“Definition of manifold
2. Poincare Conjecture Proven and Disproved Using…
www.ijmrem.com IJMREM Page 44
1 a: marked by diversity or variety
• performs the manifold duties required of him
b: many [4]
As the word manifold means many or diverse or variety, based on word definition alone, something that is
diverse varied and many is not similar to a 3 sphere. Linguistic Disproof based on diverse, many, varied does
not mean 3 sphere is simple to argue for or support.
Case studies of Imaginary Manifolds, Imaginary Numbers and Always Changing Manifolds and Sun
Imaginary Manifold or Imaginary Number Disproof
For a definition of imaginary number, I again rely on Wolfram MathWorld accessed 12/31/2017. Imaginary
Number means
“Although Descartes originally used the term "imaginary number" to refer to what is today known as a complex
number, in standard usage today, "imaginary number" means a complex number that has zero real part (i.e., such
that ). For clarity, such numbers are perhaps best referred to as purely imaginary numbers.
A (purely) imaginary number can be written as a real number multiplied by the "imaginary unit" i (equal to the
square root ), i.e., in the form . [5]
An imaginary manifold form can be imagined which does not actually exist other than in imagination. Manifolds
that are imaginary would not easily be similar or deformable into an actual 3 sphere. An imaginary number like
“i” is not a 3 sphere. Imaginary numbers are manifolds, but imaginary numbers are not similar to 3 spheres.
Poincare disproven based on imaginary manifolds and imaginary numbers.
As we do recognize imaginary numbers like “i” as existing, we can see that an i or imaginary number
is not a 3 sphere and is not similar in form to a 3 sphere. To maintain the meaning of similarity in form, we should
be able to say an “i” or imaginary number is not similar to a 3 sphere. Something that is imaginary in form is not
similar in form to an objective 3 sphere. A real number multiplied by an imaginary unit is not a 3 sphere.
Poincare Conjecture Proved Based on Imaginary Manifolds and Numbers: One still could prove the Poincare
conjecture too by showing an imaginary manifold that deforms into a 3 sphere. Such a deformation from imaginary
manifold to 3 spheres is based on the ability to imagine or draw or see deformation without cutting from an
imaginary number like I into a 3 sphere. The “i” or imaginary number grows on all sides and becomes a 3 sphere.
Deformation from I to 3 sphere is a possibility. We take an imaginary manifold or number like i, make it a real
manifold and then we deform the manifold into a 3 sphere. Simple growth or expansion can be used for
deformation.
Proof and disproof were just shown and illustrated with imaginary manifolds. Just expand I into a 3 sphere and
the deformation is viewable. Just look at the expansion or growth of I into a 3 sphere and we can see that I and 3
spheres are similar.
In the real world, we have imaginary particles or virtual particles. In the real world we have imaginary numbers.
I was taught imaginary numbers in Algebra in sophomore year of high school. Imaginary numbers are well
known as the square roots of negative numbers. Imaginary numbers are a branch of numbers similar to e’s or pi;
important numbers in number theory. An imaginary number can be deformed into a 3 sphere, but is not similar
to a 3 sphere.
Poincare conjecture is both provable and disproved using imaginary numbers. An imaginary manifold can be
seen as not similar to a 3 sphere and not deformable into a 3 sphere. Something imaginary cannot become real
arguably. On the other hand, something imaginary like an imaginary manifold could be deformed into a real
manifold and then seen as deformable into a 3 sphere. Proof and disproof are both supported by examination of
imaginary numbers and imaginary manifolds.
Always Changing Manifolds. I introduced this argument for always changing manifolds not being
homeomorphic to 3 spheres in July 2010.
Always Changing Manifold Disproof: An always changing form can be imagined. Manifolds that are always
changing would not be similar to or deformed into a stable 3 sphere. A manifold can always be oscillating,
disappearing, transforming, and changing forms. Such a manifold would not be similar or deformable into a stable
3 sphere. Poincare Conjecture can be disproven based on the always changing manifold with varied, diverse, or
many forms not being similar or deformable into a stable 3 sphere.
Always Changing Manifold Proof: On the other hand, one can have an always changing manifold and an always
changing 3 spheres.
3. Poincare Conjecture Proven and Disproved Using…
www.ijmrem.com IJMREM Page 45
As a type of proof of Poincare conjecture, always changing manifolds can be similar and deformable into always
changing 3 spheres. Even from an always changing manifold, a deformation to stop the changing characteristic or
form of manifold would be similar and deformable into a 3 sphere.
Sun or Stars Disproof: The Sun also can be described as both similar to a 3 sphere and deformable into a 3 sphere
and not similar and not deformable into a 3 sphere. The Sun arguably is a simple compact closed manifold. The
Sun has roughly 333,000 times the size of Earth. [6] The Sun with much larger size is not similar to a very small
3 sphere. The Sun is constantly shooting spicules up in the air “at a rate of 20 km/s (or 72,000 km/h) and can
reach several thousand kilometers in height before collapsing and fading away.” [7] The Sun which is always
changing is not similar to a stable 3 sphere. We could deform the Sun into one stable 3 sphere, but a Sun which is
333,000 times the size of the Earth or always shooting off spicules is not similar in form to a very small 3 sphere.
Let’s take all the stars considered as a manifold in comparison to one 3 spheres. In our galaxy alone, there are
from 100 to 400 billion stars. [8] If there are 100 to 400 billion stars, those many stars are not similar in form to
one 3 spheres. We could argue that each individual star is similar to a sphere, but the collection of all 100 to 400
billion stars in our galaxy would not be directly similar in form to one 3 sphere. The Sun and Stars and their
differences in form, appearance, structure, activity from a 3 sphere can be seen as a disproof of the Poincare
Conjecture. Exploding stars, binary stars, interacting stars, Supernovae, dying stars are not the same as a 3 sphere.
Sun and Stars Proof of Poincare Conjecture: The sun and stars as more numerous and much larger and changing
could still be seen as vaguely similar to a 3 sphere. Similar is an arbitrary term. Is something like something else
or different? Is a star similar to a 3 sphere or is a star dissimilar than a 3 sphere? One massive star or many
numerous stars with changing spicules can be seen still as similar to 3 spheres. Stars and Suns are sometimes like
3 spheres, but Suns and Stars movement makes them different.
How about deformability? We do not need to rely on Dr. Grigori Perelman’s discussion of Italian Mathematician
Gregorio Ricci and his heat flow work. From Wikipedia.org accessed on December 31, 2017 “Gregorio Ricci-
Curbastro (Italian: [ɡreˈɡɔːrjo ˈrittʃi kurˈbastro]; 12 January 1853 – 6 August 1925) was an Italian mathematician
born in Lugo di Romagna. He is most famous as the inventor of tensor calculus, but also published important
works in other fields.” [9]
Ricci was not working on Poincare Conjecture when he invented the Ricci Flow. As Ricci flow was not intended
to be a proof of the Poincare Conjecture as Perelman used the Ricci flow, we cannot be sure the application is
entirely appropriate. What did Ricci really intend the Ricci Flow to be used for? That purpose can never be
determined due to a lack of evidence how Ricci intended his flow to be used. Aside from the Ricci Flow issue
however, can a star be deformed into a 3 sphere? Arguably, yes stars can be deformed into 3 spheres. Also No
stars cannot be deformed into 3 spheres as there would need to be folding or cutting of spicules, sunspots and
coronal mass ejections. We can imagine many numerous stars and one massive star and Sun as deformable into a
3 sphere. Deformation means changing into without folding or cutting. We could change a Sun into a 3 sphere.
We can deform many 200 billion stars in our galaxy into a 3 sphere. Imagination allows these transformations
without cutting or folding. Shrinking, deflation, Growth, Inflation ideas would be involved in making a Sun or
Star into a small 3 sphere or a very large 3 sphere. We do not need to rely on any kind of flow or Ricci Flow to
do deformation!
II. RHOMBUS AND TRAPEZOID DISCUSSION
A trapezoid is “In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred
to as a trapezoid[1][
Here is an image accessed from Wikipedia.org article on the subject. This trapezoid shape
[10]
Is not the same as a 3 sphere! This shape however could be deformed into a 3 sphere. The Poincare Conjecture
again easily disproved and provable.
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Similarly, with a Rhombus.
A rhombus is defined as “In Euclidean geometry, a rhombus(◊) (plural rhombi or rhombuses) is a simple (non-
self-intersecting) quadrilateral whose four sides all have the same length”
[11]
This shape is not a 3 sphere, so the Poincare conjecture is disproved. Rhombus are not 3 sphere. A rhombus is
different than a 3 sphere not the same. Could we deform a rhombus into a 3 sphere? We could stretch the sides
into a more spherical structure and create deformation into a 3 sphere. The rhombus is both different than a 3
sphere but also deformable into a sphere. This Poincare Conjecture can be both proven and disproven.
III. ELLIPSE DISCUSSION
From Wikipedia.org an ellipse is “In mathematics, an ellipse is a curve in a plane surrounding two focal points
such that the sum of the distances to the two focal points is constant for every point on the curve.” [12]
Some ellipses are here
[13]: Look at the third ellipse, which is not the same as a 3 sphere. Poincare Conjecture can be disproved by
showing that manifolds like ellipses are not 3 spheres. Word meaning should mean something. An ellipse and a 3
sphere should be comprehended as having differences and different appearance!
One could compress the shape and make it three dimensional however to create a 3 sphere. Growth or universal
expansion of all the parts in the ellipse could produce or deform into a 3 sphere. We can argue for a Struck Flow
like the Ricci Flow that an object can transform or deform into a 3 sphere. Struck Flow would not be like heat
flow in Ricci’s work or Ricci’s Flow, but rather a transformation based on expansion or deflation so that one shape
can be transformed into a 3-sphere shape. Poincare Conjecture can be proven also based on the ability to imagine
one shape being transformed into a 3 sphere shape. Struck Flow does not involve heat, but rather expansion and
deflation as deformation methods.
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IV. SQUARE DISCUSSION
From Wikipedia.org, a square is “In geometry, a square is a regular quadrilateral, which means that it has four
equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles).[1]
It can also be
defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be
denoted ◻ {displaystyle square } ABCD.” [14]
A square looks like
[14]
A square is not a sphere. Since a square is not a 3 sphere, a square manifold is not homeomorphic with a 3
sphere. A square could be deformed into a sphere however through growth in various areas of the square
structure. Still using the same definition of homeomorphic, a square is different than a 3 sphere. Poincare
Conjecture disproved and Poincare conjecture supported using an analysis of a square.
V. TRIANGLE DISCUSSION
A triangle is another basic shape in geometry. Here is how Wikipedia.org defines a triangle accessed on 2/5/2018
“Triangle
From Wikipedia, the free encyclopedia
This article is about the basic geometric shape. For other uses, see Triangle (disambiguation).
Equilateral triangle
A regular triangle
Type Regular polygon
Edges and vertices 3
Schläfli symbol {3}
Coxeter diagram
Symmetry group Dihedral (D3), order 2×3
Internal angle
(degrees)
60°
Dual polygon Self
Properties
Convex, cyclic, equilateral, isogonal,
isotoxal
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Triangle
A triangle
Edges and vertices 3
Schläfli symbol {3} (for equilateral)
Area
various methods;
see below
Internal angle
(degrees)
60° (for equilateral)
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle
with vertices A, B, and C is denoted.”[16] So if we use the definition of homeomorphic meaning same, we see
that triangles are not the same as 3 spheres. A triangle with 3 sides, 3 edges is not the same as a 3 sphere. If we
use the definition of homeomorphic meaning deformable, we can do an expansion of the areas of the triangle into
a 3 sphere. So we can both disprove the Poincare conjecture by showing that a triangle is not a 3 sphere and prove
the Poincare conjecture showing that we can transform a triangle into a 3 sphere through deformation.
VI. PARALLELOGRAM DISCUSSION
We can do the same type of discussion with a parallelogram. Here is what a parallelogram is from wikipeida.org
accessed on 2/5/2018.
“Parallelogram
From Wikipedia, the free encyclopedia
This article is about the quadrilateral shape.
Parallelogram
This parallelogram is a rhomboid as it has no right angles and
unequal sides.
Type quadrilateral
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Edges and
vertices
4
Symmetry group C2, [2]+
, (22)
Area
b × h (base × height);
ab sin θ (product of adjacent sides and sine
of any vertex angle)
Properties convex
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel
sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram
are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the
Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel
postulate or one of its equivalent formulations.” [17] So since we have parallel sides, we do not have a 3 sphere.
Since a parallelogram has 4 sides, 4 sides are not the same as a 3 sphere. Poincare conjecture disproven as a
quadrilateral shape with parallel 4 sides is not a 3 sphere shape with the edges all equal distance from the center
as in a 3 sphere. On the other hand with the definition of homeomorphic as deformable, we could do a deformation
of a parallelogram into a 3 sphere. Struck Flow could be used; Struck flow is expansion and growth and deflation
or shrinking without involving heat or a Ricci Flow into a 3 sphere. Parallelograms are not the same as 3 spheres,
but parallelograms can be deformed into 3 spheres. Poincare conjecture disproved and proven using the
parallelogram case study.
VII. CONCLUSIONS
Conjectures can be proved and disproved. Poincare Conjecture can easily be disproved as always changing forms
or manifolds are not similar or deformable into 3 spheres. Poincare Conjecture can be easily proved also as a
particular 3 sphere manifold is the same and deformable into a 3 sphere. Proof and disproof of the Poincare
conjecture is possible. Discussion of the imaginary number, imaginary manifold, and always changing manifolds
supports both proof and disproof of the Poincare Conjecture at the same time. Similarity and deformation both are
possible and not possible between types of manifolds and 3 spheres.
Suns and stars support also disproof and proof of the Poincare Conjecture. Linguistic discussion supports an
argument that something always changing, imaginary, the Sun, the Stars are not really similar in form to stable 3
spheres. The idea of difference supports the idea that simply connected closed manifolds, or many diverse, varied
forms, are not similar in form to 3 spheres as linguistically manifolds are different than 3 spheres. I find support
for proof, disproof and ultimately disproof of the Poincare conjecture to maintain an idea of difference between
manifolds and 3 spheres.
Additionally, as we are not completely certain what Jules Henri Poincare meant by his conjecture; there is some
concern as a type of disproof that we do not really know what Henri Poincare meant or was hypothesizing. Henri
Poincare lived from 29 April 1854 – 17 July 1912, [18] we cannot directly speak with him about what his
conjecture was discussing exactly.
Henri Poincare invented his conjecture in about 1900 and 1904 and there is reason to believe he supported my
disproof based on the Poincare Conjecture’s origin. See Wikipedia.org’s discussion of the Poincare conjecture
accessed 12/31/2017
“Poincaré claimed in 1900 that homology, a tool he had devised based on prior work by Enrico Betti, was
sufficient to tell if a 3-manifold was a 3-sphere. However, in a 1904 paper he described a counterexample to this
claim, a space now called the Poincaré homology sphere.” [19]
Further support that Jules Henri Poincare saw the Poincare homology sphere as a counterexample can be found.
“Poincaré originally conjectured [4] that a homology 3-sphere (http://planetmath.org/HomologySphere) must
be homeomorphic to S3
. He later found a counterexample based on the group of rotations of the regular
dodecahedron (http://planetmath.org/RegularPolyhedron), and restated his conjecture in of the fundamental
group. (See [5]). To be accurate, the restatement took the form of a question. However it has always been referred
to as Poincaré’s Conjecture.)” [20]
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The Poincare Homology sphere discussion shows that he knew of some support for a Poincare conjecture disproof
very different than Grigori Perelman’s proof. Disproof can be supported by Poincare’s own Poincare homology
sphere of 1904! My discussion of stars, Sun, imaginary numbers, imaginary manifolds, always changing
manifolds more different than 3 spheres provides further support for a disproof of the Poincare conjecture.
I submitted dozens of disproof’s and proofs also since 2010 from the disproof idea that I do not want to be
deformed into a 3 sphere to the proof idea that a specific manifold of a 3 sphere is homeomorphic to a particular
3 sphere. An imaginary manifold existing only in imagination is NOT homeomorphic to a specific 3 sphere.
There are mathematicians who object to the idea of imaginary numbers, imaginary numbers objected to can be
seen more different than 3 spheres. “Many other mathematicians were slow to adopt the use of imaginary numbers,
including René Descartes, who wrote about them in his La Géométrie, where the term imaginary was used and
meant to be derogatory.[ [7][8]”
[21]
The rhombus and trapezoid discussion also shows that rhombus and trapezoids are different than 3 spheres, but
also deformable into 3 spheres. Poincare Conjecture can be both disproven with the meaning of homeomorphic
as same and proven with the meaning of homeomorphic as deformable. Ellipse provide more support that an
ellipse is a manifold that is not the same as a 3 sphere, so Poincare Conjecture can be easily disproven. Ellipse are
not equal to 3 spheres. When a star explodes or goes supernova, an exploding star is not similar to a 3 sphere. In
addition, an ellipse can be transformed or flow into a 3 sphere so the Poincare Conjecture can also be supported
or proven. Proof and disproof of the Poincare Conjecture are supported by examination of a number of cases and
examples!
Parallelograms, squares, triangles provide further support that these shapes are not homeomorphic or the same as
3 spheres, but these shapes can be deformed into 3 spheres. Poincare Conjecture is easily disproven given the
meaning of homeomorphic as same and proven given the meaning of homeomorphic as deformable. The famous
Poincare Conjecture can be disproven and proven using case studies of parallelograms, squares, rhombus,
trapezoid, ellipse, imaginary numbers, imaginary manifold, stars, Suns, always changing manifolds.
The original objection I had around July 2010 to the Poincare Conjecture that an always changing, many, diverse
shape manifold is not the same as a 3 sphere remains. We can deform a manifold, or a shape always changing,
diverse, varied shapes into a 3 sphere, but an always changing, diverse, varied manifold or changing or diverse
shape is not the same as a 3 sphere. My objection that varied, diverse, changing shapes are not the same as 3
spheres applies as much to the work of Richard Hamilton and as much to Michael Freedman in 1982 as to Grigori
Perelman’s work in 2006. Rene Descartes was known for his understanding of all life and philosophy linked to
Geometry called Cartesian Philosophy. The Poincare Conjecture can be seen as an extension of the importance of
Cartesian Philosophy. We can disagree with both Rene Descartes and Jules Henri Poincare and their assertions
about geometry and topology. Something diverse and varied like a 2 dimensional or 1 dimensional shape or 10-
dimensional shape or 200-dimensional shape can be seen as not one to one to a ball in 4-dimensional space. A 3
Sphere is defined as “It consists of the set of points equidistant from a fixed central point in 4-
dimensional Euclidean space.” [22] A line, dodecahedron, parabola, hyperbola would not be one to one to the 3
spheres as the shapes are different.
Let’s look at a set of points that are not equal distance from a fixed central point. The set of point’s not equal
distance from the fixed central point is not going to be one to one to the 3 spheres or the set of points that is equal
distance to a fixed set of points. I invent then the “Struck Manifold-Set of Points of all Different, Varied or
Changing Distance from Fixed Central Point” to show that the Struck Manifold is not one to one to a set of points
of equal distance to a central point! Manifolds of varied distance from central points are not homeomorphic or
one to one to 3 spheres with all points equal distance to a central point.
Acknowledgements- My mom Jane Frances Back Struck gave me the confidence to work on math problems by
mom’s getting an A in Economics at Mundelein College and B in Psychology at Loyola University, so I wanted
to thank her for her help. Mom died 7/15/2017. Thank you to Arthur Loevy, Jon Loevy and Andy Thayer who
loaned me $50 to get the article published as journals pay fees to be indexed.
REFERENCE
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3. Weinstein, Eric W. "Homeomorphic." From Math World--A Wolfram Web Resource.
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4. https://www.merriam-webster.com/dictionary/manifold accessed on 12/31/2017
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