Mathematics in nature
•Download as PPTX, PDF•
2 likes•3,100 views
Mathematics in Nature presented by St. George's School shows how mathematical patterns like fractals appear throughout nature in mountains, rivers, clouds, and hydrothermal springs. It discusses Euclid's calculation of the golden ratio and how artists like Da Vinci and Mondrian incorporated the golden ratio and Fibonacci sequence into works like the Mona Lisa, Parthenon, and Broadway Boogie Woogie. The presentation also notes how the golden ratio appears in biology through dolphin flippers, the nautilus shell, the cochlea of the inner ear, and the proportions of Da Vinci's Vitruvian Man.
Report
Share
Report
Share
Recommended
Maths in nature
This document discusses the relationship between mathematics and nature. It provides examples of symmetry, patterns, ratios and shapes found in nature that relate to mathematical concepts like the golden ratio, pi, the Fibonacci sequence, fractals and perfect shapes. These natural phenomena were inspiration for mathematical discoveries made by ancient civilizations. Symmetry is seen in structures like starfish and flowers, while spirals in shells, pinecones and sunflowers relate to the Fibonacci sequence. The human body and works of art also exhibit mathematical proportions. Overall, the document argues that mathematics is deeply embedded throughout nature.
Mathematics in nature
The document discusses how mathematics is present in nature. It provides examples of symmetry, shapes, parallel lines, and the Fibonacci spiral that can be observed in the natural world. Radial and bilateral symmetry are seen in structures like flowers and the human body. Common shapes found in nature include spheres, hexagons used by bees to build hives efficiently, and cones formed by volcanoes. Parallel lines can be seen in dune formations, and the Fibonacci spiral appears in nautilus shells. The document aims to show how nature demonstrates mathematical concepts and patterns.
Maths of nature and nature of maths 130513 vor
1) Mathematics is present throughout nature in patterns like bubbles, waves, branches and more. The hexagonal shape of honeycombs and compound eyes maximizes their efficiency.
2) Fibonacci numbers appear in nature, like the spiral patterns of sunflowers and pinecones. They also describe rabbit populations.
3) Bees, flowers, galaxies and more display the golden ratio/spiral, an irrational number close to 1.618 seen in divisions of the Fibonacci sequence. This divine proportion is found throughout nature.
The fibonacci sequence
The Fibonacci sequence is a sequence where each number is the sum of the two preceding numbers. This sequence appears frequently in nature, such as the spiral patterns of shells, flowers, pine cones, and galaxies. The golden ratio is the number approximately equal to 1.6180 that results from dividing any number in the Fibonacci sequence by its predecessor. Both the Fibonacci sequence and golden ratio are found in architecture, like the Parthenon, as well as in music scales.
OBSERVATIONAL ASTRONOMY
Optical telescopes use either lenses or mirrors to gather and focus light, allowing astronomers to see objects that are too faint or distant to view with the naked eye. Refracting telescopes use lenses to bend and focus light, while reflecting telescopes use curved mirrors. Spectroscopy reveals properties of astronomical objects like temperature, velocity, and composition by separating light into its component wavelengths. Astronomers use several techniques to measure the vast distances to stars and galaxies, including trigonometric parallax for nearby stars, and variable star properties like period-luminosity relationships for more distant objects.
Maths in nature (complete)
Radial, bilateral, translational, and wallpaper symmetries are prevalent in nature. Examples include starfish with dihedral symmetry, trees with translational strip patterns, hexagonal structures like honeycombs and the Giant's Causeway that tessellate plane patterns, and the approximate bilateral symmetry found in human faces. Symmetry represents a balance and order that is reflected in both man-made and natural designs.
541 Interactive ppt Fibonacci Sequence
The document discusses the Fibonacci sequence and its relationship to the golden ratio. It begins by introducing Leonardo of Pisa, who helped spread the use of the modern number system and knowledge of the Fibonacci sequence. The sequence is defined as a pattern where each number is the sum of the two preceding ones, starting with 1, 1, 2, 3, 5, etc. This sequence appears throughout nature and can be seen in spirals of shells, pinecones, and sunflowers. The ratio of consecutive Fibonacci numbers approaches the golden ratio, about 1.618, an irrational number important in art and architecture considered aesthetically pleasing. The golden ratio can also be observed in proportions of the human body.
The Nature of Mathematics
Mathematics is present all around us in nature. The chapter discusses several mathematical patterns that exist in the natural world such as sequences like the Fibonacci sequence, symmetries, fractals, and tessellations. Specific examples of each pattern are provided like the spiral patterns of pinecones and sunflowers following the Fibonacci sequence. Symmetries can be seen in structures like zebra stripes. Fractals exhibit self-similarity and can be seen in shapes like ferns and coastlines. Hexagonal tessellation is an efficient pattern used by honeybees to construct their hives. Nature demonstrates optimization of forms through mathematical regularities.
Recommended
Maths in nature
This document discusses the relationship between mathematics and nature. It provides examples of symmetry, patterns, ratios and shapes found in nature that relate to mathematical concepts like the golden ratio, pi, the Fibonacci sequence, fractals and perfect shapes. These natural phenomena were inspiration for mathematical discoveries made by ancient civilizations. Symmetry is seen in structures like starfish and flowers, while spirals in shells, pinecones and sunflowers relate to the Fibonacci sequence. The human body and works of art also exhibit mathematical proportions. Overall, the document argues that mathematics is deeply embedded throughout nature.
Mathematics in nature
The document discusses how mathematics is present in nature. It provides examples of symmetry, shapes, parallel lines, and the Fibonacci spiral that can be observed in the natural world. Radial and bilateral symmetry are seen in structures like flowers and the human body. Common shapes found in nature include spheres, hexagons used by bees to build hives efficiently, and cones formed by volcanoes. Parallel lines can be seen in dune formations, and the Fibonacci spiral appears in nautilus shells. The document aims to show how nature demonstrates mathematical concepts and patterns.
Maths of nature and nature of maths 130513 vor
1) Mathematics is present throughout nature in patterns like bubbles, waves, branches and more. The hexagonal shape of honeycombs and compound eyes maximizes their efficiency.
2) Fibonacci numbers appear in nature, like the spiral patterns of sunflowers and pinecones. They also describe rabbit populations.
3) Bees, flowers, galaxies and more display the golden ratio/spiral, an irrational number close to 1.618 seen in divisions of the Fibonacci sequence. This divine proportion is found throughout nature.
The fibonacci sequence
The Fibonacci sequence is a sequence where each number is the sum of the two preceding numbers. This sequence appears frequently in nature, such as the spiral patterns of shells, flowers, pine cones, and galaxies. The golden ratio is the number approximately equal to 1.6180 that results from dividing any number in the Fibonacci sequence by its predecessor. Both the Fibonacci sequence and golden ratio are found in architecture, like the Parthenon, as well as in music scales.
OBSERVATIONAL ASTRONOMY
Optical telescopes use either lenses or mirrors to gather and focus light, allowing astronomers to see objects that are too faint or distant to view with the naked eye. Refracting telescopes use lenses to bend and focus light, while reflecting telescopes use curved mirrors. Spectroscopy reveals properties of astronomical objects like temperature, velocity, and composition by separating light into its component wavelengths. Astronomers use several techniques to measure the vast distances to stars and galaxies, including trigonometric parallax for nearby stars, and variable star properties like period-luminosity relationships for more distant objects.
Maths in nature (complete)
Radial, bilateral, translational, and wallpaper symmetries are prevalent in nature. Examples include starfish with dihedral symmetry, trees with translational strip patterns, hexagonal structures like honeycombs and the Giant's Causeway that tessellate plane patterns, and the approximate bilateral symmetry found in human faces. Symmetry represents a balance and order that is reflected in both man-made and natural designs.
541 Interactive ppt Fibonacci Sequence
The document discusses the Fibonacci sequence and its relationship to the golden ratio. It begins by introducing Leonardo of Pisa, who helped spread the use of the modern number system and knowledge of the Fibonacci sequence. The sequence is defined as a pattern where each number is the sum of the two preceding ones, starting with 1, 1, 2, 3, 5, etc. This sequence appears throughout nature and can be seen in spirals of shells, pinecones, and sunflowers. The ratio of consecutive Fibonacci numbers approaches the golden ratio, about 1.618, an irrational number important in art and architecture considered aesthetically pleasing. The golden ratio can also be observed in proportions of the human body.
The Nature of Mathematics
Mathematics is present all around us in nature. The chapter discusses several mathematical patterns that exist in the natural world such as sequences like the Fibonacci sequence, symmetries, fractals, and tessellations. Specific examples of each pattern are provided like the spiral patterns of pinecones and sunflowers following the Fibonacci sequence. Symmetries can be seen in structures like zebra stripes. Fractals exhibit self-similarity and can be seen in shapes like ferns and coastlines. Hexagonal tessellation is an efficient pattern used by honeybees to construct their hives. Nature demonstrates optimization of forms through mathematical regularities.
The fibonacci sequence
This ppt contains everything about Fibonacci sequence.
From its origin to where it is used and where it is found-EVERYTHING.Hope you like it
Fibonacci Sequence and Golden Ratio
The document discusses Fibonacci numbers and the golden ratio, explaining how Fibonacci discovered the Fibonacci sequence by modeling rabbit populations and how ratios between numbers in the sequence converge on the golden ratio. It provides many examples of how the golden ratio appears frequently in nature, art, architecture, and the human body, demonstrating its aesthetic appeal and role in design.
Fibonacci series and Golden ratio
The document discusses the Fibonacci sequence and the golden ratio. It begins by introducing the Fibonacci sequence of numbers: 1, 1, 2, 3, 5, 8, etc., where each number is the sum of the previous two. It then explains that the ratios of successive numbers in the sequence converge on the golden ratio, approximately 1.618. The golden ratio is found throughout nature, such as in the proportions of the human body and in vegetation. The document also provides methods for constructing a golden rectangle using squares and diagonals, with a final ratio matching the golden ratio.
Math in Nature
This document discusses different types of patterns found in nature and their definitions. It covers symmetry patterns like bilateral, mirror, radial and rotational symmetry. It also discusses fractals and their repeating patterns at every scale, as well as Fibonacci spirals emanating from a central point. Additionally, it examines common shapes like circles, spheres, hexagons and cones, providing their definitions.
GEOMETRIC ART -SYMMETRY
This document discusses different types of symmetry in geometric art. It defines symmetry as an object having two or more equal sides when split in half. There are three main types of symmetry discussed: reflection symmetry (also called line symmetry), where an object can be folded in half and the halves match; point symmetry, where every part has a matching part the same distance from the central point but in the opposite direction; and rotational symmetry, where an object looks the same when rotated by certain angles. The number of positions an object can be rotated and still look the same is called its order of rotational symmetry. Examples given include squares and circles. In conclusion, the document provides an overview of key concepts in symmetry as it relates to geometry and art
Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]
Recent Trends of Mathematics in Education
Mathematical activity has changed in every field. We discuss some of these trends and how they could influence the future of mathematical education. The aim of this paper is to study the recent trends in the present day mathematics and the role of mathematics in other disciplines. Dr. A. K. Yadav | Dr. Sushil Kumar | Dr. Rashmi Chaudhary "Recent Trends of Mathematics in Education" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-4 , June 2020, URL: https://www.ijtsrd.com/papers/ijtsrd31130.pdf Paper Url :https://www.ijtsrd.com/mathemetics/other/31130/recent-trends-of-mathematics-in-education/dr-a-k-yadav
Trabajo final "Matemáticas en la pintura" pfdz 2013
Este documento presenta información sobre las matemáticas en la pintura. Explica conceptos como los cuadrados mágicos, la proporción áurea, la espiral de Durero, y cómo artistas como Velázquez y Leonardo da Vinci incorporaron estas ideas matemáticas en obras maestras como Las Meninas y La Gioconda. También analiza las teselaciones y figuras imposibles creadas por el artista M. C. Escher, que demuestran una comprensión profunda de conceptos geométricos.
Parts-of-the-Science-Investigatory-Project-PPT.pptx
This document outlines the key parts and sections of a science investigatory project. It discusses the importance of having a clear and concise title that indicates the project purpose. It states that the abstract should summarize the research problem, methods, and conclusions in 1-2 paragraphs. It provides details on what should be included in each section of Chapter 1 such as the introduction/background, statement of the problem, hypotheses formulation, significance of the study, scope and limitations. It also notes that definitions of terms should include dictionary meanings and operational definitions for terms as used in the specific research project.
Chapter 1
This document provides an overview of physics as a science. It discusses how physics is a systematic body of knowledge based on observations and experiments. Physics is divided into classical and modern physics. Classical physics includes mechanics, acoustics, optics, thermodynamics, and electromagnetism while modern physics includes atomic, nuclear, quantum, relativistic, solid state, and plasma physics. The document also discusses how physics employs the scientific method and notes that physics and technology are partners for progress, with physics furthering our understanding of nature and technology applying that understanding. Mathematics and measurement are also presented as essential tools for physics.
Polygons (its meaning, nature and types) for grade v
This document defines and describes different types of polygons. Polygons are 2-dimensional plane shapes made of straight lines that form a closed figure. There are regular polygons with all equal sides and angles and irregular polygons without equal sides and angles. Polygons can also be convex with no inward angles, concave with at least one internal angle greater than 180 degrees, simple with one boundary not crossing over itself, or complex intersecting with itself. The document provides examples to illustrate these different types of polygons.
Book 1
This document discusses how mathematical concepts like symmetry, shapes, patterns and sequences are evident in nature. It provides examples of bilateral symmetry (like in humans and butterflies), radial symmetry (like in flowers and starfish), parallel lines (like in leaf veins and zebra stripes), basic shapes (like hexagons in bee hives and spheres in planets), the Fibonacci sequence (seen in rabbit birth rates), and patterns (like leaf arrangements, zebra fur and sand ripples). The document emphasizes that mathematics can be observed throughout nature from atoms to galaxies.
PowerPoint Presentation on Golden Ratio
The document is a presentation on the golden ratio. It defines the golden ratio as an irrational number approximated to 1.618, often denoted by Greek letters tau or phi. It describes two quantities being in a golden ratio if the ratio between their sum and the larger quantity equals the ratio between the larger and smaller quantities. The golden ratio is used in architecture, painting, book design, nature, aesthetics, and perceptual studies. A golden triangle is an isosceles triangle where the smaller side is in golden ratio to the adjacent side, and they can be found in pentagrams and stellated polyhedra.
Types of mirrors
This document discusses different types of mirrors and their properties. It describes plane mirrors and two types of curved mirrors: convex and concave. Convex mirrors form a smaller virtual image than the object, while concave mirrors form a magnified virtual image. The document also provides formulas for calculating the focal length and magnification of curved mirrors based on the object and image distances and radius of curvature. Key properties of mirror reflections like being virtual, erect, and laterally inverted are also noted.
Circle theorems
Euclidean geometry is very important in Math, and it weighs a lot of marks in High school Math. This branch of mathematics develops critical thinking and reasoning skills to a learner.
Artificial Intelligence Quiz
Artificial Intelligence(AI) Quiz questions and answers
Related Videos:
What are AI and Big Data? Simple Tutorial about Artificial Intelligence (AI)
https://www.youtube.com/watch?v=ROaw4if2o7E
What is Artificial Intelligence (AI)? Discussion about Benefits, Risks and Uses of AI
https://www.youtube.com/watch?v=1K_ATYqvHTs
Microscope uses Artificial Intelligence to find cancer cells more efficiently
https://www.youtube.com/watch?v=Iv1wBvPMguE
Artificial intelligence produces Realistic Sounds that fool Humans
https://www.youtube.com/watch?v=_2w3mvWk0po
Artificial Intelligence "Libratus" Beats Top Poker Pros
https://www.youtube.com/watch?v=8iEN19vMUyw
Sundar Pichai's Talk about AI and Google Assistant
https://www.youtube.com/watch?v=MtujWybGKyU
Chem m15 changes that matter undergoes
This module discusses various chemical and phase changes that occur in everyday life. It is divided into four lessons: (1) Changing Phases explains the differences between melting, freezing, evaporation, condensation, sublimation and deposition; (2) When Does a Chemical Change Occur? describes the indicators of a chemical change and differentiates chemical from physical changes; (3) Types of Chemical Changes outlines four types of chemical reactions - combination, decomposition, single replacement and double displacement; (4) Chemical Changes Around Us provides examples of changes that happen in the human body during digestion and exercise as well as in cleaning products like soap. The module aims to help students understand and identify different types of changes in their environment.
Symmetry Presentation By Manali
This document discusses different types of symmetry found in nature, architecture, art, religious symbols, and music. It provides examples of line symmetry seen in leaves, snowflakes, and butterflies. Architectural symmetry is seen at various scales from overall building designs to individual elements. Symmetry is also used in art forms like beadwork and furniture as well as religious symbols like the Star of David. In music, symmetry has been used as a compositional constraint and in concepts of permutation and invariance. Rotational symmetry makes an object look the same after certain rotations and examples include objects with order 3 and order 6 rotational symmetry.
Subsets of real numbers
This document discusses different subsets of real numbers. It begins by explaining how primitive man counted using objects like stones and evolved to create number systems over hundreds of years. It then provides activities to identify subsets of numbers for different situations and defines key terms for subsets like natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Examples are given for each subset. Later, exercises are provided to identify which subset different numbers belong to.
Basics of geometry
Points, lines, and planes are the undefined terms in geometry that form its foundations. A point has no dimensions and marks a location in space, a line extends in one dimension, and a plane extends in two dimensions. The basic elements of 2D space are points, lines, line segments, rays, angles, and their intersections. Rays and angles are defined using points and lines, with rays having a starting point and angles consisting of two rays with the same starting point.
Maths and music ppt
Math and music are closely related. Rhythm can be measured mathematically through time signatures and beat divisions. The pitch of musical notes corresponds to measurable frequencies. Pythagoras discovered that notes were based on simple fractional string lengths that created pleasing harmonic ratios. He believed music and mathematics were intrinsically linked. Over time, composers used mathematical patterns like the golden ratio and Fibonacci sequence. The 12-tone scale solved issues with transposing between keys, linking music to irrational numbers rather than strict ratios.
Math and Music
The document discusses the mathematical relationships between music and rhythm. It explains that rhythm can be compared to numbers in math and that the pitch of musical notes corresponds to specific frequencies measured in hertz. Pythagoras discovered that the ratios between string lengths produced harmonious musical notes and the 12-tone scale developed from applying these ratios. While this helped tune instruments to each other, it caused problems when transposing between keys, which was solved by using irrational number ratios in the well-tempered scale.
More Related Content
What's hot
The fibonacci sequence
This ppt contains everything about Fibonacci sequence.
From its origin to where it is used and where it is found-EVERYTHING.Hope you like it
Fibonacci Sequence and Golden Ratio
The document discusses Fibonacci numbers and the golden ratio, explaining how Fibonacci discovered the Fibonacci sequence by modeling rabbit populations and how ratios between numbers in the sequence converge on the golden ratio. It provides many examples of how the golden ratio appears frequently in nature, art, architecture, and the human body, demonstrating its aesthetic appeal and role in design.
Fibonacci series and Golden ratio
The document discusses the Fibonacci sequence and the golden ratio. It begins by introducing the Fibonacci sequence of numbers: 1, 1, 2, 3, 5, 8, etc., where each number is the sum of the previous two. It then explains that the ratios of successive numbers in the sequence converge on the golden ratio, approximately 1.618. The golden ratio is found throughout nature, such as in the proportions of the human body and in vegetation. The document also provides methods for constructing a golden rectangle using squares and diagonals, with a final ratio matching the golden ratio.
Math in Nature
This document discusses different types of patterns found in nature and their definitions. It covers symmetry patterns like bilateral, mirror, radial and rotational symmetry. It also discusses fractals and their repeating patterns at every scale, as well as Fibonacci spirals emanating from a central point. Additionally, it examines common shapes like circles, spheres, hexagons and cones, providing their definitions.
GEOMETRIC ART -SYMMETRY
This document discusses different types of symmetry in geometric art. It defines symmetry as an object having two or more equal sides when split in half. There are three main types of symmetry discussed: reflection symmetry (also called line symmetry), where an object can be folded in half and the halves match; point symmetry, where every part has a matching part the same distance from the central point but in the opposite direction; and rotational symmetry, where an object looks the same when rotated by certain angles. The number of positions an object can be rotated and still look the same is called its order of rotational symmetry. Examples given include squares and circles. In conclusion, the document provides an overview of key concepts in symmetry as it relates to geometry and art
Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]
Recent Trends of Mathematics in Education
Mathematical activity has changed in every field. We discuss some of these trends and how they could influence the future of mathematical education. The aim of this paper is to study the recent trends in the present day mathematics and the role of mathematics in other disciplines. Dr. A. K. Yadav | Dr. Sushil Kumar | Dr. Rashmi Chaudhary "Recent Trends of Mathematics in Education" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-4 , June 2020, URL: https://www.ijtsrd.com/papers/ijtsrd31130.pdf Paper Url :https://www.ijtsrd.com/mathemetics/other/31130/recent-trends-of-mathematics-in-education/dr-a-k-yadav
Trabajo final "Matemáticas en la pintura" pfdz 2013
Este documento presenta información sobre las matemáticas en la pintura. Explica conceptos como los cuadrados mágicos, la proporción áurea, la espiral de Durero, y cómo artistas como Velázquez y Leonardo da Vinci incorporaron estas ideas matemáticas en obras maestras como Las Meninas y La Gioconda. También analiza las teselaciones y figuras imposibles creadas por el artista M. C. Escher, que demuestran una comprensión profunda de conceptos geométricos.
Parts-of-the-Science-Investigatory-Project-PPT.pptx
This document outlines the key parts and sections of a science investigatory project. It discusses the importance of having a clear and concise title that indicates the project purpose. It states that the abstract should summarize the research problem, methods, and conclusions in 1-2 paragraphs. It provides details on what should be included in each section of Chapter 1 such as the introduction/background, statement of the problem, hypotheses formulation, significance of the study, scope and limitations. It also notes that definitions of terms should include dictionary meanings and operational definitions for terms as used in the specific research project.
Chapter 1
This document provides an overview of physics as a science. It discusses how physics is a systematic body of knowledge based on observations and experiments. Physics is divided into classical and modern physics. Classical physics includes mechanics, acoustics, optics, thermodynamics, and electromagnetism while modern physics includes atomic, nuclear, quantum, relativistic, solid state, and plasma physics. The document also discusses how physics employs the scientific method and notes that physics and technology are partners for progress, with physics furthering our understanding of nature and technology applying that understanding. Mathematics and measurement are also presented as essential tools for physics.
Polygons (its meaning, nature and types) for grade v
This document defines and describes different types of polygons. Polygons are 2-dimensional plane shapes made of straight lines that form a closed figure. There are regular polygons with all equal sides and angles and irregular polygons without equal sides and angles. Polygons can also be convex with no inward angles, concave with at least one internal angle greater than 180 degrees, simple with one boundary not crossing over itself, or complex intersecting with itself. The document provides examples to illustrate these different types of polygons.
Book 1
This document discusses how mathematical concepts like symmetry, shapes, patterns and sequences are evident in nature. It provides examples of bilateral symmetry (like in humans and butterflies), radial symmetry (like in flowers and starfish), parallel lines (like in leaf veins and zebra stripes), basic shapes (like hexagons in bee hives and spheres in planets), the Fibonacci sequence (seen in rabbit birth rates), and patterns (like leaf arrangements, zebra fur and sand ripples). The document emphasizes that mathematics can be observed throughout nature from atoms to galaxies.
PowerPoint Presentation on Golden Ratio
The document is a presentation on the golden ratio. It defines the golden ratio as an irrational number approximated to 1.618, often denoted by Greek letters tau or phi. It describes two quantities being in a golden ratio if the ratio between their sum and the larger quantity equals the ratio between the larger and smaller quantities. The golden ratio is used in architecture, painting, book design, nature, aesthetics, and perceptual studies. A golden triangle is an isosceles triangle where the smaller side is in golden ratio to the adjacent side, and they can be found in pentagrams and stellated polyhedra.
Types of mirrors
This document discusses different types of mirrors and their properties. It describes plane mirrors and two types of curved mirrors: convex and concave. Convex mirrors form a smaller virtual image than the object, while concave mirrors form a magnified virtual image. The document also provides formulas for calculating the focal length and magnification of curved mirrors based on the object and image distances and radius of curvature. Key properties of mirror reflections like being virtual, erect, and laterally inverted are also noted.
Circle theorems
Euclidean geometry is very important in Math, and it weighs a lot of marks in High school Math. This branch of mathematics develops critical thinking and reasoning skills to a learner.
Artificial Intelligence Quiz
Artificial Intelligence(AI) Quiz questions and answers
Related Videos:
What are AI and Big Data? Simple Tutorial about Artificial Intelligence (AI)
https://www.youtube.com/watch?v=ROaw4if2o7E
What is Artificial Intelligence (AI)? Discussion about Benefits, Risks and Uses of AI
https://www.youtube.com/watch?v=1K_ATYqvHTs
Microscope uses Artificial Intelligence to find cancer cells more efficiently
https://www.youtube.com/watch?v=Iv1wBvPMguE
Artificial intelligence produces Realistic Sounds that fool Humans
https://www.youtube.com/watch?v=_2w3mvWk0po
Artificial Intelligence "Libratus" Beats Top Poker Pros
https://www.youtube.com/watch?v=8iEN19vMUyw
Sundar Pichai's Talk about AI and Google Assistant
https://www.youtube.com/watch?v=MtujWybGKyU
Chem m15 changes that matter undergoes
This module discusses various chemical and phase changes that occur in everyday life. It is divided into four lessons: (1) Changing Phases explains the differences between melting, freezing, evaporation, condensation, sublimation and deposition; (2) When Does a Chemical Change Occur? describes the indicators of a chemical change and differentiates chemical from physical changes; (3) Types of Chemical Changes outlines four types of chemical reactions - combination, decomposition, single replacement and double displacement; (4) Chemical Changes Around Us provides examples of changes that happen in the human body during digestion and exercise as well as in cleaning products like soap. The module aims to help students understand and identify different types of changes in their environment.
Symmetry Presentation By Manali
This document discusses different types of symmetry found in nature, architecture, art, religious symbols, and music. It provides examples of line symmetry seen in leaves, snowflakes, and butterflies. Architectural symmetry is seen at various scales from overall building designs to individual elements. Symmetry is also used in art forms like beadwork and furniture as well as religious symbols like the Star of David. In music, symmetry has been used as a compositional constraint and in concepts of permutation and invariance. Rotational symmetry makes an object look the same after certain rotations and examples include objects with order 3 and order 6 rotational symmetry.
Subsets of real numbers
This document discusses different subsets of real numbers. It begins by explaining how primitive man counted using objects like stones and evolved to create number systems over hundreds of years. It then provides activities to identify subsets of numbers for different situations and defines key terms for subsets like natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Examples are given for each subset. Later, exercises are provided to identify which subset different numbers belong to.
Basics of geometry
Points, lines, and planes are the undefined terms in geometry that form its foundations. A point has no dimensions and marks a location in space, a line extends in one dimension, and a plane extends in two dimensions. The basic elements of 2D space are points, lines, line segments, rays, angles, and their intersections. Rays and angles are defined using points and lines, with rays having a starting point and angles consisting of two rays with the same starting point.
What's hot (20)
Trabajo final "Matemáticas en la pintura" pfdz 2013
Trabajo final "Matemáticas en la pintura" pfdz 2013
Parts-of-the-Science-Investigatory-Project-PPT.pptx
Parts-of-the-Science-Investigatory-Project-PPT.pptx
Polygons (its meaning, nature and types) for grade v
Polygons (its meaning, nature and types) for grade v
Viewers also liked
Maths and music ppt
Math and music are closely related. Rhythm can be measured mathematically through time signatures and beat divisions. The pitch of musical notes corresponds to measurable frequencies. Pythagoras discovered that notes were based on simple fractional string lengths that created pleasing harmonic ratios. He believed music and mathematics were intrinsically linked. Over time, composers used mathematical patterns like the golden ratio and Fibonacci sequence. The 12-tone scale solved issues with transposing between keys, linking music to irrational numbers rather than strict ratios.
Math and Music
The document discusses the mathematical relationships between music and rhythm. It explains that rhythm can be compared to numbers in math and that the pitch of musical notes corresponds to specific frequencies measured in hertz. Pythagoras discovered that the ratios between string lengths produced harmonious musical notes and the 12-tone scale developed from applying these ratios. While this helped tune instruments to each other, it caused problems when transposing between keys, which was solved by using irrational number ratios in the well-tempered scale.
The Beauty Of Mathematics
This document presents a mathematical pattern showing that certain words can add up to percentages or more when the letters of those words are assigned numerical values from 1 to 26. It shows that "HARDWORK" equals 98%, "KNOWLEDGE" equals 96%, "ATTITUDE" equals 100%, and "LOVEOFGOD" equals 101%, demonstrating that the love of God can help one achieve more than 100%. The document suggests that while hard work and knowledge are important, it is one's attitude and the love of God that can truly help one succeed.
Maths in food
This document discusses the connections between mathematics and food. It provides examples of how concepts like symmetry, ratios, pi, and proportions are seen in foods. Recipes also involve using mathematics through quantities, fractions, temperatures, and times. Creating a balanced diet and salad pyramid also relies on mathematical ratios and proportions. Overall, the document aims to show how mathematics can be found in many aspects of food.
Nature and principles of teaching and learning math
This document discusses effective teaching of mathematics. It outlines three phases of mathematical inquiry: (1) abstraction and symbolic representation, (2) manipulating mathematical statements, and (3) application. It also discusses the nature and principles of teaching mathematics, including that mathematics relies on both logic and creativity. Effective teaching requires understanding what students know and challenging them, as well as using worthwhile tasks to engage them intellectually. Teachers must have mathematical knowledge and commit to students' understanding.
Math in nature
The document discusses the Fibonacci sequence and how it relates to patterns found in nature, such as spirals in pinecones and sunflowers. It provides examples of the golden ratio in art and architecture, including the Parthenon and paintings like the Mona Lisa. The author questions why math, which can explain these natural patterns and ratios, should be considered "ugly" by some.
Maths in Our Daily Life
Mathematics is essential in daily life and has a long history of practical applications. It first arose from needs to count and measure, and early civilizations used math for tasks like construction and accounting. Over millennia, mathematical concepts and applications have expanded greatly. Today, areas like statistics, calculus, and other quantitative fields inform domains from politics to transportation to resource management. Many people misunderstand math as only involving formulas, but it really involves abstract problem-solving and modeling real-world situations. Core topics in daily use include commercial math, algebra, statistics, and financial calculations for tasks like budgeting and investing.
"Mathematics in day to day life"
This slide was presented by the Maths Department of Cochin Refineries School for the Inter-School workshop conducted as a part of World Mathematics Day celebration. "Mathematics in day to day life"
Viewers also liked (8)
Nature and principles of teaching and learning math
Nature and principles of teaching and learning math
Recently uploaded
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
The History of Stoke Newington Street Names
Presented at the Stoke Newington Literary Festival on 9th June 2024
www.StokeNewingtonHistory.com
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Community pharmacy- Social and preventive pharmacy UNIT 5
Covered community pharmacy topic of the subject Social and preventive pharmacy for Diploma and Bachelor of pharmacy
How to Make a Field Mandatory in Odoo 17
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...National Information Standards Organization (NISO)
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Recently uploaded (20)
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Mathematics in nature
- 1. Mathematics in Nature Presented By: St.George’s School, Alaknanda
- 3. Fractals Mountains, Tibet Fractal Rivers in Savannah, Georgia Fractal Patterns in a Hydrothermal Spring Fractals in Clouds
- 5. Levy patterns of Sharks
- 6. EUCLID OF ALEXANDRIA CALCULATION OF GOLDEN RATIO
- 7. MONA LISA – Da VinciPARHTENON Broadway Boogie Woogie- Mondrean
- 8. RELATION BETWEEN GOLDEN RATIO AND FIBONACCI SEQUENCE FIBONACCI SPIRAL
- 11. COCHLEA: Inner Ear VITRUVIAN MAN: Da Vinci Ratio between forearm and handGolden ratio in finger bones