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Mahavira was an influential 9th century Indian mathematician from southern India. He wrote the Ganita-Sara Samagraha, one of the earliest and most important texts entirely devoted to mathematics in India. The text consisted of 9 chapters covering all mathematical knowledge of the mid-9th century, including arithmetic operations, fractions, equations, areas, and volumes. It built upon the work of earlier mathematicians like Brahmagupta but also advanced mathematical understanding with original contributions such as techniques for solving various types of equations and approximate formulas for the areas of ellipses. The text provides a valuable record of the state of Indian mathematics in the 9th century.

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pointers in c language and how it is utilize in data structure a, where pointers are applicable and how to use pointers

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This document provides information about different types of job interviews and tips for successful interviewing. It discusses one-to-one interviews, panel interviews, stress interviews, technical interviews, and personal/HR interviews. It lists common interview questions and emphasizes the importance of preparing, performing well during the interview, following up after the interview, dressing appropriately, communicating verbally and nonverbally, and showing thanks after the interview. The document also includes dos and don'ts for interviews as well as checklists for various aspects of interviewing.

Resume Building for Teens

Print this out and use it as a guide for writing your resume. This is a great tool for high school students and graduates translate their skills and experience to apply to real world careers.

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Los prototipos textuales son las características estructurales y de lenguaje que definen los diferentes tipos de textos. Los principales prototipos son la narración, descripción, exposición, argumentación y diálogo. Cada uno tiene características externas e internas particulares y una intención comunicativa distinta, como contar una historia, informar sobre un tema o convencer a un lector.

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This document discusses optimizing the orientation of an offshore oil and gas platform through computational fluid dynamics (CFD) modeling. Key parameters like natural ventilation, helideck impairment from exhaust, wind chill effects, lifeboat drift, and tendon stress were considered. CFD simulations using STAR-CCM+ were conducted for different platform orientations. The results showed the optimum orientation balanced all parameters, with the platform's north facing true east-southeast. This approach integrates engineering judgment and CFD to achieve a safer design compared to relying only on past experience.

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Kevin Wallace is a security professional from Montgomery, AL who is expected to graduate from Alabama State University with a CIS degree in May 2017. He has over 15 years of experience working in security roles, including monitoring inmates at Alabama Department of Corrections from 2003 to 2008 and protecting million-dollar artwork as security at the Montgomery Museum of Fine Arts since 2008. Wallace is certified in firearms, tasers, and non-lethal restraint training.

Al khwarismi

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This document provides information about an organization called Success With Self that teaches mathematics using concepts from Vedic mathematics. It describes some Vedic math techniques like the digital root or Anka Mula method for adding digits in a number. Other techniques discussed include the Nava Sesha Paddhati method for digital roots, Nikhilam Sutra for subtraction, and the Aadhaara Antara method for multiplication of numbers close to a base. The document explains how these intuitive Vedic math methods can make math fun and build confidence compared to traditional teaching styles. Success With Self offers different levels of courses in Vedic math techniques.

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Here are the solutions to the problems:
1. a) A lies in the interior of the circle because PA < PQ.
b) B lies in the exterior of the circle because PB > PQ.
c) The circles with radii PQ and PB are called concentric circles.
2. One tangent.
3. 12
4. 15
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Diophantus was a Greek mathematician who lived in Alexandria during the 3rd century CE. He wrote the Arithmetica, which was divided into 13 books and introduced symbolic notation for unknowns and exponents. The Arithmetica contained problems involving determining integer and rational solutions to polynomial equations. Pappus of Alexandria lived in the 4th century CE and wrote the Synagoge or Collection, which contained summaries of earlier mathematical work across various topics, including constructions, number theory, and properties of curves and polyhedra. The Collection helped preserve important mathematical concepts and problems from antiquity.

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Time t =
f(n) =
1 second
1 hour
1 day
1 month
=30 days
n2
1,609,968
lg n
n3
2n
n lg n
2,755,147,513
2. Use loop counting to give a O( ) characterization of each of the following loops basing each upon the size of its input:
a. Algorithm Loop1(n):
s ← 0
for i ← 1 to n do
s ← s + i
b. Algorithm Loop2(p):
p ← 1
for i ← 1 to 2n do
p ← p * i
c. Algorithm Loop3(n):
p ← 1
for j ← 1 to n2 do
p ← p * i
d. Algorithm Loop4(n):
s ← 0
for j ← 1 to 2n do
for k ← 1 to j do
s ← s + j
e. Algorithm Loop5(n):
k ← 0
for r ← 1 to n2 do
for s ← 1 to r do
k ← k + r
3. Order the following functions from smallest to largest by their big-O notation—you can use the letters in your answer rather than copying each formula. Be clear which is smallest and which is largest, and which functions are asymptotically equivalent. For example, if g, h, and m are all O(n lg n), you would write g = h = m = O(n lg n).
a. 562 log3 108
b. n3
c. 2n lg n
d. lg nn
e. n3 lg n
f. (n3 lg n3)/2
g. nn
h. 56n
i. log5 (n!)
j. ncos n
k. n / lg n
l. lg* n
m.
4. a. Which of these equations is true, and why?
b. Which of these is smaller for very large n?
Trisecting the Circle: A Case for Euclidean Geometry
Author(s): Alfred S. Posamentier
Source: The Mathematics Teacher, Vol. 99, No. 6 (FEBRUARY 2006), pp. 414-418
Published by: National Council of Teachers of Mathematics
Stable URL: http://www.jstor.org/stable/27972006
Accessed: 09-02-2018 18:19 UTC
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide
range of content in a trusted digital archive. We use information technology and tools to increase productivity and
facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
http://about.jstor.org/terms
National Council of Teachers of Mathematics is collaborating with JSTOR to digitize,
preserve and extend access to The Mathematics Teacher
This content downloaded ...

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4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
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This document provides a review for algebra sections on various topics including:
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2) Finding sums, differences, and ratios of numbers.
3) Representing word problems using tables and equations.
4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
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Gshshhshshshshshshshshssgsjdvdhdbdbdhdhsksbdsisvddodj nskshddjdjdbkddbdjddbhdiddbdhnddjjdd

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Ge Mlec1

The document provides an overview of early Egyptian mathematics, including:
1) Egyptian numerals were an additive system that grouped in units of 10. They multiplied using a method of doubling numbers.
2) Egyptians rejected general fractions like n/m and insisted on expressing fractions as sums of unit fractions like 1/2, 1/3, etc. They had developed algorithms for decomposing fractions into Egyptian fractions.
3) Egyptian geometry was empirical and intuitive, lacking deductive proof. They computed volumes of shapes like truncated pyramids.

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1. The document examines the fractal dimension equation written by Koch in 1904. It explores applying the equation to the Koch snowflake fractal.
2. Using Python code, the document attempts to derive the value of e by taking the difference between exponential functions as x approaches infinity. However, this method does not account for all factors that determine e^x.
3. The document then examines how the derivative of the exponential function C^x relates to the base C, finding that d(2^x)/dx = 2^(x-1), d(3^x)/dx = (f(x)-f(x-1))*3/f(x), and beginning an analysis of d(

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Six students presented on the importance of mathematics in daily life. They discussed how mathematics originated from words meaning "what is learnt" and how it has been defined as the science of quantity and figures. They provided examples of how mathematics is used in areas like commerce, banking, foreign exchange, and more. Famous mathematicians from India and other parts of the world were discussed along with their contributions. In conclusion, the presentation emphasized that mathematics is essential for both educated and uneducated people in their daily lives and activities.

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This document provides information about an organization called Success With Self that teaches mathematics using concepts from Vedic mathematics. It describes some Vedic math techniques like the digital root or Anka Mula method for adding digits in a number. Other techniques discussed include the Nava Sesha Paddhati method for digital roots, Nikhilam Sutra for subtraction, and the Aadhaara Antara method for multiplication of numbers close to a base. The document explains how these intuitive Vedic math methods can make math fun and build confidence compared to traditional teaching styles. Success With Self offers different levels of courses in Vedic math techniques.

CEM REVIEWER

Here are the solutions to the problems:
1. a) A lies in the interior of the circle because PA < PQ.
b) B lies in the exterior of the circle because PB > PQ.
c) The circles with radii PQ and PB are called concentric circles.
2. One tangent.
3. 12
4. 15
5. 16

history in math_1.pptx

Diophantus was a Greek mathematician who lived in Alexandria during the 3rd century CE. He wrote the Arithmetica, which was divided into 13 books and introduced symbolic notation for unknowns and exponents. The Arithmetica contained problems involving determining integer and rational solutions to polynomial equations. Pappus of Alexandria lived in the 4th century CE and wrote the Synagoge or Collection, which contained summaries of earlier mathematical work across various topics, including constructions, number theory, and properties of curves and polyhedra. The Collection helped preserve important mathematical concepts and problems from antiquity.

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This document contains a presentation on how mathematics is used in everyday life. It provides examples of how math is applied in art, business, cooking, music, and other domains. It also summarizes the contributions of important mathematicians like Pythagoras, Ramanujan, and properties of rational numbers, squares, cubes, and their roots. The presentation aims to demonstrate the pervasive and practical role of mathematics in various activities.

1. Assume that an algorithm to solve a problem takes f(n) microse.docx

1. Assume that an algorithm to solve a problem takes f(n) microseconds for some function f of the input size n. For each time t labeled across the top, determine the exact largest value of n which can be solved in time f(n) where f(n) ≤ t. Use a calculator! You will find it helpful to convert the t values to microseconds, and you may find it helpful to insert a row for n. Note that “lg n” is the log2 n. Note that the only row you can’t write out the values for fully is the “lg n” row—only there may you write 2x for the appropriate value of x. Use the Windows built-in scientific calculator (under Accessories menu) as necessary. A couple values are filled in to get you started. Important: “exact values” means precisely that. Check your answers with values above and below!
Time t =
f(n) =
1 second
1 hour
1 day
1 month
=30 days
n2
1,609,968
lg n
n3
2n
n lg n
2,755,147,513
2. Use loop counting to give a O( ) characterization of each of the following loops basing each upon the size of its input:
a. Algorithm Loop1(n):
s ← 0
for i ← 1 to n do
s ← s + i
b. Algorithm Loop2(p):
p ← 1
for i ← 1 to 2n do
p ← p * i
c. Algorithm Loop3(n):
p ← 1
for j ← 1 to n2 do
p ← p * i
d. Algorithm Loop4(n):
s ← 0
for j ← 1 to 2n do
for k ← 1 to j do
s ← s + j
e. Algorithm Loop5(n):
k ← 0
for r ← 1 to n2 do
for s ← 1 to r do
k ← k + r
3. Order the following functions from smallest to largest by their big-O notation—you can use the letters in your answer rather than copying each formula. Be clear which is smallest and which is largest, and which functions are asymptotically equivalent. For example, if g, h, and m are all O(n lg n), you would write g = h = m = O(n lg n).
a. 562 log3 108
b. n3
c. 2n lg n
d. lg nn
e. n3 lg n
f. (n3 lg n3)/2
g. nn
h. 56n
i. log5 (n!)
j. ncos n
k. n / lg n
l. lg* n
m.
4. a. Which of these equations is true, and why?
b. Which of these is smaller for very large n?
Trisecting the Circle: A Case for Euclidean Geometry
Author(s): Alfred S. Posamentier
Source: The Mathematics Teacher, Vol. 99, No. 6 (FEBRUARY 2006), pp. 414-418
Published by: National Council of Teachers of Mathematics
Stable URL: http://www.jstor.org/stable/27972006
Accessed: 09-02-2018 18:19 UTC
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide
range of content in a trusted digital archive. We use information technology and tools to increase productivity and
facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
http://about.jstor.org/terms
National Council of Teachers of Mathematics is collaborating with JSTOR to digitize,
preserve and extend access to The Mathematics Teacher
This content downloaded ...

Pythagoras theorem

Pythagoras was an ancient Greek philosopher and mathematician born on the island of Samos in around 570 BC. He is best known for the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. While Pythagoras likely did not discover this theorem himself, he is credited as being the first to prove why it is true. The Pythagorean theorem is one of the earliest and most important theorems in mathematics.

Magic square

This document explores magic squares, their history, construction, and applications. Magic squares are arrangements of numbers where the sums of each row, column, and diagonal are equal. They have been known in China since 650 BCE and were introduced to Arab mathematicians by the 8th century. There are several methods for constructing magic squares, and they exist for all values of n except 2. Magic squares have been applied to music rhythms and are related to Sudoku puzzles. While once thought to have mystical properties, mathematicians now understand magic squares as numerical arrangements following specific rules.

Rumus Algebra.pdf

1) The document discusses algebraic formulas and expressions. It provides examples of writing formulas based on word problems and situations.
2) Key terms discussed include: algebraic formula, algebraic expression, variables, operations, equations, and relating factors.
3) The document also contains exercises on writing formulas, expressing variables as subjects of formulas, evaluating formulas for given values, and solving word problems algebraically.

Maths herons formula

Heron's formula provides a way to calculate the area of a triangle when only the lengths of the three sides are known. It was derived by the Greek mathematician Heron of Alexandria around 10 AD. The formula expresses the area of a triangle in terms of its semiperimeter (s = (a + b + c)/2) and the lengths of its three sides (a, b, c). It can be written as: A = √s(s-a)(s-b)(s-c), where A is the area of the triangle. The document provides an example of using Heron's formula to find the area of an equilateral triangle and discusses applications of the formula.

Algebreviewer

This document provides a review for algebra sections on various topics including:
1) Solving word problems involving equations with one unknown variable.
2) Finding sums, differences, and ratios of numbers.
3) Representing word problems using tables and equations.
4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
5) Graphing linear equations and finding slopes of lines from equations or two points.
6) Writing equations of lines in different forms given information like slopes, intercepts, or two points.

Egyptian Mathematics

For great Egyptians
Prof. Mokhtar Elnomrossy
VISIONEERING:: Enabling Technologies Consulting Engineers
http://www.visioneering-etce.com/

Mathematics model papers for class xi

APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students .

project

This document is a project report submitted by a student for a Bachelor of Science degree in Mathematics. It provides an introduction to the field of topology. The report includes a title page, certificate, declaration, acknowledgements, table of contents, and several chapters. The introduction defines topology and provides some examples. It states that the project aims to provide a thorough grounding in general topology.

10140006abcathsgsjdgnsvsshbssjdvdvdvdbdhdhhdhdhf.ppt

Gshshhshshshshshshshshssgsjdvdhdbdbdhdhsksbdsisvddodj nskshddjdjdbkddbdjddbhdiddbdhnddjjdd

diophantine equation and congruence puzzles

Mahavira’s puzzle
Hundred fowls puzzle
Monkey and coconuts puzzle
learn about 3 interesting puzzles...

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Ge Mlec1

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20230124 PLOS Fractal Manuscript 8.docx

20230124 PLOS Fractal Manuscript 8.docx

Mathematics

Mathematics

Vegam booklet converted word file

Vegam booklet converted word file

CEM REVIEWER

CEM REVIEWER

history in math_1.pptx

history in math_1.pptx

Maths

Maths

1. Assume that an algorithm to solve a problem takes f(n) microse.docx

1. Assume that an algorithm to solve a problem takes f(n) microse.docx

Pythagoras theorem

Pythagoras theorem

Magic square

Magic square

Rumus Algebra.pdf

Rumus Algebra.pdf

Maths herons formula

Maths herons formula

Algebreviewer

Algebreviewer

Algebreviewer

Algebreviewer

Egyptian Mathematics

Egyptian Mathematics

Mathematics model papers for class xi

Mathematics model papers for class xi

project

project

10140006abcathsgsjdgnsvsshbssjdvdvdvdbdhdhhdhdhf.ppt

10140006abcathsgsjdgnsvsshbssjdvdvdvdbdhdhhdhdhf.ppt

diophantine equation and congruence puzzles

diophantine equation and congruence puzzles

Diabetes

There are four main types of diabetes: type 1, type 2, gestational diabetes, and prediabetes. Type 1 is an autoimmune disease where the body attacks the pancreas, type 2 is caused by the body not producing enough insulin or cells not responding to insulin properly. Gestational diabetes occurs during pregnancy. Prediabetes means blood sugar levels are higher than normal but not high enough to be classified as diabetes. Complications of diabetes include cardiovascular, kidney, nerve and eye diseases. Diabetes is tested through A1C, fasting plasma glucose, and oral glucose tolerance tests. Treatment options include oral medications, insulin injections, surgery, and lifestyle changes like diet and exercise. Future treatments may include gene therapy for type 1

Polynomials

This document provides an overview of polynomials, including:
- Defining polynomials as expressions involving variables and coefficients using addition, subtraction, multiplication, and exponents.
- Discussing the history of polynomial notation pioneered by Descartes.
- Explaining the different types of polynomials like monomials, binomials, and trinomials.
- Outlining common uses of polynomials in mathematics, science, and other fields.
- Describing how to find the degree of a polynomial and graph polynomial functions.
- Explaining arithmetic operations like addition, subtraction, and division that can be performed on polynomials.

Advertising

Advertising is a paid, non-personal form of communication used to promote ideas, products, or services. The objectives of advertising include introducing new products to convince customers to try them, retaining existing customers, and winning back customers who have switched to competitors. Advertising provides benefits like employment opportunities and economic growth while allowing consumers to learn about and compare products. However, critics argue that advertising increases product prices and can confuse consumers with similar claims. Overall, while some criticisms exist, advertising plays an important role in modern business by facilitating communication with customers.

old age

This presentation discusses the importance of elders and issues they face. Elders share their life experiences and promote cultural values, acting as mentors. However, they often face neglect from busy children, loneliness, abuse, hopelessness, and helplessness. To help, the government launched pension programs, there are awareness days for elder abuse, and we can increase awareness, education, respite care, counseling, and celebrate grandparents. The presentation concludes by advocating for letting elders age gracefully with dignity and respect.

Chemistry

Osmosis is the movement of solvent molecules through a semi-permeable membrane from an area of higher solvent concentration to lower solvent concentration. The document defines hypertonic, isotonic, and hypotonic solutions and explains how osmosis causes cell shrinkage or swelling depending on the solution. It also provides examples of how osmosis is used in desalination, food concentration, and dairy concentration processes.

Diabetes mellitus

There are four main types of diabetes: type 1, type 2, gestational diabetes, and prediabetes. Type 1 is an autoimmune disease where the body attacks the pancreas, type 2 is caused by the body not producing enough insulin or cells not responding to insulin properly. Gestational diabetes occurs during pregnancy. Prediabetes means blood sugar levels are higher than normal but not high enough to be classified as diabetes. Complications of diabetes include cardiovascular, kidney, nerve and eye diseases. Diabetes is tested through A1C, fasting plasma glucose, and oral glucose tolerance tests. Treatment options include oral medications, insulin injections, surgery, and lifestyle changes like diet and exercise. Future treatments may include gene therapy for type 1

WATER CRISIS “Prediction of 3rd world war”

The document discusses the global water crisis and issues around water management. It notes that water scarcity is increasing due to rising populations and demands for water exceeding supply. The document also discusses historical water management practices, current issues like decreasing groundwater levels, and calls for sustainable water management through conservation efforts, innovative practices, and ensuring access to safe drinking water for all. Scientists warn that without addressing water shortages, wars may be fought over water in the future and ecosystems will suffer serious damage.

Issue of Shares

The document discusses key differences between private and public companies. It states that private companies have restrictions on the number of members and cannot invite the public to subscribe to its shares, while public companies can have an unlimited number of members and can invite public subscription. Additionally, private companies have restrictions on the transfer of shares while public companies do not.

My experience my values 7th

The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.

Solid

The document summarizes key concepts about crystalline and amorphous solids, including:
- Crystalline solids exhibit long-range order while amorphous solids only have short-range order.
- Ionic crystals like NaCl and CsCl form face-centered cubic or body-centered cubic structures to maximize interactions between oppositely charged ions.
- The cohesive energy of ionic crystals can be calculated by considering contributions from Coulomb attraction, electron overlap repulsion, ionization energies, and electron affinities.

Smart class

This document discusses the factors that influence demand, including price, income, and the prices of substitute and complementary goods. It defines quantity demanded as a change in demand due to a change in price, while a change in demand is due to other factors. A demand schedule shows the inverse relationship between price and quantity demanded in a table. A demand curve graphs this relationship, with quantity demanded on the y-axis and price on the x-axis. Movement along the demand curve occurs when quantity demanded changes due to a change in price.

S107

Cancer immunotherapy harnesses the body's immune system to fight cancer by developing antibodies or T cells that target and destroy cancer cells. Researchers are working to develop new immunotherapy approaches that use antibodies or T cells to identify and eliminate cancer cells while leaving normal cells unharmed. Immunotherapy holds promise as a revolutionary new approach for treating many cancer types by giving the body's own immune system tools to fight the disease.

S104

Solid is a state of matter where particles are arranged closely together. Constituent particles in solids can be atoms, molecules, or ions arranged in a definite pattern with no definite shape or volume. There are different types of unit cell structures that describe the arrangement of particles in solids, including primitive, body-centered, and face-centered unit cells. Close packing of spheres in two and three dimensions results in different crystal structures depending on how additional layers are arranged in the voids between lower layers.

S103

This document summarizes different types of work, energy, and collisions. It defines positive, negative, and zero work done based on the angle between the applied force and displacement. Kinetic energy is defined as the energy of motion, while potential energy is the energy due to position. The equations for kinetic and potential energy are provided. Conservation of energy and conservative versus non-conservative forces are also summarized. Kinetic energy and total linear momentum are stated to be conserved, while inelastic collisions are defined as those where the initial and final kinetic energies are not equal.

S102

This document discusses the structure and function of neurons and the nervous system. It describes the key parts of a neuron including the cell body, dendrites, and axon. It explains how nerve impulses are transmitted across synapses using neurotransmitters. The document then provides an overview of the major structures of the brain including the cerebrum, cerebellum, brainstem, and how the brain acts as the command center to integrate sensory input and control coordination.

S101

The document provides tips for conserving electricity and reducing energy costs, such as turning off lights and appliances when not in use, using more efficient appliances like CFL bulbs and gas water heaters, avoiding unnecessary opening of refrigerators, not leaving devices on standby, doing laundry in batches, and installing solar panels. It also notes that Energy Star certified devices use 20-30% less energy.

Projectile motion

Projectile motion can be thought of as the combination of horizontal and vertical motion. The horizontal motion is unaffected by gravity and follows the equation x=u*cosθ*t, while the vertical motion is affected by gravity and follows the equation y=u*sinθ*t - 0.5*g*t^2. The path of a projectile forms a parabolic curve. Factors like the launch angle and initial velocity determine the time of flight, maximum height, and horizontal range of the projectile. Projectile motion has applications in various sports to calculate the optimal angle for maximum distance.

Mansi

Anees Jung's book Lost Spring focuses on stories of children from deprived backgrounds who face difficult circumstances like being kidnapped and forced to work in the carpet industry. Some children are maltreated by alcoholic fathers, married off early, or sexually abused. In this chapter, Jung expresses concern over the exploitation of children forced to do hazardous jobs like bangle making and rag picking due to poverty and traditions. This results in the loss of childhood, education, and opportunities. One story focuses on Mukesh, who lives with his brother doing bangle making in Firozabad but wants a different career, though people believe their fate is predetermined by their previous birth. The theme of the book and awards is to create awareness about child

Gravitation

1. The document summarizes Newton's theory of gravitation and key concepts in physics such as the four fundamental forces, Newton's law of universal gravitation, and gravitational potential energy.
2. It also discusses Einstein's theory of general relativity, which improved on Newton's theory by accounting for the fact that gravity propagates at the speed of light rather than instantaneously.
3. The principle of equivalence formed the basis for general relativity and implies that accelerated frames are equivalent to gravitational fields.

Diabetes

Diabetes

Polynomials

Polynomials

Advertising

Advertising

old age

old age

Chemistry

Chemistry

Diabetes mellitus

Diabetes mellitus

WATER CRISIS “Prediction of 3rd world war”

WATER CRISIS “Prediction of 3rd world war”

Issue of Shares

Issue of Shares

My experience my values 7th

My experience my values 7th

Solid

Solid

Smart class

Smart class

S107

S107

S104

S104

Mera anubhav meri siksha 7th

Mera anubhav meri siksha 7th

S103

S103

S102

S102

S101

S101

Projectile motion

Projectile motion

Mansi

Mansi

Gravitation

Gravitation

- 1. By Mrs. Sarita D. Mirzapure. N.M.Model Jr. College Nagpur.
- 2. Mahavira Born: about 800 ad. in Mysore, India Died: about 870 in India
- 3. Mahavira was of the Jain religion and was familiar with jain mathematics. He worked in Mysore in southern India where he was a member of a School of mathematics. This great mathematician monk wrote “Ganita- Sara Samagraha” in 850 AD during the regime of the great Rashtrakuta king Amoghavarsha .
- 4. This book was designed as an updating of Bramhagupta’s book. Filliozat writes :This book deals with the teaching of Bramha-gupta but contains both simplifications and additional information..... Although like all Indian versified texts,it is extremely condensed, this work ,from a educational point of view, has a significant advantage over earlier texts.
- 5. This book consisted of nine chapters and included all mathematical knowledge of mid- ninth century India. There were many Indian mathematian during the time of Mahavira ,but their work on mathe- matics is always contained in text which discuss other topics such as Astronomy . The Ganita Sara Samgraha is the only early Indian text which is devoted entirely to mathematics .
- 6. In the introduction to the work Mahavira paid tribute to the mathematicians whose work formed the basis of his book. Mahavira writes:- With the help of accomplished holy sages, who are worthy to be worshipped by the lords of the world....I glean from the great ocean of the knowledge of numbers a little of its essence,
- 7. in the manner in which gems are picked from the sea , gold from the stony rock and the pearl from the oyster shell; and I give out according to power of my intelligence, the Sara Samgraha, a small work on arithmetic, which is however not small in importance.
- 8. The nine chapters of the Ganita Sara Samgraha are: 1. Terminology 2. Arithmetical operations 3. Operations involving fractions 4. Miscellaneous operations 5. Operations involving the rule of three 6. Mixed operations 7. Operations relating to the calculations of area 8. Operations relating to the excavations 9. Operations relating to the shadows.
- 9. Ex. on Indeterminate equation. Three merchants find a purse lying in the road. One merchant says, If I keep the purse,I shall have twice as much money as the two of you together. Give me the purse and I shall have three times as much, said the second. The third said ,I shall be much better off than either of you if I keep the purse,I shall have five times as much as the two of you together. How much money is in the purse? How much money does each have?
- 10. If the first merchant has x, the second y, the third z, the amount in the purse is p, Then p+x = 2(y+z); p+y = 3(x+z); p+z = 5(x+y) Solution: p=15, x=1, y=3, z=5.
- 11. Some of the interesting things in Ganita-sara- samgraha are: A naming shame for numbers from 10^24,which are eka,dasha,.......mahakshobha. Formulas for obtaining cubes of sums. No real square root of the negative numbers can exists. Techniques for least common denominators. Techniques for combinations. Techniques for solving linear,quadratic,higher order equations. Several arithmetic and geometric series. Techniques for calculating areas and volumes.
- 12. “Construction of a Rhombus of a given area "is a topic from the 7th chapter “Operations relating to the calculations of area ”from Ganita Sara Samgraha .
- 13. To construct a Rhombus of a given area. To construct a Rhombus of an area =2mn Consider a Rectangle ABCD with sides 2m and 2n . 2m D C 2n A B
- 14. Area of Rectangle ABCD =2m×2n =4mn. Let E,F,G,H be the midpoints of the sides of a Rectangle . D G C Join POINTS :E,F,G,H . H F A E B
- 15. Now to prove that Quadrilateral EFGH is a Rhombus, and its area=2mn. D G C n n H F n n B A m E m B
- 16. From the fig. In .EFGH lt.(EF)=lt.(FG)=lt.(GH)=lt.(EH)= √m 2 +n 2 EFGH is a Rhombus. Now Area of EFG=1/2(mn)
- 17. Similarly Area of GFC=Area of HDG =Area of AEH= ½(mn) Sum of area of all four s = 4 (1/2 mn ) = 2 mn .
- 18. Area of Rhombus = Area of Rectangle ABCD - Sum of area of all four triangles. = 4 mn -2 mn =2 mn Hence proved : Area of Rhombus = 2 mn So this is the simplest method for the construction of a Rhombus of given area .
- 19. Mahavira also attempts to solve certain mathematical problems which had not been studied by other Indian mathematicians . For ex. he gave an approximate formula for the area and the perimeter of an Ellipse. Hayashi writes : the formulas for conch like fig. have so far been found only in the works of Mahavira and Narayana.
- 20. References An article recently published in Vishva Viveka(a Hindi quarterly published from New Orleans,USA)by Prof.S.C.Agrawal and Dr. Anupama Jain-via web sights. An article by J J O’Corner and E F Robertson- via web- sights. Hindi Translation on Ganita Sar Samgraha by Prof. L.C. Jain. Via-www.jaingranths.com