this presentation is about famous mathematician and scientist " PYTHAGORAS".
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Pythagoras of Samos is considered one of the first pure mathematicians. He founded the religious movement called Pythagoreanism in Croton, Italy. Very little is reliably known about Pythagoras' life and achievements due to information being recorded centuries later. He is best known for the Pythagorean theorem relating the sides of a right triangle, though some question how much he personally contributed to mathematics. The Pythagorean brotherhood he established was devoted to his religious and philosophical teachings.
Pythagoras was a Greek philosopher, mathematician, and founder of the Pythagorean movement. He made important contributions to mathematics, discovering the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras also studied properties of numbers, geometry, music, and astronomy. He believed that numbers underlie all things and that mathematical relations exist in music, discovering musical intervals based on whole number ratios between string lengths. Pythagoras made many advances in geometry as well, constructing regular polygons and the five regular solids.
Pythagoras was a Greek mathematician born in 569 BC in Samos, Ionia. He founded a school in Croton that studied mathematics and its relationship to music, nature, and the cosmos. Pythagoras is credited with important theorems and discoveries in mathematics. He is especially 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. Pythagoras believed that mathematics and numbers could describe and explain all aspects of the universe.
Pythagoras was a Greek philosopher born in 570 BC on the island of Samos who greatly influenced Western thought. He believed that reality is best understood through mathematics and that the soul can achieve divine union. He made important contributions to astronomy by teaching that the Earth was spherical and located at the center of the universe, that the moon's orbit was inclined, and that Venus and the morning star were the same planet. Pythagoras also proposed the harmony of the spheres, where planetary motions produce sounds described by mathematics.
Pythagoras was an influential ancient Greek mathematician and philosopher born on the island of Samos in the 6th century BCE. He founded a school of philosophy called the Pythagoreans in Croton, Italy, where he established strict rules for his followers to live by. Pythagoras is best known for discovering the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Little is definitively known about Pythagoras's life and mathematical achievements due to the secrecy of his society and lack of surviving writings.
Indian architecture followed principles of vastu shastra, aligning buildings with cosmic movements. Cities like Harappa and Mohenjo-Daro were precisely planned using mathematical drawings. Jaipur's design was based on a nine-square mandala representing the universe, with the royal palace at the center. Ancient Greek architectural orders like Doric, Ionic, and Corinthian influenced styles worldwide, and the golden ratio of 1.618 was incorporated into designs like the Parthenon and buildings as diverse as the Taj Mahal and United Nations headquarters.
Pythagoras was a Greek mathematician who contributed much to the mathematical world, mainly because of Pythagorean Theorem. The following PPT contains all the necessary information about Pythagoras's early and later life, as well as about his works and explanations.(If you find the fonts a little weird, its not my fault as Slideshare doesn't supports many fonts)
Pythagoras of Samos is considered one of the first pure mathematicians. He founded the religious movement called Pythagoreanism in Croton, Italy. Very little is reliably known about Pythagoras' life and achievements due to information being recorded centuries later. He is best known for the Pythagorean theorem relating the sides of a right triangle, though some question how much he personally contributed to mathematics. The Pythagorean brotherhood he established was devoted to his religious and philosophical teachings.
Pythagoras was a Greek philosopher, mathematician, and founder of the Pythagorean movement. He made important contributions to mathematics, discovering the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras also studied properties of numbers, geometry, music, and astronomy. He believed that numbers underlie all things and that mathematical relations exist in music, discovering musical intervals based on whole number ratios between string lengths. Pythagoras made many advances in geometry as well, constructing regular polygons and the five regular solids.
Pythagoras was a Greek mathematician born in 569 BC in Samos, Ionia. He founded a school in Croton that studied mathematics and its relationship to music, nature, and the cosmos. Pythagoras is credited with important theorems and discoveries in mathematics. He is especially 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. Pythagoras believed that mathematics and numbers could describe and explain all aspects of the universe.
Pythagoras was a Greek philosopher born in 570 BC on the island of Samos who greatly influenced Western thought. He believed that reality is best understood through mathematics and that the soul can achieve divine union. He made important contributions to astronomy by teaching that the Earth was spherical and located at the center of the universe, that the moon's orbit was inclined, and that Venus and the morning star were the same planet. Pythagoras also proposed the harmony of the spheres, where planetary motions produce sounds described by mathematics.
Pythagoras was an influential ancient Greek mathematician and philosopher born on the island of Samos in the 6th century BCE. He founded a school of philosophy called the Pythagoreans in Croton, Italy, where he established strict rules for his followers to live by. Pythagoras is best known for discovering the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Little is definitively known about Pythagoras's life and mathematical achievements due to the secrecy of his society and lack of surviving writings.
Indian architecture followed principles of vastu shastra, aligning buildings with cosmic movements. Cities like Harappa and Mohenjo-Daro were precisely planned using mathematical drawings. Jaipur's design was based on a nine-square mandala representing the universe, with the royal palace at the center. Ancient Greek architectural orders like Doric, Ionic, and Corinthian influenced styles worldwide, and the golden ratio of 1.618 was incorporated into designs like the Parthenon and buildings as diverse as the Taj Mahal and United Nations headquarters.
Pythagoras was a Greek mathematician who contributed much to the mathematical world, mainly because of Pythagorean Theorem. The following PPT contains all the necessary information about Pythagoras's early and later life, as well as about his works and explanations.(If you find the fonts a little weird, its not my fault as Slideshare doesn't supports many fonts)
Pythagoras was born in 570 BC in Samos, Greece. He studied in Egypt and Babylon before founding a school in Crotona, Italy around 518 BC where he taught mathematics, philosophy and developed theories on music and ethics. Pythagoras is best known for discovering the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. He died around 495 BC in Metapontum, Italy at around age 75.
Pythagoras was born in 570 BC on the island of Samos in what is now Turkey. He traveled extensively in his youth to Egypt and India to study with various teachers. Pythagoras founded a school in Croton, Italy around 530 BC where he taught his beliefs that mathematics and music were deeply interconnected and could explain the order of the universe. He is most famous for the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, though he may not have discovered it himself. Pythagoras made important contributions to both music and astronomy.
Aryabhata was an Indian mathematician and astronomer from the classical age of Indian mathematics and astronomy. Some of his key contributions include:
1) Developing a place-value system with a symbol for zero, implicitly demonstrating knowledge of zero.
2) Calculating pi to four decimal places.
3) Introducing sine, versine (1-cosine), and trigonometric identities to mathematics.
4) Providing formulas for sums of squares, cubes, and arithmetic series.
5) Asserting that the earth rotates about its axis and orbits the sun.
La filosofía y las matemáticas surgieron juntas en Grecia en el siglo VI a. C. Figuras importantes como Tales de Mileto, Pitágoras, Euclides y Arquímedes hicieron contribuciones fundamentales al desarrollo de las matemáticas griegas. Las matemáticas se desarrollaron inicialmente en conexión con la filosofía, pero luego obtuvieron autonomía durante el período helenístico, con centros importantes en Alejandría, Perga y Rodas.
This document provides an introduction to a presentation on mathematics. It lists the names of five presenters and then provides three paragraphs explaining what mathematics is, why it is called the "mother of all sciences", and how mathematics is the foundation of other subjects. It includes brief quotes from scientists about the importance and role of mathematics in understanding the universe and reality.
Mathematics is the study of topics such as quantity, structure, space, and change. It is used in many fields including science, engineering, and finance. Art includes activities that create visual works, performing arts, literature, and other media. Mathematics and art are closely related through concepts like fractals, the golden ratio, symmetry, patterns, and geometric shapes that appear in both natural and human-made works. Many artists use mathematical principles in their compositions to achieve balance, proportion and other aesthetic goals.
Pythagoras, an ancient Greek mathematician, is traditionally credited with discovering the Pythagorean theorem around 570 BC. The theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It has numerous proofs and can be generalized beyond right triangles. The Pythagorean theorem is fundamental in areas like navigation, land surveying, and ramp design and has attracted interest outside mathematics for its symbolic power.
Pythagoras was a 6th century BC Greek philosopher and mathematician who founded a secretive group. He is most famous for discovering mathematical relationships between musical intervals and string lengths. Pythagoras believed that mathematics described the harmony of the universe and that numbers held mystical properties. His followers studied mathematics, lived communally, and believed music could cure illness through its mathematical harmonies.
Concretisation and abstract ideas in Mathematics.pptxaleena568026
The document discusses different learning aids that can be used to help students understand abstract mathematical concepts. It describes how examples, illustrations, models, and hands-on objects can make abstract ideas more concrete. Specifically, it outlines graphical aids like diagrams, charts, and graphs, display boards like blackboards and bulletin boards, and three-dimensional aids like models, real objects, and mock-ups. The learning aids are meant to stimulate student participation, make teaching more engaging, and help students apply mathematics in different situations.
The slide show was developed by me and my student Snehasis on account of Mathematics day and presented in National Meet at NCERT,New Delhi
Pratima Nayak (pnpratima@gmail.com)
The tools of mathematics at the maximum applied part has continuously been utilized in an important manner in the formation of art and architecture. The straightedge and the lowly compass since the ancient times augmented by other craftsmen’s tools and simple draftsmen’s tools have been put into use for the creation of attractive projects comprehended in the beautification of cathedrals, fortresses and mosques and also in architecture (Gomez 1983). A testament to the imaginative use of ancient geometric knowledge is the intricate Moorish tessellations in crick, tile and stucco which decorate their structures and also the complex tracery of Gothic interiors and windows.
Presentation on famous mathematicians in indiaFabeenaKMP
(1) Aryabhata was a famous Indian mathematician from the classical age who lived in the 5th century AD. Some of his key contributions included a place value numeral system, approximations of pi, and trigonometric formulas.
(2) Brahmagupta was a 7th century Indian mathematician who is known for being the first to use zero as a number and introduce basic algebraic rules and formulas.
(3) Bhaskara was a 12th century mathematician whose main work Siddhanta Shiromani covered topics in arithmetic, algebra, astronomy and advanced mathematics. He made contributions in calculus, arithmetic progressions, and solving indeterminate equations.
Ancient Indian mathematicians made significant contributions to mathematics through texts like the Shatpatha Brahmana and Sulabasutras. During the Indus Valley civilization, precise mathematical calculations were used in constructions at sites like Harappa and Mohenjo-Daro. Vedic texts also described geometric constructions used during this period. While mathematics was mostly applied to practical problems, some early developments in algebra also occurred. Famous ancient Indian mathematicians included Apastamba, Baudhayana, Katyayana, Manava, Panini, Pingala, and Yajnavalkya. Apastamba wrote the Kalpasutra between 600-540 BC, which included the Dharmasutra and
Mathematics is the study of relationships among quantities, magnitudes, and properties, as well as logical operations to deduce unknowns. Historically, it was regarded as the science of quantity in fields like geometry, arithmetic, and algebra. The history of mathematics is nearly as old as humanity itself and has evolved from simple counting and measurement to the complex discipline we know today. Ancient civilizations developed practical mathematics for tasks like trade, construction, and tracking seasons, which required numeration systems, arithmetic techniques, and measurement strategies.
This document summarizes the contributions of several important Indian mathematicians, including Aryabhata who developed the place value system and approximations of pi, Brahmagupta who made innovations in algebra and trigonometry, Ramanujan who made breakthroughs in divergent series and number theory, and Bhaskaracharya who made early contributions to calculus and solving algebraic expressions. It also outlines the work of mathematician Dr. Kaprekar, including his discovery of self numbers and the Kaprekar constant.
Presented by:
Lyndon Earl Dalen
Niño Zedhic M. Villanueva
Daryl Sinugbuhan
Nico Bryan Sta. Ana
Paolo Fortun
Christian James Salvacion
Albert Limbaña
Elijah Hope Diamante
This document discusses the importance and applications of mathematics. It begins with an introduction and then discusses how mathematics is used in everyday life and various careers. Specific topics in mathematics like arithmetic, geometry, and trigonometry are explained along with their real-world uses. The document emphasizes that mathematics is essential for many fields and should be taken seriously by students to keep future career options open. It concludes by quoting that mathematics forms logical thinking from an early age.
Mathematics and art have a long historical relationship. The Golden ratio, Geometric patterns, Fractals are all fascinating mathematical ideas that have inspired artists and architects for centuries, I am just exploring these ideas in this presentation
Pythagoras was an ancient Greek philosopher, mathematician, and founder of the Pythagorean movement. He was born in Samos, Greece in the 6th century BC and made important contributions to mathematics and philosophy. Some of his key ideas included the Pythagorean theorem, the concept of perfect numbers and ratios, and the idea that mathematics and numbers underlie all of reality. He founded a secretive religious movement based on these mathematical and philosophical principles that was influential for centuries.
Pythagoras was a 6th century BC Greek philosopher, mathematician and astronomer who is famous for discovering the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. He and his followers also discovered sets of three positive integers known as Pythagorean triples that satisfy this theorem, such as 3, 4, 5. Pythagoras explored the relationships between mathematics and music, discovering numerical ratios underlying musical harmonies and is credited with the discovery of the octave.
Pythagoras was born in 570 BC in Samos, Greece. He studied in Egypt and Babylon before founding a school in Crotona, Italy around 518 BC where he taught mathematics, philosophy and developed theories on music and ethics. Pythagoras is best known for discovering the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. He died around 495 BC in Metapontum, Italy at around age 75.
Pythagoras was born in 570 BC on the island of Samos in what is now Turkey. He traveled extensively in his youth to Egypt and India to study with various teachers. Pythagoras founded a school in Croton, Italy around 530 BC where he taught his beliefs that mathematics and music were deeply interconnected and could explain the order of the universe. He is most famous for the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, though he may not have discovered it himself. Pythagoras made important contributions to both music and astronomy.
Aryabhata was an Indian mathematician and astronomer from the classical age of Indian mathematics and astronomy. Some of his key contributions include:
1) Developing a place-value system with a symbol for zero, implicitly demonstrating knowledge of zero.
2) Calculating pi to four decimal places.
3) Introducing sine, versine (1-cosine), and trigonometric identities to mathematics.
4) Providing formulas for sums of squares, cubes, and arithmetic series.
5) Asserting that the earth rotates about its axis and orbits the sun.
La filosofía y las matemáticas surgieron juntas en Grecia en el siglo VI a. C. Figuras importantes como Tales de Mileto, Pitágoras, Euclides y Arquímedes hicieron contribuciones fundamentales al desarrollo de las matemáticas griegas. Las matemáticas se desarrollaron inicialmente en conexión con la filosofía, pero luego obtuvieron autonomía durante el período helenístico, con centros importantes en Alejandría, Perga y Rodas.
This document provides an introduction to a presentation on mathematics. It lists the names of five presenters and then provides three paragraphs explaining what mathematics is, why it is called the "mother of all sciences", and how mathematics is the foundation of other subjects. It includes brief quotes from scientists about the importance and role of mathematics in understanding the universe and reality.
Mathematics is the study of topics such as quantity, structure, space, and change. It is used in many fields including science, engineering, and finance. Art includes activities that create visual works, performing arts, literature, and other media. Mathematics and art are closely related through concepts like fractals, the golden ratio, symmetry, patterns, and geometric shapes that appear in both natural and human-made works. Many artists use mathematical principles in their compositions to achieve balance, proportion and other aesthetic goals.
Pythagoras, an ancient Greek mathematician, is traditionally credited with discovering the Pythagorean theorem around 570 BC. The theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It has numerous proofs and can be generalized beyond right triangles. The Pythagorean theorem is fundamental in areas like navigation, land surveying, and ramp design and has attracted interest outside mathematics for its symbolic power.
Pythagoras was a 6th century BC Greek philosopher and mathematician who founded a secretive group. He is most famous for discovering mathematical relationships between musical intervals and string lengths. Pythagoras believed that mathematics described the harmony of the universe and that numbers held mystical properties. His followers studied mathematics, lived communally, and believed music could cure illness through its mathematical harmonies.
Concretisation and abstract ideas in Mathematics.pptxaleena568026
The document discusses different learning aids that can be used to help students understand abstract mathematical concepts. It describes how examples, illustrations, models, and hands-on objects can make abstract ideas more concrete. Specifically, it outlines graphical aids like diagrams, charts, and graphs, display boards like blackboards and bulletin boards, and three-dimensional aids like models, real objects, and mock-ups. The learning aids are meant to stimulate student participation, make teaching more engaging, and help students apply mathematics in different situations.
The slide show was developed by me and my student Snehasis on account of Mathematics day and presented in National Meet at NCERT,New Delhi
Pratima Nayak (pnpratima@gmail.com)
The tools of mathematics at the maximum applied part has continuously been utilized in an important manner in the formation of art and architecture. The straightedge and the lowly compass since the ancient times augmented by other craftsmen’s tools and simple draftsmen’s tools have been put into use for the creation of attractive projects comprehended in the beautification of cathedrals, fortresses and mosques and also in architecture (Gomez 1983). A testament to the imaginative use of ancient geometric knowledge is the intricate Moorish tessellations in crick, tile and stucco which decorate their structures and also the complex tracery of Gothic interiors and windows.
Presentation on famous mathematicians in indiaFabeenaKMP
(1) Aryabhata was a famous Indian mathematician from the classical age who lived in the 5th century AD. Some of his key contributions included a place value numeral system, approximations of pi, and trigonometric formulas.
(2) Brahmagupta was a 7th century Indian mathematician who is known for being the first to use zero as a number and introduce basic algebraic rules and formulas.
(3) Bhaskara was a 12th century mathematician whose main work Siddhanta Shiromani covered topics in arithmetic, algebra, astronomy and advanced mathematics. He made contributions in calculus, arithmetic progressions, and solving indeterminate equations.
Ancient Indian mathematicians made significant contributions to mathematics through texts like the Shatpatha Brahmana and Sulabasutras. During the Indus Valley civilization, precise mathematical calculations were used in constructions at sites like Harappa and Mohenjo-Daro. Vedic texts also described geometric constructions used during this period. While mathematics was mostly applied to practical problems, some early developments in algebra also occurred. Famous ancient Indian mathematicians included Apastamba, Baudhayana, Katyayana, Manava, Panini, Pingala, and Yajnavalkya. Apastamba wrote the Kalpasutra between 600-540 BC, which included the Dharmasutra and
Mathematics is the study of relationships among quantities, magnitudes, and properties, as well as logical operations to deduce unknowns. Historically, it was regarded as the science of quantity in fields like geometry, arithmetic, and algebra. The history of mathematics is nearly as old as humanity itself and has evolved from simple counting and measurement to the complex discipline we know today. Ancient civilizations developed practical mathematics for tasks like trade, construction, and tracking seasons, which required numeration systems, arithmetic techniques, and measurement strategies.
This document summarizes the contributions of several important Indian mathematicians, including Aryabhata who developed the place value system and approximations of pi, Brahmagupta who made innovations in algebra and trigonometry, Ramanujan who made breakthroughs in divergent series and number theory, and Bhaskaracharya who made early contributions to calculus and solving algebraic expressions. It also outlines the work of mathematician Dr. Kaprekar, including his discovery of self numbers and the Kaprekar constant.
Presented by:
Lyndon Earl Dalen
Niño Zedhic M. Villanueva
Daryl Sinugbuhan
Nico Bryan Sta. Ana
Paolo Fortun
Christian James Salvacion
Albert Limbaña
Elijah Hope Diamante
This document discusses the importance and applications of mathematics. It begins with an introduction and then discusses how mathematics is used in everyday life and various careers. Specific topics in mathematics like arithmetic, geometry, and trigonometry are explained along with their real-world uses. The document emphasizes that mathematics is essential for many fields and should be taken seriously by students to keep future career options open. It concludes by quoting that mathematics forms logical thinking from an early age.
Mathematics and art have a long historical relationship. The Golden ratio, Geometric patterns, Fractals are all fascinating mathematical ideas that have inspired artists and architects for centuries, I am just exploring these ideas in this presentation
Pythagoras was an ancient Greek philosopher, mathematician, and founder of the Pythagorean movement. He was born in Samos, Greece in the 6th century BC and made important contributions to mathematics and philosophy. Some of his key ideas included the Pythagorean theorem, the concept of perfect numbers and ratios, and the idea that mathematics and numbers underlie all of reality. He founded a secretive religious movement based on these mathematical and philosophical principles that was influential for centuries.
Pythagoras was a 6th century BC Greek philosopher, mathematician and astronomer who is famous for discovering the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. He and his followers also discovered sets of three positive integers known as Pythagorean triples that satisfy this theorem, such as 3, 4, 5. Pythagoras explored the relationships between mathematics and music, discovering numerical ratios underlying musical harmonies and is credited with the discovery of the octave.
Pythagoras was a Greek philosopher and mathematician born on the island of Samos in the 6th century BC. He founded a secretive religious society called the Pythagoreans that was focused on mathematics and music. The Pythagoreans believed that numbers underpinned the order of the universe and discovered that consonant musical intervals could be expressed as simple numerical ratios. They theorized that the movement of celestial bodies produced a harmonic "music of the spheres" inaudible to human ears.
Pythagoras was born in Samos in the 6th century BC and received an education in mathematics, science, and philosophy from teachers like Thales and Anaximander. He traveled widely, spending time in Egypt, Babylon, and other places to further his learning. Pythagoras eventually settled in Croton, where he founded a religious community called the Brotherhood and made several important mathematical discoveries with his followers, including the Pythagorean theorem and theory of proportions. However, political conflicts arose and the Brotherhood was destroyed, possibly leading to Pythagoras' death. His work influenced later philosophers like Plato and established Pythagoreanism as an important tradition of thought.
Pythagoras was a Greek mathematician and philosopher who is best known for developing the Pythagorean theorem. He founded a school in Croton, Italy where he taught mathematics and proved the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Though he did not discover the theorem, he helped popularize it. Plato was influenced by Pythagoras' work and studied his writings.
Pythagoras was a Greek mathematician and philosopher born around 572 BC. He spent over 20 years traveling and educating himself in Egypt and Babylon before settling in Crotona, Italy, where he formed an exclusive society called the Pythagoreans devoted to mathematics. The Pythagoreans made contributions in many fields including music and medicine. Pythagoras is best known for deriving the proof of the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides. He made other contributions such as connecting numbers and geometry and bringing philosophy and mathematics together.
The presentation is fully about the pythagoras thoerem.Professor R. Smullyan in his book 5000 B.C. and Other Philosophical Fantasies tells of an experiment he ran in one of his geometry classes. He drew a right triangle on the board with squares on the hypotenuse and legs and observed the fact the the square on the hypotenuse had a larger area than either of the other two squares. Then he asked, "Suppose these three squares were made of beaten gold, and you were offered either the one large square or the two small squares. Which would you choose?" Interestingly enough, about half the class opted for the one large square and half for the two small squares. Both groups were equally amazed when told that it would make no difference.
The Pythagorean (or Pythagoras') Theorem is the statement that the sum of (the areas of) the two small squares equals (the area of) the big one.In algebraic terms, a² + b² = c² where c is the hypotenuse while a and b are the legs of the triangle.
The role mathematics has played in changing the world has been very much underplayed. This slide was made with intention to show the inventions of some of the greatest mathematicians who have graced the surface of this Earth
1. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
2. The theorem has been known for over 4000 years, though Pythagoras is credited with first proving it around 500 BC in Greece.
3. The theorem plays an important role in many fields of mathematics like trigonometry and connecting geometry and algebra.
1. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
2. The theorem has been known for over 4000 years, though Pythagoras is often credited with its discovery around 500 BC in ancient Greece.
3. While the earliest proofs are unknown, Euclid provided the first written proof around 200 BC, and there are now over 600 different proofs of the Pythagorean theorem.
The document discusses several famous mathematicians throughout history including:
- Pythagoras of Samos, a Greek philosopher and founder of Pythagoreanism who believed that mathematics was the ultimate reality.
- René Descartes, a French mathematician and philosopher who is considered the founder of analytic geometry and the Cartesian coordinate system.
- Isaac Newton, an English physicist and mathematician who laid the foundations for classical mechanics with his laws of motion and universal gravitation.
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1. The document discusses the history of how numbers and mathematics have been integral to art and civilization. It traces the earliest uses of counting on artifacts like the Ishango bone from 20,000 years ago through ancient civilizations like Sumeria, Egypt, Greece, and more.
2. A key point is that the Sumerians developed one of the earliest writing systems based on accounting with clay tokens that represented amounts and quantities of goods. This led to the development of basic arithmetic.
3. Pythagoras believed that numbers represented the essence of all things in the universe and that harmony in music and aesthetics could be explained by mathematical principles and ratios. He saw mathematics as fundamental to understanding areas like music, geometry
1. The document discusses the history of the relationship between numbers and art from ancient times to today. It explores how civilizations like the Sumerians, Egyptians, Greeks, and others incorporated mathematics into art and design.
2. A key figure discussed is Pythagoras, who believed that numbers were the essence of all things and that harmony in music and nature could be explained by mathematical ratios and proportions. He is credited with discovering relationships like octaves and discovering platonic solids.
3. The document also discusses the "Golden Section" or "Golden Ratio" of approximately 1.618, which appeared in designs from the Egyptians to the Greeks and Leonardo Da Vinci. It was considered
Pythagoras was a Greek mathematician who lived in the 6th century BC. He founded a religious movement called the Pythagoreans who believed that everything could be explained through mathematics and numbers. Pythagoras studied in Egypt and discovered several important mathematical principles, including his famous Pythagorean theorem that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Later in life he fled to Metapontum where he died at around 90 years old. The Pythagoreans made many contributions to mathematics, discovering irrational numbers and identifying the five regular solids.
The document discusses the history and origins of the Pythagorean theorem. It states that while Pythagoras is typically credited with discovering the theorem, evidence shows that earlier civilizations like the Babylonians and ancient Indians understood relationships in right triangles and some versions of the Pythagorean theorem as early as 1000 BC. Specifically, the document notes that the ancient Indian mathematician Baudhayana described and proved the theorem in the Baudhayana Sulba Sutra text from around 800-600 BC, making it one of the earliest known statements of the Pythagorean theorem.
The document discusses the history and origins of the Pythagorean theorem. It states that while Pythagoras is typically credited with discovering the theorem, earlier civilizations like the Babylonians and ancient Indian mathematicians like Baudhayan had known about and demonstrated the theorem centuries before Pythagoras. It provides evidence that Baudhayan was the first to document the theorem in written form in his text Baudhayan Sutra from 800-600 BC, proving it geometrically and numerically. While Pythagoras may have independently discovered it as well, he did not provide a written proof and was not credited for it until centuries later. The document aims to give proper acknowledgment to the earlier civilizations that
Contribution of roman and indian mathematicianAshwani Koushal
This document summarizes the contributions of important Roman and Indian mathematicians. It discusses 5 influential Roman mathematicians including Euclid, known as the father of geometry; Pythagoras, known for the Pythagorean theorem; Archimedes, known for inventions in mechanics; Thales of Miletus, the first to attribute a mathematical discovery; and Aristotle, who made diverse contributions. It also outlines 5 key Indian mathematicians such as Aryabhata, the first to describe the place value system; Brahmagupta, who introduced the concept of zero; Srinivasa Ramanujan, known for discoveries in number theory and continued fractions; P.C. Mahalanobis, founder of the Indian
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. There are many different proofs of this theorem, including algebraic proofs using similarity, geometric proofs comparing areas, and vector-based proofs. Pythagoras was a famous Greek mathematician and philosopher from Samos in the 6th century BC who is credited with discovering or proving the Pythagorean theorem, though some of his accomplishments may have been made by his colleagues or successors.
What impact did Pythagoras have on EuclidSolutionPythagorasP.pdfformaxekochi
What impact did Pythagoras have on Euclid?
Solution
Pythagoras
Probably the most famous name during the development of Greek geometry is Pythagoras, even
if only for the famous law concerning right angled triangles. This mathematician lived in a secret
society which took on a semi-religious mission. From this, the Pythagoreans developed a number
of ideas and began to develop trigonometry. The Pythagoreans added a few new axioms to the
store of geometrical knowledge.
1)The sum of the internal angles of a triangle equals two right angles 180*.
2)The sum of the external angles of a triangle equals four right angles 360*
3)The sum of the interior angles of any polygon equals 2n-4 right angles, where n is the number
of sides.
4)The sum of the exterior angles of a polygon equals four right angles, however many sides.
5)The three polygons, the triangle, hexagon, and square completely fill the space around a point
on a plane - six triangles, four squares and three hexagons. In other words, you can tile an area
with these three shapes, without leaving gaps or having overlaps.
6)For a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of
the other two sides.
Most of these rules are instantly familiar to most students, as basic principles of geometry and
trigonometry. One of his pupils, Hippocrates, took the development of geometry further. He was
the first to start using geometrical techniques in other areas of maths, such as solving quadratic
equations, and he even began to study the process of integration. He solved the problem of
Squaring a Lune and showed that the ratio of the areas of two circles equalled the ratio between
the squares of the radii of the circles.
Euclid
Alongside Pythagoras, Euclid is a very famous name in the history of Greek geometry. He
gathered the work of all of the earlier mathematicians and created his landmark work, \'The
Elements,\' surely one of the most published books of all time. In this work, Euclid set out the
approach for geometry and pure mathematics generally, proposing that all mathematical
statements should be proved through reasoning and that no empirical measurements were
needed. This idea of proof still dominates pure mathematics in the modern world.
The reason that Euclid was so influential is that his work is more than just an explanation of
geometry or even of mathematics. The way in which he used logic and demanded proof for every
theorem shaped the ideas of western philosophers right up until the present day. Great
philosopher mathematicians such as Descartes and Newton presented their philosophical works
using Euclid\'s structure and format, moving from simple first principles to complicated
concepts. Abraham Lincoln was a fan, and the US Declaration of Independence used Euclid\'s
axiomatic system.
Apart from the Elements, Euclid also wrote works about astronomy, mirrors, optics, perspective
and music theory, although many of his works are lost to posterity. Certainl.
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2. # INTRODUCTION
# LIFE HISTORY
# PYTHAGORAS TEACHER
# PYTHAGOREANS
# PTHAGORAS WORK
# PYTHAGORAS & MUSIC
# PYTHAGORAS & UNIVERSE
# PYTHAGOREAN THEOREM & ITS USES
# PYTHAGORAS – the creator of pure mathematics
# CONCLUSION
# REFERENCES
3. Mathematics is a field that many people shy away from but there are some
who had a passion for numbers and making discoveries regarding
equations , measurement , and other numerical solution in history .
Some famous mathematician and scientists who contributed in the field of
science and mathematics are as follows – Albert Einstein , Pythagoras ,
Newton , Thales, Archimedes , Pascal , Aryabhata ,S. Ramanujan , Omar
Khayyam , John Neumann , Pierre de Fermat etc.
Pythagoras was the greatest mathematician of all time .
4. Pythagoras was greek mathematician and a philosopher
He was born around 572 B.C. on the island of Samos .
His father was merchant and his mother name was Pythais .
For 22 years , Pythagoras spent time in travelling through Egypt and
Babylonia to educate himself .
At about 530 B.C. , he settle in a Greek town in southern Italy called
Crotona
.
Pythagoras founded a school in city’s aristocrats in Crotona.
Pythagoras died in Metapontum around 497 B.C.
5. Among his teachers there were at least three philosophers who had great
influence on pythagoras .
The one was Pherekydes.
The other two philosopher were Thales and his pupil Anaximander , both
lived in Miletus.
Thales created phythagoras interest in mathematics and astronomy .
Anaximander was extremely interested in geometry and cosmology and
many of his ideas wold influence pythagoras’s own view .
6. Pythagoras followers were called “ Pythagoreans”.
Pythagoras school motto was “ ALL IS NUMBER” which means that all thing
in the universe obey the rules of number .
The pythagoreans tried to bring the realms of science , religion , and
philosophy all under the rules of number .
The school impose strict code of conduct on its members which included –
vegetarianism , secrecy and a curious taboo of eating of beans .
Mathematical results were considered to be the property of Pythagorean’s
school.
7.
8. Pythagoras made important development in music and astronomy .
Pythagoras observed that plucked string of different lengths gave off
different tones, he came up with the “ musical scale” , which is still used
today .
Pythagoras was accomplished musician at playing the Lyre .
9. Pythagoras was among the first to mentioned that the Earth was spherical
in shape and the planets , the sun , and the moon have an independent
motion of their own from west to east .
Pythagoras belived that the planets and stars moved according to the
mathematical rules which correspond to musical notes .
His beliefs eventually led to the “Copernican theory of universe”
10. The theorem says that in a right triangle , the square of the hypotenuse
equals the sum of the squares of the other two sides .
If you know the value of two sides of right triangle , you can easily calculate
the missing side .
14. 1. Determine the side length of triangle
2. To find height , distance of object
3. Range finding
4. Architecture , engineering ,surveying
5. Military applications
6. Cartography
15.
16. PYTHAGOREAN NUMBERS
The three sides of right triangle are called Pythagorean numbers . Example - 3,4,5
.
POLYGONAL NUMBERS
Pythagoras made important discovery about number theory and geometry .
The Pythagoras represented whole numbers by using arrangements of dots or
pebbles .
The number 3,6,10,and so on were called triangular numbers because pebbles
could be arrange to form triangles.
The numbers 4.9.16.and so on were called square numbers because pebbles can
be arrange as square
17. PERFECT NUMBERS
The Pythagoras were interested in number for their mystical and numerological
properties .
A perfect number is one whose proper divisor sum to the number itself .
Example – the number 6 has the proper divisor 1,2,and 3 and 1+2+3 = 6
AMICABLE NUMBERS
Amicable numbers are two different numbers such that the sum of the proper
divisor of one number equals the other and vice – versa .
For example the two numbers 220 and 284
The divisor of 220 are 1,2,4,5,10,11,22,55, and 110 of which the sum is 284.
The divisor of 284 are 1,2,4,71,and 142 of which the sum is 220
18. Overall Pythagoras was a legend and a renowed mathematician and
philosopher.
Although Pythagoras had some strange and usual beliefs but his
mathematical work still exist in the modern day and are being used every
day .
He will be always remembered through his discoveries , most importantly
,the “Pythagorean theorem”
19. Katz,V.J(2009).A history of mathematics – an introduction (3rd edition)
.Addision wesley.
Livio,M.(2010) .Is god a mathematician ?.New York :Simon and Schuster
Paperbacks.
Kline,M.(1972) . Mathematical thought from ancient to modern times.New
York : Oxford university press .