The document discusses the history of trigonometry from ancient civilizations to modern times. It describes how trigonometry began with the Babylonians and Egyptians around 4000 years ago, who used trigonometric ratios for tasks like agriculture and construction. It then progressed with the Greeks, including Hipparchus who created trigonometric tables. Trigonometry was further advanced by Indian, Arabic, and later Western mathematicians and astronomers. Key figures mentioned include Ptolemy, Al-Battani, Napier, Newton, and Euler, who helped establish trigonometry into its modern form.
This document provides an overview of ancient Egyptian mathematics and its timeline. It discusses the Egyptian numeral system, which was additive, as well as their arithmetic operations of addition, multiplication and division. The Egyptians were able to solve linear equations and used arithmetic and geometric progressions. They could also express fractions as a sum of unit fractions. Overall, the document demonstrates the Egyptians had sophisticated mathematical knowledge and methods as early as 3000 BC.
The document discusses mathematics in ancient Babylonian and Egyptian civilizations. It describes how the Babylonians developed a system of writing called cuneiform using wedge-shaped symbols carved into clay tablets around 3000 BC. It also details their sexagesimal (base-60) numerical system and how they were able to perform advanced mathematical operations and solve equations. The document then explains the development of hieroglyphic numerals by the ancient Egyptians, including their base-10 system and specific symbols used to represent fractions and operations. Key sources of information about Babylonian and Egyptian mathematics included cuneiform tablets and Egyptian papyri such as the Rhind Mathematical Papyrus.
This document provides an overview of ancient mathematics in Babylon and Egypt. It describes how early mathematics developed out of practical needs in early civilizations along rivers like the Nile, Tigris, Euphrates, Indus, and Huangho. Archaeologists have uncovered hundreds of thousands of clay tablets in Mesopotamia containing early mathematical concepts. These include arithmetic, algebra, geometry, and early use of tables and formulas. Egyptian mathematics is also discussed and sources of early mathematical knowledge from Egypt are described, including papyri, monuments, and other inscriptions.
The document provides a brief history of mathematics from ancient to modern periods. It covers the development of numeration systems and arithmetic, geometry, algebra, trigonometry, calculus, and analytic geometry. Key developments include ancient civilizations developing practical math for trade and construction, Greeks establishing logic-based math and Euclidean geometry, Hindus and Arabs advancing the decimal numeral system and algebra, and Europeans in the early modern period making advances in trigonometry, logarithms, analytic geometry, and calculus.
History of Math is a project in which students worked together in learning about historical development of mathematical ideas and theories. They were exploring about mathematical development from Sumer and Babylon till Modern age, and from Ancient Greek mathematicians till mathematicians of Modern age, and they wrote documents about their explorations. Also they had some activities in which they could work "together" (like writing a dictionary, taking part in the Eratosthenes experiment, measuring and calculating the height of each other schools, cooperating in given tasks) and activities that brought out their creativity and Math knowledge (making Christmas cards with mathematical details and motives and celebrating the PI day). Also they were able to visit Museum, exhibition "Volim matematiku" and to prepare (and lead) workshops for the Evening of mathematics (Večer matematike). At the end they have presented their work to other students and teachers.
The document summarizes the early mathematical system developed by the Sumerians in Mesopotamia between the Tigris and Euphrates Rivers. Key points:
- The Sumerians developed one of the earliest known writing systems, cuneiform script, which enabled recording of early mathematics on clay tablets.
- They used a sexagesimal (base-60) numeric system combined with a place-value notation, which was superior to later Greek and Roman systems for calculating fractions and powers.
- Much of what is known about early Mesopotamian mathematics comes from clay tablets dating to the Old Babylonian period from around 1800-1600 BCE. These included table texts and problem texts.
This document provides an overview of ancient Egyptian mathematics and its timeline. It discusses the Egyptian numeral system, which was additive, as well as their arithmetic operations of addition, multiplication and division. The Egyptians were able to solve linear equations and used arithmetic and geometric progressions. They could also express fractions as a sum of unit fractions. Overall, the document demonstrates the Egyptians had sophisticated mathematical knowledge and methods as early as 3000 BC.
The document discusses mathematics in ancient Babylonian and Egyptian civilizations. It describes how the Babylonians developed a system of writing called cuneiform using wedge-shaped symbols carved into clay tablets around 3000 BC. It also details their sexagesimal (base-60) numerical system and how they were able to perform advanced mathematical operations and solve equations. The document then explains the development of hieroglyphic numerals by the ancient Egyptians, including their base-10 system and specific symbols used to represent fractions and operations. Key sources of information about Babylonian and Egyptian mathematics included cuneiform tablets and Egyptian papyri such as the Rhind Mathematical Papyrus.
This document provides an overview of ancient mathematics in Babylon and Egypt. It describes how early mathematics developed out of practical needs in early civilizations along rivers like the Nile, Tigris, Euphrates, Indus, and Huangho. Archaeologists have uncovered hundreds of thousands of clay tablets in Mesopotamia containing early mathematical concepts. These include arithmetic, algebra, geometry, and early use of tables and formulas. Egyptian mathematics is also discussed and sources of early mathematical knowledge from Egypt are described, including papyri, monuments, and other inscriptions.
The document provides a brief history of mathematics from ancient to modern periods. It covers the development of numeration systems and arithmetic, geometry, algebra, trigonometry, calculus, and analytic geometry. Key developments include ancient civilizations developing practical math for trade and construction, Greeks establishing logic-based math and Euclidean geometry, Hindus and Arabs advancing the decimal numeral system and algebra, and Europeans in the early modern period making advances in trigonometry, logarithms, analytic geometry, and calculus.
History of Math is a project in which students worked together in learning about historical development of mathematical ideas and theories. They were exploring about mathematical development from Sumer and Babylon till Modern age, and from Ancient Greek mathematicians till mathematicians of Modern age, and they wrote documents about their explorations. Also they had some activities in which they could work "together" (like writing a dictionary, taking part in the Eratosthenes experiment, measuring and calculating the height of each other schools, cooperating in given tasks) and activities that brought out their creativity and Math knowledge (making Christmas cards with mathematical details and motives and celebrating the PI day). Also they were able to visit Museum, exhibition "Volim matematiku" and to prepare (and lead) workshops for the Evening of mathematics (Večer matematike). At the end they have presented their work to other students and teachers.
The document summarizes the early mathematical system developed by the Sumerians in Mesopotamia between the Tigris and Euphrates Rivers. Key points:
- The Sumerians developed one of the earliest known writing systems, cuneiform script, which enabled recording of early mathematics on clay tablets.
- They used a sexagesimal (base-60) numeric system combined with a place-value notation, which was superior to later Greek and Roman systems for calculating fractions and powers.
- Much of what is known about early Mesopotamian mathematics comes from clay tablets dating to the Old Babylonian period from around 1800-1600 BCE. These included table texts and problem texts.
The Royal Botanical Expedition to New Granada took place from 1783 to 1816 in territories that now make up several South American countries. The expedition was led by José Celestino Mutis, a Spanish botanist, and aimed to catalog the rich plant life of the region. Over 25 years, Mutis and his team explored over 8,000 square kilometers, discovering around 6,000 new plant species. Their work resulted in detailed drawings, descriptions and classifications of plants, contributing significantly to the field of botany.
The Rhind Mathematical Papyrus is an ancient Egyptian mathematics text from around 1650 BCE. It was purchased in Egypt by Scottish lawyer A. Henry Rhind in 1858 and is now housed at the British Museum. The papyrus is over 18 feet long and contains mathematical problems and tables involving fractions, arithmetic, algebra, geometry, and calculations related to construction projects. It is significant in that it provides insight into the mathematics understood by ancient Egyptian scribes over 3,500 years ago.
This document provides a brief history of mathematics from ancient civilizations like Egypt and Babylon through modern times. It outlines key developments and contributors to mathematics over time, including the Greeks who established foundations of geometry and number theory, Islamic mathematicians who advanced algebra and algorithms, and modern mathematicians who developed calculus, probability, logarithms, and other critical concepts. The document suggests mathematics will continue having applications in fields like biology, cybernetics, and help solve open problems like the P vs. NP and Riemann hypothesis.
What is Mathematics? What are the History of Mathematics?
Sir Isaac Newton and Gottfried Wilhelm Leibniz have such great contribution to the History of Mathematics as of 17th Century.
Mathematics(History,Formula etc.) and brief description on S.Ramanujan.Mayank Devnani
A brief description on the history of math, many famous mathematicians and also women mathematicians..
And very huge description ( bio-data, formulas etc.) on famous mathematician S.Ramanujan.
Trigonometry originated in ancient Greece through the studies of Hipparchus of Bithynia, who used trigonometric ratios to calculate the position of planets. The Chinese later introduced the tangent, and Indians produced their own sine and cosine tables using high approximation techniques. Islamic mathematicians then translated and expanded on Indian works, formally introducing the cosine and other trig functions. In the 16th century, trigonometry began to be used for navigation and mapmaking.
Pythagoras and Zeno made early contributions to mathematics and philosophy. Pythagoras is credited with the first proof of the Pythagorean theorem, while Zeno conceived paradoxes to support Parmenides' view that motion is illusory. Archimedes made seminal advances in geometry, measurement of pi, and buoyancy. Euclid's Elements was a principal geometry text for over 2000 years, developing proofs from postulates including the parallel postulate. Later mathematicians like Descartes, Fermat, Pascal, Newton, Euler, Cantor further advanced fields like algebra, calculus, probability, and the theory of infinite sets.
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................Pratik Sidhu
DESCRIBES IN DETAIL ANCIENT AGE ,MEDIEVAL AND PRESENT AGE OF MATHS AND ALSO THE FAMOUS MATHEMATICIANS.REALLY AN AMAZING ONE WITH ANIMATED SLIDE DESIGND..............
Anecdotes from the history of mathematics ways of selling mathematiDennis Almeida
1) The development of mathematics, including number systems and arithmetic, was driven by practical needs in areas like trade, taxation, and military affairs. Place value systems like the Hindu-Arabic numerals made complex calculations possible.
2) Early algebra developed out of solving practical problems involving lengths and areas. Techniques like extracting roots and solving quadratic equations were applied to problems in areas like right triangles and bone setting.
3) Geometry originated from practical construction needs but was formalized by Euclid into a deductive system. It influenced fields like art and tiling patterns. Relating geometric concepts to algebraic formulas helped develop modern algebra.
The document discusses Egyptian mathematics as recorded in historical papyri. It describes how the Egyptians developed mathematics out of practical needs like commerce, construction, and taxation of agricultural land. Much of our knowledge comes from the Rhind and Moscow papyri, which contain early examples of arithmetic operations like multiplication and fraction decomposition. The Rosetta Stone later helped decipher Egyptian hieroglyphics. Key figures who advanced the field include Champollion, who established the translation of hieroglyphics, and Rhind and Moscow, after whom the important papyri are named. The document provides several examples of early Egyptian arithmetic techniques.
HISTORY OF MATHEMATICS SLIDE PRESENTATION;ResmiResmi Nair
The document provides a historical overview of the development of mathematics from ancient to modern times. It covers major periods and developments, including ancient numeration systems; Greek logic, philosophy, and Euclidean geometry; the Hindu-Arabic numeral system and algebraic advances by Islamic mathematicians; the transmission and spread of knowledge in Europe during 1000-1500 AD; and key figures and discoveries in the early modern period such as logarithms, analytic geometry, and calculus developed by Newton, Leibniz, and Euler. The document uses examples of important works, thinkers, and mathematical concepts to illustrate the evolution of mathematics across civilizations over thousands of years.
The document summarizes key developments and figures from the Scientific Revolution period including:
- The development of modern scientific notation and concepts like calculus, logarithms, and probability by figures like Descartes, Newton, Leibniz, Napier, and Pascal.
- Advancements in fields like astronomy, physics, and mathematics through inventions like the telescope and discoveries in mechanics, projective geometry, and analytic geometry.
- The establishment of organizations and institutions like the Royal Society of London that helped facilitate scientific progress during this era.
Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometric Functions
Math was not invented by a single person, but developed over time as early humans made notches on bones to count things and observed patterns in nature and the sky. Ancient civilizations like the Egyptians, Greeks, Chinese, and Indians all made important early contributions to mathematics, with the Greeks focusing more on proofs and reasoning. The field of mathematics has continued to evolve and expand over the centuries as new concepts, theories, and applications have been discovered and built upon knowledge from prior civilizations.
The history of mathematics began with early civilizations developing basic arithmetic and geometry. Some of the earliest and most influential mathematical texts came from ancient Mesopotamia, Egypt, China, and India. Greek mathematics built upon earlier traditions and introduced deductive reasoning and mathematical rigor. Key Greek mathematicians included Thales, Pythagoras, Plato, Euclid, Archimedes, and Apollonius, who made seminal contributions to geometry, number theory, and the early study of functions and calculus. Following this Golden Age of Greek mathematics, mathematical advances continued within the Islamic world and medieval Europe.
The document provides a history of mathematics from ancient times through its development in various regions. It discusses:
1) Early counting methods and the origins of numerals in places like ancient Egypt, Mesopotamia, and India.
2) The mathematical advances of early civilizations like the Greeks, Chinese, Hindus, Babylonians and Egyptians - including concepts like zero, algebra, trigonometry, and geometry.
3) The transmission of mathematics from these early civilizations to medieval Islamic mathematics and eventually to European mathematics during the Renaissance, leading to modern developments.
The document is a student paper on the history of mathematics. It covers the development of mathematics from prehistoric times through modern eras in different regions, including Prehistoric, Babylonian, Egyptian, Greek, Chinese, Indian, Islamic, Medieval European, Renaissance, and Modern mathematics. The paper provides an overview of key mathematical concepts, texts, and figures from each historical period and location.
This document provides an overview of the history of mathematics, beginning with ancient civilizations like Babylonia, Egypt, and Greece. It discusses important mathematicians and their contributions, including Pythagoras, Euclid, Archimedes, Brahmagupta, Fibonacci, Descartes, Newton, Euler, Gauss, and Ramanujan. Key advances and discoveries are highlighted, such as the development of algebra, calculus, complex numbers, and non-Euclidean geometry. The document traces the evolution of mathematics from ancient times through the modern era.
The first trigonometric table was compiled by Hipparchus, who is now.pdfajitdoll
The first trigonometric table was compiled by Hipparchus, who is now known as \"the father of
trigonometry.\"Sumerian astronomers studied angle measure, using a division of circles into 360
degrees.They and the Babylonians studied the ratios of the sides of similar triangles and
discovered some properties of these ratios, but did not turn that into a systematic method for
finding sides and angles of triangles. The ancient Nubians used a similar method. The ancient
Greeks transformed trigonometry into an ordered science.
Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of
chords and inscribed angles in circles, and proved theorems that are equivalent to modern
trigonometric formulae, although they presented them geometrically rather than algebraically.
Claudius Ptolemy expanded upon Hipparchus\' Chords in a Circle in his Almagest. The modern
sine function was first defined in the Surya Siddhanta, and its properties were further
documented by the 5th century Indian mathematician and astronomer Aryabhata. These Greek
and Indian works were translated and expanded by medieval Islamic mathematicians. By the
10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated
their values, and were applying them to problems in spherical geometry. Knowledge of
trigonometric functions and methods reached Europe via Latin translations of the works of
Persian and Arabic astronomers such as Al Battani and Nasir al-Din al-Tusi. One of the earliest
works on trigonometry by a European mathematician is De Triangulis by the 15th century
German mathematician Regiomontanus. Trigonometry was still so little known in 16th century
Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium
to explain its basic concepts.
Driven by the demands of navigation and the growing need for accurate maps of large
geographic areas, trigonometry grew into a major branch of mathematics. Bartholomaeus
Pitiscus was the first to use the word, publishing his Trigonometria in 1595. Gemma Frisius
described for the first time the method of triangulation still used today in surveying. It was
Leonhard Euler who fully incorporated complex numbers into trigonometry. The works of James
Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the
development of trigonometric series. Also in the 18th century, Brook Taylor defined the general
Taylor series.
Solution
The first trigonometric table was compiled by Hipparchus, who is now known as \"the father of
trigonometry.\"Sumerian astronomers studied angle measure, using a division of circles into 360
degrees.They and the Babylonians studied the ratios of the sides of similar triangles and
discovered some properties of these ratios, but did not turn that into a systematic method for
finding sides and angles of triangles. The ancient Nubians used a similar method. The ancient
Greeks transformed trigonometry into an ord.
Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles and the calculations of trigonometric functions. It has many applications in fields like navigation, surveying, physics, engineering and more. Some key aspects covered are the definitions of trigonometric functions like sine, cosine and tangent; common trigonometric identities; formulae for calculating unknown sides and angles of triangles; and the history of trigonometry dating back to ancient Greek and Indian mathematicians.
This document provides an overview of trigonometry and its applications. It begins with definitions of trigonometry, its history and etymology. It discusses trigonometric functions like sine, cosine and their properties. It covers trigonometric identities and applications in fields like astronomy, navigation, acoustics and more. It also discusses angle measurement in degrees and radians. Laws of sines and cosines are explained. The document concludes with examples of trigonometric equations and their applications.
Geometry originated in response to practical problems like surveying land. It developed techniques for measuring spatial relationships and properties of space. Geometry was revolutionized by Euclid, who introduced mathematical rigor and axiomatic methods still used today. In modern times, geometric concepts have become highly abstract and complex, connected to calculus and algebra.
The Royal Botanical Expedition to New Granada took place from 1783 to 1816 in territories that now make up several South American countries. The expedition was led by José Celestino Mutis, a Spanish botanist, and aimed to catalog the rich plant life of the region. Over 25 years, Mutis and his team explored over 8,000 square kilometers, discovering around 6,000 new plant species. Their work resulted in detailed drawings, descriptions and classifications of plants, contributing significantly to the field of botany.
The Rhind Mathematical Papyrus is an ancient Egyptian mathematics text from around 1650 BCE. It was purchased in Egypt by Scottish lawyer A. Henry Rhind in 1858 and is now housed at the British Museum. The papyrus is over 18 feet long and contains mathematical problems and tables involving fractions, arithmetic, algebra, geometry, and calculations related to construction projects. It is significant in that it provides insight into the mathematics understood by ancient Egyptian scribes over 3,500 years ago.
This document provides a brief history of mathematics from ancient civilizations like Egypt and Babylon through modern times. It outlines key developments and contributors to mathematics over time, including the Greeks who established foundations of geometry and number theory, Islamic mathematicians who advanced algebra and algorithms, and modern mathematicians who developed calculus, probability, logarithms, and other critical concepts. The document suggests mathematics will continue having applications in fields like biology, cybernetics, and help solve open problems like the P vs. NP and Riemann hypothesis.
What is Mathematics? What are the History of Mathematics?
Sir Isaac Newton and Gottfried Wilhelm Leibniz have such great contribution to the History of Mathematics as of 17th Century.
Mathematics(History,Formula etc.) and brief description on S.Ramanujan.Mayank Devnani
A brief description on the history of math, many famous mathematicians and also women mathematicians..
And very huge description ( bio-data, formulas etc.) on famous mathematician S.Ramanujan.
Trigonometry originated in ancient Greece through the studies of Hipparchus of Bithynia, who used trigonometric ratios to calculate the position of planets. The Chinese later introduced the tangent, and Indians produced their own sine and cosine tables using high approximation techniques. Islamic mathematicians then translated and expanded on Indian works, formally introducing the cosine and other trig functions. In the 16th century, trigonometry began to be used for navigation and mapmaking.
Pythagoras and Zeno made early contributions to mathematics and philosophy. Pythagoras is credited with the first proof of the Pythagorean theorem, while Zeno conceived paradoxes to support Parmenides' view that motion is illusory. Archimedes made seminal advances in geometry, measurement of pi, and buoyancy. Euclid's Elements was a principal geometry text for over 2000 years, developing proofs from postulates including the parallel postulate. Later mathematicians like Descartes, Fermat, Pascal, Newton, Euler, Cantor further advanced fields like algebra, calculus, probability, and the theory of infinite sets.
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................Pratik Sidhu
DESCRIBES IN DETAIL ANCIENT AGE ,MEDIEVAL AND PRESENT AGE OF MATHS AND ALSO THE FAMOUS MATHEMATICIANS.REALLY AN AMAZING ONE WITH ANIMATED SLIDE DESIGND..............
Anecdotes from the history of mathematics ways of selling mathematiDennis Almeida
1) The development of mathematics, including number systems and arithmetic, was driven by practical needs in areas like trade, taxation, and military affairs. Place value systems like the Hindu-Arabic numerals made complex calculations possible.
2) Early algebra developed out of solving practical problems involving lengths and areas. Techniques like extracting roots and solving quadratic equations were applied to problems in areas like right triangles and bone setting.
3) Geometry originated from practical construction needs but was formalized by Euclid into a deductive system. It influenced fields like art and tiling patterns. Relating geometric concepts to algebraic formulas helped develop modern algebra.
The document discusses Egyptian mathematics as recorded in historical papyri. It describes how the Egyptians developed mathematics out of practical needs like commerce, construction, and taxation of agricultural land. Much of our knowledge comes from the Rhind and Moscow papyri, which contain early examples of arithmetic operations like multiplication and fraction decomposition. The Rosetta Stone later helped decipher Egyptian hieroglyphics. Key figures who advanced the field include Champollion, who established the translation of hieroglyphics, and Rhind and Moscow, after whom the important papyri are named. The document provides several examples of early Egyptian arithmetic techniques.
HISTORY OF MATHEMATICS SLIDE PRESENTATION;ResmiResmi Nair
The document provides a historical overview of the development of mathematics from ancient to modern times. It covers major periods and developments, including ancient numeration systems; Greek logic, philosophy, and Euclidean geometry; the Hindu-Arabic numeral system and algebraic advances by Islamic mathematicians; the transmission and spread of knowledge in Europe during 1000-1500 AD; and key figures and discoveries in the early modern period such as logarithms, analytic geometry, and calculus developed by Newton, Leibniz, and Euler. The document uses examples of important works, thinkers, and mathematical concepts to illustrate the evolution of mathematics across civilizations over thousands of years.
The document summarizes key developments and figures from the Scientific Revolution period including:
- The development of modern scientific notation and concepts like calculus, logarithms, and probability by figures like Descartes, Newton, Leibniz, Napier, and Pascal.
- Advancements in fields like astronomy, physics, and mathematics through inventions like the telescope and discoveries in mechanics, projective geometry, and analytic geometry.
- The establishment of organizations and institutions like the Royal Society of London that helped facilitate scientific progress during this era.
Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometric Functions
Math was not invented by a single person, but developed over time as early humans made notches on bones to count things and observed patterns in nature and the sky. Ancient civilizations like the Egyptians, Greeks, Chinese, and Indians all made important early contributions to mathematics, with the Greeks focusing more on proofs and reasoning. The field of mathematics has continued to evolve and expand over the centuries as new concepts, theories, and applications have been discovered and built upon knowledge from prior civilizations.
The history of mathematics began with early civilizations developing basic arithmetic and geometry. Some of the earliest and most influential mathematical texts came from ancient Mesopotamia, Egypt, China, and India. Greek mathematics built upon earlier traditions and introduced deductive reasoning and mathematical rigor. Key Greek mathematicians included Thales, Pythagoras, Plato, Euclid, Archimedes, and Apollonius, who made seminal contributions to geometry, number theory, and the early study of functions and calculus. Following this Golden Age of Greek mathematics, mathematical advances continued within the Islamic world and medieval Europe.
The document provides a history of mathematics from ancient times through its development in various regions. It discusses:
1) Early counting methods and the origins of numerals in places like ancient Egypt, Mesopotamia, and India.
2) The mathematical advances of early civilizations like the Greeks, Chinese, Hindus, Babylonians and Egyptians - including concepts like zero, algebra, trigonometry, and geometry.
3) The transmission of mathematics from these early civilizations to medieval Islamic mathematics and eventually to European mathematics during the Renaissance, leading to modern developments.
The document is a student paper on the history of mathematics. It covers the development of mathematics from prehistoric times through modern eras in different regions, including Prehistoric, Babylonian, Egyptian, Greek, Chinese, Indian, Islamic, Medieval European, Renaissance, and Modern mathematics. The paper provides an overview of key mathematical concepts, texts, and figures from each historical period and location.
This document provides an overview of the history of mathematics, beginning with ancient civilizations like Babylonia, Egypt, and Greece. It discusses important mathematicians and their contributions, including Pythagoras, Euclid, Archimedes, Brahmagupta, Fibonacci, Descartes, Newton, Euler, Gauss, and Ramanujan. Key advances and discoveries are highlighted, such as the development of algebra, calculus, complex numbers, and non-Euclidean geometry. The document traces the evolution of mathematics from ancient times through the modern era.
The first trigonometric table was compiled by Hipparchus, who is now.pdfajitdoll
The first trigonometric table was compiled by Hipparchus, who is now known as \"the father of
trigonometry.\"Sumerian astronomers studied angle measure, using a division of circles into 360
degrees.They and the Babylonians studied the ratios of the sides of similar triangles and
discovered some properties of these ratios, but did not turn that into a systematic method for
finding sides and angles of triangles. The ancient Nubians used a similar method. The ancient
Greeks transformed trigonometry into an ordered science.
Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of
chords and inscribed angles in circles, and proved theorems that are equivalent to modern
trigonometric formulae, although they presented them geometrically rather than algebraically.
Claudius Ptolemy expanded upon Hipparchus\' Chords in a Circle in his Almagest. The modern
sine function was first defined in the Surya Siddhanta, and its properties were further
documented by the 5th century Indian mathematician and astronomer Aryabhata. These Greek
and Indian works were translated and expanded by medieval Islamic mathematicians. By the
10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated
their values, and were applying them to problems in spherical geometry. Knowledge of
trigonometric functions and methods reached Europe via Latin translations of the works of
Persian and Arabic astronomers such as Al Battani and Nasir al-Din al-Tusi. One of the earliest
works on trigonometry by a European mathematician is De Triangulis by the 15th century
German mathematician Regiomontanus. Trigonometry was still so little known in 16th century
Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium
to explain its basic concepts.
Driven by the demands of navigation and the growing need for accurate maps of large
geographic areas, trigonometry grew into a major branch of mathematics. Bartholomaeus
Pitiscus was the first to use the word, publishing his Trigonometria in 1595. Gemma Frisius
described for the first time the method of triangulation still used today in surveying. It was
Leonhard Euler who fully incorporated complex numbers into trigonometry. The works of James
Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the
development of trigonometric series. Also in the 18th century, Brook Taylor defined the general
Taylor series.
Solution
The first trigonometric table was compiled by Hipparchus, who is now known as \"the father of
trigonometry.\"Sumerian astronomers studied angle measure, using a division of circles into 360
degrees.They and the Babylonians studied the ratios of the sides of similar triangles and
discovered some properties of these ratios, but did not turn that into a systematic method for
finding sides and angles of triangles. The ancient Nubians used a similar method. The ancient
Greeks transformed trigonometry into an ord.
Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles and the calculations of trigonometric functions. It has many applications in fields like navigation, surveying, physics, engineering and more. Some key aspects covered are the definitions of trigonometric functions like sine, cosine and tangent; common trigonometric identities; formulae for calculating unknown sides and angles of triangles; and the history of trigonometry dating back to ancient Greek and Indian mathematicians.
This document provides an overview of trigonometry and its applications. It begins with definitions of trigonometry, its history and etymology. It discusses trigonometric functions like sine, cosine and their properties. It covers trigonometric identities and applications in fields like astronomy, navigation, acoustics and more. It also discusses angle measurement in degrees and radians. Laws of sines and cosines are explained. The document concludes with examples of trigonometric equations and their applications.
Geometry originated in response to practical problems like surveying land. It developed techniques for measuring spatial relationships and properties of space. Geometry was revolutionized by Euclid, who introduced mathematical rigor and axiomatic methods still used today. In modern times, geometric concepts have become highly abstract and complex, connected to calculus and algebra.
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.
This document discusses the history and origins of geometry. It explains that geometry was developed by ancient peoples to measure objects on Earth and that Euclid is considered the "father of geometry." The earliest recorded use of geometry can be traced back to ancient civilizations like the Indus Valley and Babylonia around 3000 BC, and it was the ancient Greeks who developed the principles of modern geometry, with Thales of Miletus credited as bringing geometry from Egypt to Greece. Several massive ancient structures are provided as examples of how geometry was used in architectural designs in the past.
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles in triangles. The key concepts are the trigonometric functions sine, cosine, and tangent, which describe ratios of sides of a right triangle. Trigonometry has applications in fields like navigation, music, engineering, and more. It has evolved significantly from its origins in ancient Greece and India, with modern definitions extending it to all real and complex number arguments.
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.
The document provides a history of mathematics from ancient civilizations to modern times. It discusses how mathematics originated in ancient Babylon and Egypt around 3000 BC, with the Egyptians having an advanced decimal number system and knowledge of geometry. It also describes the Babylonian sexagesimal system of representing numbers. Key figures discussed include Pythagoras, whose theorem is summarized, and Carl Gauss, a mathematical genius whose contributions transformed number theory and other fields in the 19th century. The document concludes by outlining the fundamental purposes and objectives of teaching mathematics.
Trigonometry developed from studying right triangles in ancient Egypt and Babylon, with early work done by Hipparchus and Ptolemy. It was further advanced by Indian, Islamic, and Chinese mathematicians. Key developments include Madhava's sine table, al-Khwarizmi's sine and cosine tables, and Shen Kuo and Guo Shoujing's work in spherical trigonometry. European mathematicians like Regiomontanus, Rheticus, and Euler established trigonometry as a distinct field and defined functions analytically. Trigonometry is now used in many areas beyond triangle calculations.
This document provides an overview of the history and development of geometry. It discusses how geometry originated with early peoples discovering principles like the Pythagorean theorem thousands of years before Pythagoras. It then covers the major developments of geometry in ancient cultures like Egypt, Babylon, Greece, China, Islamic caliphates, and the modern era. Key figures discussed include Euclid, who introduced rigorous logic and axioms still used today, and Archimedes, considered one of the greatest mathematicians for his approximations of pi and work on limits.
The document discusses trigonometry, which studies triangles and relationships between lengths of sides and angles. It defines the trigonometric functions of sine, cosine, and tangent, which describe these relationships. Trigonometry has applications in fields like surveying, physics, and engineering. The history of trigonometry is then summarized, noting contributions from ancient Greek, Indian, Islamic, and Chinese mathematicians.
Surveying involves determining the positions of points on the Earth's surface and the distances and angles between them. This information is used for mapping boundaries, construction projects, and other purposes. A surveyor uses equipment like total stations, GNSS receivers, and drones to precisely measure locations. The history of surveying dates back to ancient times but modern techniques involving triangulation and electronic distance measurement have improved accuracy and efficiency.
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.
The history of algebra began thousands of years ago and has progressed through different civilizations. Ancient Egyptians, Babylonians, Greeks, Indians, Arabs, and Europeans all made contributions. Quadratic equations in particular date back to ancient Babylonians around 1800 BC. Key developments include factoring, completing the square, and the quadratic formula. Today, quadratic equations are used in many areas of real life like physics, engineering, and finance.
This document provides a history of geometry from ancient times through the modern era. It describes how early geometrical concepts and principles were developed by ancient cultures including the Egyptians, Babylonians, and Indians. It then discusses the significant developments in geometry by ancient Greek mathematicians such as Thales, Pythagoras, Plato, Aristotle, and Euclid. Euclid is credited with revolutionizing geometry by introducing logical rigor and the axiomatic method in his influential textbook The Elements. The document continues discussing later developments in geometry through Hellenistic times and the modern era.
Mathematics has evolved from simple counting and measurement used by early humans to the complex discipline it is today. Key developments include the establishment of number systems and algebra in ancient Mesopotamia and Egypt, advances in geometry and logic by ancient Greeks, transmission of knowledge to other ancient cultures like China and India, and the establishment of concepts like calculus and logarithms in Europe during the 16th-18th centuries. The 19th-20th centuries saw unprecedented growth in mathematical concepts and ideas through the work of mathematicians around the world, including Indians like Ramanujan who made seminal contributions despite facing disadvantages.
This document is a slideshow presentation on trigonometry given by Anjaya Bhattarai. The presentation provides definitions of trigonometry, a brief history of the subject, descriptions of right triangles and trigonometric ratios. It also covers Pythagoras' theorem, its proof, and uses of trigonometry. The objective is to clarify basic trigonometry concepts and solve any confusion. In conclusion, trigonometry measures triangle sides and angles through important formulas, and it has many applications in fields like engineering, navigation, and more.
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1. COLEGIO SAN BARTOLOMÉ LA MERCED
Área: Matemáticas y Lengua Castellana
Estudiante: Sebastián Jiménez Elías
Curso: 10C Fecha: febrero 27 de 2017.
Profesora: Margarita María Teresa Santamaría y Luz Adriana Rodríguez
El progreso de la civilización humana y el progreso de la
Trigonometría han ido de la mano.
Al hablar de la trigonometría, usualmente se toca un concepto del agrado de pocos, especialmente
para la gente que conoce o entiende poco del tema, lo que no saben es que esta rama de la
matemática ha sido indispensable para la historia de la humanidad.
Sin los descubrimientos griegos, árabes e hindúes en trigonometría, la navegación en
océanos abiertos hubiera sido una tarea aún más aventurada de lo que fue cuando los
grandes marinos abrieron los seis continentes. Las rutas comerciales de China a Europa, o
de Indonesia a las Américas, se mantenían unidas por un invisible hilo matemático. La
sociedad de hoy no podría funcionar sin matemáticas. Prácticamente todo lo que hoy nos
parece natural, desde la televisión hasta los teléfonos móviles, desde los grandes aviones
de pasajeros hasta los sistemas de navegación por satélite en los automóviles, desde los
programas de los trenes hasta los escáneres médicos, se basa en ideas y métodos
matemáticos. A veces son matemáticas de mil años de edad; otras veces son matemáticas
descubiertas la semana pasada. La mayoría de nosotros nunca nos damos cuenta de que
están presentes, trabajando entre bastidores para facilitar esos milagros de la tecnología
moderna. (Stewart, S.F, págs. 2-3).
Con lo anterior, se puede afirmar que la trigonometría no estaba plenamente formada. Fue
haciéndose gracias a los esfuerzos acumulativos de muchas personas que procedían de muchas
culturas y hablaban diferentes lenguas. Ideas matemáticas que se siguen utilizando hoy, surgidas
hace más de 4.000 años.
2. Para comenzar, es necesario definir el concepto de la trigonometría. Esta área es la
encargada de "estudiar las relaciones entre los lados y los ángulos de los triángulos" (Flores Gil,
2008, pág. 6) De una forma más concreta, es la encargada de encontrar la medida de los triángulos.
Esta área, está principalmente relacionada al campo de la geometría y por un tiempo estuvo muy
ligada a la astronomía, sufriendo algunos cambios en estos enfoques de los cuales se hablará más
adelante.
Para empezar, los comienzos de la trigonometría se remontan a las matemáticas de la
antigüedad. Se va a ir viendo su evolución por los distintos pueblos y culturas donde se ha ido
desarrollando.
Primeramente, es necesario regresar aproximadamente 4.000 años atrás, con las
civilizaciones babilónicas y egipcias. Los babilónicos, registraban sus conocimientos en tablillas
de barro. Estos ya empleaban los ángulos de un triángulo y las razones trigonométricas en sus que
haceres diarios. Los babilonios utilizaban estas razones para realizar medidas en agricultura. De
hecho, esto se puede evidenciar en la tablilla Plimpton 322, esta tabla muestra lo que ahora se
llaman ternas pitagóricas, es decir, números enteros a, b, c que satisfacen 𝑎2
+𝑏2
= 𝑐2
. (Eliatron,
Una breve historia impresionista de la Trigonometría: de Babilonia a la India, 2010). Por otro
lado, la trigonometría también fue aplicada por los babilonios en “los primeros estudios de
astronomía para el cálculo de la posición de cuerpos celestes y la predicción de sus órbitas, en los
calendarios y el cálculo del tiempo, y por supuesto en navegación para mejorar la exactitud de la
posición y de las rutas.” (Eliatron, Una breve historia impresionista de la Trigonometría: de
Babilonia a la India, 2010, pág. parrafo 6). Sin embargo, los egipcios también toman conciencia
del problema de la medición de ángulos. Fueron ellos quienes establecieron la medida de los
ángulos en grados, minutos y segundos, criterio que se ha mantenido hasta nuestros días, y
utilizaron la medición de triángulos en la construcción de las pirámides. (Flores Gil, 2008). Los
alcances de estás civilizaciones son realmente impresionantes, sin los mismos ni parecidos
recursos tecnológicos lograron descubrir grandes avances.
Es así, como la trigonometría comienza a dar sus primeros pasos en la historia del hombre,
facilitando las tareas de aquellos tiempos. Tiempo después, se pasaría a Grecia, donde se aprecia
al matemático y astrónomo Hiparco de Nicea, quien fue uno de los mayores desarrolladores de la
trigonometría.
3. Hiparco construyó las tablas de “cuerdas” para la resolución de triángulos planos, que
fueron las precursoras de las tablas de las funciones trigonométricas de la actualidad. En
ellas iba relacionando las medidas angulares con las lineales. Para confeccionar dichas
tablas fue recorriendo una circunferencia de radio r desde los 0º hasta los 180º e iba
apuntando en la tabla la longitud de la cuerda delimitada por los lados del ángulo central y
la circunferencia a la que corta. Esa tabla es similar a la moderna tabla del seno. No se sabe
con certeza el valor que usó Hiparco para el radio r de esa circunferencia, pero sí se conoce
que 300 años más tarde el astrónomo alejandrino Tolomeo utilizó r = 60, ya que los griegos
adoptaron el sistema numérico sexagesimal (base 60) de los babilonios. (Flores Gil, 2008,
pág. 8)
Debido, a estos aportes de Hiparco acerca de la tabla de cuerdas para la solución de
triángulos, Ptolomeo puedo basar su obra literaria “El Almagesto”, donde hablaba sobre su
teorema de Menelao utilizado para resolver triángulos esféricos, y aplicó sus teorías
trigonométricas en la construcción de astrolabios y relojes de sol. La trigonometría de Ptolomeo
se empleó durante muchos siglos como introducción básica para los astrónomos.
Tiempo después, en territorio indio se desarrollaría un sistema trigonométrico basado en la
función seno en vez de cuerdas como los griegos. “Esta función seno, era la longitud del lado
opuesto a un ángulo en un triángulo rectángulo de hipotenusa dada. Los matemáticos hindúes
utilizaron diversos valores para ésta en sus tablas.” (Wikipedia, 2017). La diferencia que hay es
que actualmente la función del seno se conoce como una proporción, y los hindúes la usaban como
una longitud.
El papel de los árabes en la construcción de esta rama fue muy importante. Fueron ellos
quienes demostraron teorías fundamentales de esta área, tanto para triángulos planos como
esféricos. A la vez, se encargaron de usar lo que estaba anteriormente ya constituido para lograr
un progreso adecuado. Bell afirma:
Los árabes adoptaron y desarrollaron la trigonometría hindú. El primer progreso notable se
debió al astrónomo Al-Battani (muerto en el 929), en el siglo IX. Si bien en realidad no fue
el primero que aplicó el álgebra en lugar de la sola geometría a la trigonometría, este
astrónomo matemático fue el primero que dio un gran paso en esa dirección. Usó además
4. del seno hindú, la tangente y la cotangente. En el siglo X se calcularon tablas de estas dos
últimas, y también hicieron su aparición la secante y la cosecante como razones
trigonométricas. Por estar el concepto de función todavía unos 600 años en el futuro, nada
en su obra se parece mucho a la trigonometría elemental de hoy día.
En otras palabras, los árabes sugirieron el uso de r=1 en vez de r=60, dando lugar a los
valores modernos de las funciones trigonométricas.
También, descubrieron y demostraron teoremas fundamentales de la trigonometría, tanto
para triángulos planos como esféricos, donde incorporaron el triángulo polar. Todos estos
descubrimientos los aplicando a la astronomía, logrando medir el tiempo astronómico, e incluso
los utilizaron para encontrar la dirección de la Meca. Los científicos árabes también compilaron
tablas de gran exactitud. Por ejemplo, las tablas del seno y de la tangente, construidas con
intervalos de 1/60 de grado (1 minuto) tenían un error menor que 1 dividido por 700 millones.
(Flores Gil, 2008). Esto rectifica el papel tan grande que tuvieron los árabes en la historia de las
matemáticas y en el progreso de la civilización humana.
Del mismo modo, el Occidente se familiarizo con la trigonometría a través de traducciones
de libros de astronomía arábiga y griega, que tomaron lugar a partir del siglo XII. Resalta el trabajo
escrito del matemático y astrónomo, Johann Müller. La obra escrita estaba centrada en los tratados
de la matemática (lo que hoy se conoce como trigonometría) y tratados de astronomía. Además
describe e inventa varios instrumentos útiles para la medida y observación del tiempo. (Ruiz, S.F).
Gracias a este, el astrónomo alemán Georges Joachim, introdujo el concepto moderno de las
funciones trigonométricas como proporcionales en vez de longitudes de algunas determinadas
líneas.
A principios del siglo XVII, el matemático escocés John Napier descubrió
los logaritmos y, gracias a esto, los cálculos trigonométricos recibieron un gran empuje. Napier
logro esto “analizando la correspondencia entre las dos progresiones. Su motivación era, como era
común en toda esta época, facilitar cálculos en trigonometría esférica que se usaba en asuntos de
astronomía (de hecho, considera logaritmos de senos).” (Ruiz, S.F). Medio siglo después, los
científicos Isaac Newton y Gottfried Wilhelm Leibniz desarrollaron el cálculo diferencial e
integral. Uno de los fundamentos del trabajo de Newton fue la representación de muchas funciones
matemáticas utilizando series infinitas de potencias de la variable x. Newton encontró la serie
5. para sen x y series similares para cos x y tg x. Con la invención del Cálculo, las funciones
trigonométricas fueron incorporadas al Análisis, donde todavía hoy desempeñan un importante
papel tanto en las matemáticas puras como en las aplicadas. (Wikipedia, 2017). Gracias a este
señor se pueden representar muchas funciones matemáticas, entre ellas las trigonométricas
mediante potencias.
Por último, en el siglo XVIII, el matemático suizo Leonhard Euler fue quien
verdaderamente fundó la trigonometría moderna.
Definiendo las funciones trigonométricas mediante expresiones con exponenciales de
números complejos. Esto convirtió a la trigonometría en sólo una de las muchas aplicaciones de
los números complejos. De hecho, Euler demostró que las propiedades básicas de la trigonometría
eran simplemente producto de la aritmética de los números complejos.
Añadiendo a esto, durante el siglo XX, la trigonometría ha realizado muchos aportes
en el estudio de los fenómenos de onda y oscilación, así como el comportamiento periódico. En
astronomía, se utiliza para medir distancias a estrellas próximas, para la medición de distancias
entre puntos geográficos y en sistemas de navegación satelital.
Para finalizar se puede concluir que, la trigonometría se encuentra en todo lo que se refiere
a distancias. Se puede ver reflejada en distintas áreas del conocimiento. Por ejemplo en la
astronomía, para calcular el radio de la tierra y diversas distancias con elementos del espacio.
También, es posible verla en situaciones un poco más simples y cotidianas. En la medicina,
exactamente en los electrocardiogramas. En la arquitectura o ingenierías, para la construcción de
cualquier infraestructura. O hasta en situaciones de la vida cotidiana, practicando un deporte.
Después de estudiar a fondo la trigonometría, su historia y su importancia a lo largo del
desarrollo de la humanidad, se pude resaltar que esta área está involucrada en distintas cosas, desde
cosas muy simples a otras muy elaboradas. Esta rama de las matemáticas se encuentra en
muchísimas profesiones y le ha servido al hombre como una herramienta de progreso.
Referencias y bibliografía :
Bell.(s.f). Losgrandesmatematicos.Obtenidode
http://www.librosmaravillosos.com/grandesmatematicos/pdf/Los%20Grandes%20Matematicos
%20-%20E.%20T.%20Bell.pdf
6. Eliatron,T. (2010). Una brevehistoria impresionista dela trigonometría II:de Arabia a Europa.Obtenido
de http://naukas.com/2010/10/15/una-breve-historia-impresionista-de-la-trigonometria-ii-de-
arabia-a-europa/
Eliatron,T. (2010). Una brevehistoria impresionista dela Trigonometría:de Babilonia a la India.
Obtenidode http://naukas.com/2010/07/14/una-breve-historia-impresionista-de-la-
trigonometria-de-babilonia-a-la-india/
FloresGil,F.L. (2008). Historia y didáctica de la trigonometria.Obtenidode
file:///C:/Users/SONYA%20ELIAS/Downloads/Francisco_Luis_Flores_Gil_-
_Historia_y_Didactica_de__la_Trigonometria%20(1).pdf
Historia de la Trigonometria.(sf).Obtenidode
http://perso.wanadoo.es/amiris/trigonometria/documentos/lecturatrigo.html
Ruiz,A.(S.F). Historia y filosofia de las matematicas.Obtenidode
file:///C:/Users/SONYA%20ELIAS/Downloads/Historia%20de%20las%20matem%C3%A1ticas%20
2%20(3).pdf
Stewart,I.(S.F). Historia de las matematicasen los ultimos10.000 años.Obtenidode
http://www.librosmaravillosos.com/historiadelasmatematicasenlosultimos10000anos/pdf/Histo
ria%20de%20las%20matematicas%20-%20Ian%20Stewart.pdf
Wikipedia.(2017). Obtenidode Historiade latrigonometria:
https://es.wikipedia.org/wiki/Historia_de_la_trigonometr%C3%ADa