Who discovered trigonometry

geometry, the branch of This article begins with a brief guidepost to the major branches of geometry and then proceeds to an extensive historical treatment. For information on specific branches of geometry, see Major branches of geometry In several ancient Elements about 300 bce on the basis of 10 axioms, or postulates, from which several hundred theorems were proved by deductive logic. The Elements epitomized the axiomatic-deductive method for many centuries. Get a Britannica Premium subscription and gain access to exclusive content. Beginning in the 19th century, various mathematicians substituted Topology Topology, the youngest and most sophisticated branch of geometry, focuses on the properties of geometric objects that remain unchanged upon continuous deformation—shrinking, stretching, and folding, but not tearing. The continuous development of topology dates from 1911, when the Dutch mathematician History of geometry The earliest known unambiguous examples of written records—dating from Egypt and Mesopotamia about 3100 bce—demonstrate that ancient peoples had already begun to devise mathematical rules and techniques useful for surveying land areas, constructing buildings, and measuring storage containers. Beginning about the 6th century bce, the Greeks gathered and extended this practical knowledge and from it generalized the abstract subject now known as geometry, from the combination of the Greek words geo (“Earth”) and metron (“measure”) for the measurement of the...

Early Astronomy and the Beginnings of a Mathematical Science This is the first of three articles on the History of Trigonometry. Part 2 can be found . Some of the terms used in this article are described in more detail 1. Ancient Instruments and Measuring the Stars The most ancient device found in all early civilisations, is a "shadow stick". The shadow cast from a shadow stick was used to observe the motion of the Sun and thus to tell time. Today we call this instrument a Gnomon. The name gnomon comes from the Greek and refers to any L-shaped instrument, originally used to draw a right angle. In Euclid Book II, where Euclid deals with the transformation of areas, the gnomon takes the form of an "L-shaped" area touching two adjacent sides of a parallelogram. Today, a gnomon is the vertical rod or similar device that makes the shadow on a sundial. For more about sundials go to Leo's article - At midday the shadow of a stick is shortest, and the civilisations of Mesopotamia, Egypt, and China took the North - South direction from this alignment. In contrast, the Hindus used the East - West direction, the rising and setting of the sun, to orient their "fire-altars" for religious practices. To do this they constructed the "gnomon circle" whose radius was the square root of the sum of the square of the height of the gnomon and its shadow [See Note 2 below]. The Merkhet is one of the oldest known astronomical instruments. It was developed around 600 BCE and uses a plumb line to o...

A little over 2,000 years ago, the Greek mathematician Hipparchus of Nicaea created a table that formalized a branch of mathematics called trigonometry. As the discipline devoted to studying the relationships between a triangle's angles and sides, trigonometry had been used for hundreds of years by the Egyptians and Babylonians to design pyramids and do rudimentary astronomy. But these pre-Greek societies lacked the concept of an angle measure, so they were unable to study trigonometry proper until Hipparchus' breakthrough. This discovery is based on a new interpretation of Plimpton 322, a 3,700-year-old clay tablet discovered in the early 20th century in Iraq. In the 1940s, it was shown that the cuneiform numbers on the tablet corresponded to the Pythagorean Theorem, which states that the square of a right triangle's hypotenuse (the long side) is equal to the squared lengths of its other two sides. But for 70 years, no one could figure out what the tablet had been used for because the values for the sines and cosines (the ratios between the different sides of a right triangle) were missing. Without further evidence, many scholars concluded that the tablet was not a trigonometric table used for determining the ratios of a triangle's sides, but an ancient school text. But according to Daniel Mansfield, a mathematician at New South Wales and the lead author of the On Mansfield's new interpretation, the Plimpton tablet explored trigonometry through the ratios of the sides of ...

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The Development of Trigonometry Overview Even in the time of the ancient Babylonians and Egyptians, theorems involving ratios of sides of similar triangles were used extensively for measurement, construction, and for an attempt to understand the movement in the heavens. The Greeks began the systematic study of angles and lengths associated with these angles, again in the service of astronomy. The history of trigonometry is intimately associated with that of astronomy, being its primary mathematical tool. Trigonometry will eventually become its own branch of mathematics, as the study of the modern trigonometric functions. Background The people in the ancient civilizations in Egypt and Mesopotamia looked to the heavens. The heavens told the people when to plant and when to harvest. In order to commemorate important events, people needed a yearly calendar. Observing the position of the Sun is necessary for calendar making. In order to tell the time of day, one must look at the lengths of shadows. These shadow lengths are measured using an upright stick in the ground and measuring the length of its shadow. Trigonometry has its origins in the calculation of these measurements. Indeed, the modern degree measurement for arcs and angles has its origins in Babylonian measurement. The famous Babylonian clay tablet now known as Plimpton 322 dates from approximately 1700 b.c. This tablet is best known for its listing of Pythagorean triples, a listing of sides and the corresponding hyp...

Pythagorean theorem, the well-known geometric a 2 + b 2 = c 2. Although the theorem has long been associated with Greek mathematician-philosopher bce), it is actually far older. Four Babylonian tablets from circa 1900–1600 bce indicate some knowledge of the theorem, with a very accurate calculation of the 2 + 4 2 = 5 2, 9 + 16 = 25). The theorem is mentioned in the Baudhayana bce. Nevertheless, the theorem came to be According to the Syrian historian ce), Pythagoras was introduced to bce to further his study, was captured during an invasion in 525 bce by see figure. It was probably independently discovered in several different 36 Questions from Britannica’s Most Popular Science Quizzes Book I of the Elements ends with Euclid’s famous “windmill” proof of the Pythagorean theorem. ( See Elements, Euclid delivers an even easier demonstration using the proposition that the areas of similar triangles are proportionate to the squares of their corresponding sides. Apparently, Euclid invented the windmill proof so that he could place the Pythagorean theorem as the capstone to Book I. He had not yet demonstrated (as he would in Book V) that A great many different proofs and See

logarithm, the x is the logarithm of n to the base b if b x= n, in which case one writes x=log b n. For example, 2 3=8; therefore, 3 is the logarithm of 8 to base 2, or 3=log 28. In the same fashion, since 10 2=100, then 2=log 10100. Logarithms of the latter sort (that is, logarithms with base 10) are called n. Invented in the 17th century to speed up calculations, logarithms vastly reduced the time required for multiplying numbers with many digits. They were basic in numerical work for more than 300 years, until the perfection of mechanical calculating machines in the late 19th century and computers in the 20th century rendered them e≅2.71828 and written ln n), however, continues to be one of the most useful functions in Properties of logarithms Logarithms were quickly adopted by scientists because of various useful properties that simplified long, tedious calculations. In particular, scientists could find the product of two numbers m and n by looking up each number’s logarithm in a special table, adding the logarithms together, and then consulting the table again to find the number with that calculated logarithm (known as its antilogarithm). Expressed in terms of common logarithms, this relationship is given by log m n=log m+log n. For example, 100×1,000 can be calculated by looking up the logarithms of 100 (2) and 1,000 (3), adding the logarithms together (5), and then finding its antilogarithm (100,000) in the table. Similarly, division problems are m/ n=log m − log n....

Trigonometry is discovered by an ancient greek mathematician Hipparchus in the 2 n dcentury BC. The three most important mathematicians involved in devising Greek trigonometry are Hipparchus, Menelaus, and Ptolemy. • Hipparchus discovered the table of values of the trigonometric ratios. • Ptolemy discovered the table of arcs. • Menelaus discovered theorems for spherical trigonometry.

A little over 2,000 years ago, the Greek mathematician Hipparchus of Nicaea created a table that formalized a branch of mathematics called trigonometry. As the discipline devoted to studying the relationships between a triangle's angles and sides, trigonometry had been used for hundreds of years by the Egyptians and Babylonians to design pyramids and do rudimentary astronomy. But these pre-Greek societies lacked the concept of an angle measure, so they were unable to study trigonometry proper until Hipparchus' breakthrough. This discovery is based on a new interpretation of Plimpton 322, a 3,700-year-old clay tablet discovered in the early 20th century in Iraq. In the 1940s, it was shown that the cuneiform numbers on the tablet corresponded to the Pythagorean Theorem, which states that the square of a right triangle's hypotenuse (the long side) is equal to the squared lengths of its other two sides. But for 70 years, no one could figure out what the tablet had been used for because the values for the sines and cosines (the ratios between the different sides of a right triangle) were missing. Without further evidence, many scholars concluded that the tablet was not a trigonometric table used for determining the ratios of a triangle's sides, but an ancient school text. But according to Daniel Mansfield, a mathematician at New South Wales and the lead author of the On Mansfield's new interpretation, the Plimpton tablet explored trigonometry through the ratios of the sides of ...

logarithm, the x is the logarithm of n to the base b if b x= n, in which case one writes x=log b n. For example, 2 3=8; therefore, 3 is the logarithm of 8 to base 2, or 3=log 28. In the same fashion, since 10 2=100, then 2=log 10100. Logarithms of the latter sort (that is, logarithms with base 10) are called n. Invented in the 17th century to speed up calculations, logarithms vastly reduced the time required for multiplying numbers with many digits. They were basic in numerical work for more than 300 years, until the perfection of mechanical calculating machines in the late 19th century and computers in the 20th century rendered them e≅2.71828 and written ln n), however, continues to be one of the most useful functions in Properties of logarithms Logarithms were quickly adopted by scientists because of various useful properties that simplified long, tedious calculations. In particular, scientists could find the product of two numbers m and n by looking up each number’s logarithm in a special table, adding the logarithms together, and then consulting the table again to find the number with that calculated logarithm (known as its antilogarithm). Expressed in terms of common logarithms, this relationship is given by log m n=log m+log n. For example, 100×1,000 can be calculated by looking up the logarithms of 100 (2) and 1,000 (3), adding the logarithms together (5), and then finding its antilogarithm (100,000) in the table. Similarly, division problems are m/ n=log m − log n....