History of trigonometry

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The ancient Nubians used a similar method. 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.

History of trigonometry pdf

The intersections of the celestial equator and the ecliptic are the equinox points where the lengths of the day and night are equal. It was Leonhard Euler who fully incorporated complex numbers into trigonometry. History of Trigonometry Outline Trigonometry is, of course, a branch of geometry, but it differs from the synthetic geometry of Euclid and the ancient Greeks by being computational in nature. The Rhind papyrus , an Egyptian collection of 84 problems in arithmetic , algebra , and geometry dating from about bce, contains five problems dealing with the seked. The Babylonians measured the longitude in degrees counterclockwise from the vernal point as seen from the north pole, and they measured the latitude in degrees north or south from the ecliptic. In the fourteenth century, Persian mathematician al-Kashi and Timurid mathematician Ulugh Beg grandson of Timur produced tables of trigonometric functions as part of their studies of astronomy. A History of Mathematics.

Degree measurement was later adopted by Hipparchus. The first work on trigonometric functions related to chords of a circle.

When European authors translated the Arabic mathematical works into Latin they translated jaib into the word sinus meaning fold in Latin. The inverse functions are called the arcsine, arccosine, and arctangent, respectively.

Brief history of trigonometry

They built up an extensive collection of data, and made tables of the positions of objects in the sky at any given time through a year these tables are called ephemerides. Problems involving angles and distances in one plane are covered in plane trigonometry. Trigonometry developed from a need to compute angles and distances in such fields as astronomy , mapmaking , surveying , and artillery range finding. The next Greek mathematician to produce a table of chords was Menelaus in about AD. Cavalieri used Ta and Ta. The shape of a right triangle is completely determined, up to similarity, by the angles. The lower section contains pictures of star gods or demons. The book is particularly strong on the sine and its inverse. The truest E - W direction will be achieved by marking the end of the shadow at sunrise and sunset possibly at the equinoxes. It is thus quite difficult to decide which unit of measure was being used to construct the tables. The Dunhuang star chart, now in the British Library, is recognised to have been made about BCE by Li Chunfen and was constructed with quite remarkable accuracy. Trigonometry, of course, depends on geometry.

The Babylonians and Chinese both believed that the earth and the moon were spherical, that the earth and the moon rotated on an axis, and that the sun and the planets moved in circles round the earth.

The name tangent was first used by Thomas Fincke in In BCE Gan De made the first recorded observation of sunspots, and the moons of Jupiter and they both made accurate observations of the five major planets.

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The two acute angles therefore add up to 90 degrees: They are complementary angles. Ancient Egypt and the Mediterranean world Several ancient civilizations—in particular, the EgyptianBabylonianHindu, and Chinese—possessed a considerable knowledge of practical geometry, including some concepts that were a prelude to trigonometry.

The modern trigonometrical functions are sine, cosine, tangent, and their reciprocals, but in ancient Greek trigonometry, the chord, a more intuitive function, was used. Centuries passed before more detailed tables were produced, and Ptolemy's treatise remained in use for performing trigonometric calculations in astronomy throughout the next years in the medieval ByzantineIslamicand, later, Western European worlds.

History of trigonometry essay

All trigonometrical computations require measurement of angles and computation of some trigonometrical function. There are arithmetic relations between these functions, which are known as trigonometric identities. Using a water clock to determine timings, this arrangement of merkhets allowed people to take measurements of night-time events, for example times when certain stars crossed the vertical plumb line a "transit line". The Panca-siddhantica is a collection of five astronomical works composed in the sixth century CE by Vrahamihira. Detailed methods for constructing a table of sines for any angle were given by the Indian mathematician Bhaskara in , along with some sine and cosine formulae. In times when mathematical notation was in itself a new idea many used their own notation. The earliest written texts we have from this oral tradition date from about BCE. The abbreviations used by various authors were similar to the trigonometric functions already discussed. These came into their own when navigators around the 15th Century started to prepare tables. The term cotangens was first used by Edmund Gunter in Copernicus knew of the secant which he called the hypotenusa.

Their names and abbreviations are sine sincosine costangent tancotangent cotsecant secand cosecant csc. It is perhaps surprising that the second most important trigonometrical function during the period we have discussed was the versed sine, a function now hardly used at all.

History of trigonometry

The ability to predict some of these major astronomical events gave rise to astrology, where people believed that there was a link between heavenly and earthly events, and that the stars had some control over their lives. The Babylonians wrote down lists of numbers, in what we would call an arithmetic progression and recognised that numbers repeated themselves over periods of time. A History of Mathematics. These texts were regularly being revised and added to by different scholars. Plofker, K. Cambridge University Press The first chapter deals with ancient people and early Greek astronomy. The tangent and cotangent came via a different route from the chord approach of the sine. With these definitions the trigonometric functions can be defined for complex numbers. These laws are useful in all branches of geometry, since every polygon may be described as a finite combination of triangles. The Babylonians and angle measurement The Babylonians, sometime before B.
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A Short History Notes About Trigonometry