A history of trigonometry in mathematics

Such concepts would have been part of everyday life in hunter-gatherer societies.

A history of trigonometry in mathematics

Trigonometry is not the work of any one person or nation. Its history spans thousands of years and has touched every major civilization. Our modern word "sine", is derived from the Latin word sinus, which means "bay" or "fold", from a mistranslation via Arabic of the Sanskrit word jiva, alternatively called jya.

The words "minute" and "second" are derived from the Latin phrases partes minutae primae and partes minutae secundae. Early developments Sumerian astronomers studied angle measure, using a division of circles into degrees.

The ancient Nubians used a similar method. But pre-Hellenic societies lacked the concept of an angle measure and consequently, the sides of triangles were studied instead, a field that would be better called "trilaterometry".

Iraqi mathematics The Babylonian astronomers kept detailed records on the rising and setting of starsthe motion of the planetsand the solar and lunar eclipsesall of which required familiarity with angular distances measured on the celestial sphere.

History of trigonometry

Ancient Egyptian mathematics See also: Egyptian mathematics The Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC. In other words, the quantity he found for the seked is the cotangent of the angle to the base of the pyramid and its face.

Hellenistic mathematics The chord of an angle subtends the arc of the angle. Ancient Hellenistic mathematicians made use of the chord.

A history of trigonometry in mathematics

Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector passes through the center of the circle and bisects the angle.

Due to this relationship, a number of trigonometric identities and theorems that are known today were also known to Hellenistic mathematicians, but in their equivalent chord form.

Theorems on the lengths of chords are applications of the law of sines. And Archimedes' theorem on broken chords is equivalent to formulas for sines of sums and differences of angles. Hipparchus may have taken the idea of this division from Hypsicles who had earlier divided the day into parts, a division of the day that may have been suggested by Babylonian astronomy.

A seasonal cycle of roughly days could have corresponded to the signs and decans of the zodiac by dividing each sign into thirty parts and each decan into ten parts. In Book I, he established a basis for spherical triangles analogous to the Euclidean basis for plane triangles.

The thirteen books of the Almagest are the most influential and significant trigonometric work of all antiquity. A special case of Ptolemy's theorem appeared as proposition 93 in Euclid's Data. Ptolemy's theorem leads to the equivalent of the four sum-and-difference formulas for sine and cosine that are today known as Ptolemy's formulas, although Ptolemy himself used chords instead of sine and cosine.

Indian mathematics Statue of Aryabhata. As there is no known information regarding his appearance, any image of Aryabhata originates from an artist's conception. The next significant developments of trigonometry were in India.

Influential works from the 4th—5th century, known as the Siddhantas of which there were five, the most complete survivor of which is the Surya Siddhanta [16] first defined the sine as the modern relationship between half an angle and half a chord, while also defining the cosine, versineand inverse sine.

Early Astronomy and the Beginnings of a Mathematical Science

The words jya and kojya eventually became sine and cosine respectively after a mistranslation described above. Other Indian mathematicians later expanded on these works of trigonometry.

In the 6th century, Varahamihira used the formulas Template:Van Brummelen, G. () The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. Princeton, Princeton University Press. Princeton, Princeton University Press. This is the first major history in English of the early development of trigonometry.

Certainly, it seems that Indian contributions to mathematics have not been given due acknowledgement until very recently in modern history.

Indian astronomers used trigonometry tables to estimate the relative distance of the Earth to the Sun and Moon. Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

History of trigonometry - Wikipedia

The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Mathematics of the Heavens and the Earth is the first major history in English of the origins and early development of trigonometry.

Glen Van Brummelen identifies the earliest known trigonometric precursors in ancient Egypt, Babylon, and Greece, and he examines the revolutionary discoveries of Hipparchus, the Greek astronomer believed to have been the first to make systematic use of Reviews: 2.

Van Brummelen, G. () The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. Princeton, Princeton University Press. Princeton, Princeton University Press. This is the first major history in English of the early development of trigonometry.

The History of Trigonometry is one type of mathematics that deals with the sides and the angles. In the First paragraph I would like to explain the main history of trigonometry and also go into detail about the certain aspects of the mathematic branch.

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