Definition:Trigonometry

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Definition

Trigonometry is the branch of mathematics which studies the relationships between the lengths of sides and angles of triangles.


Plane Trigonometry

Plane trigonometry is the branch of trigonometry which concerns the measurement of triangles embedded in the plane.


Spherical Trigonometry

Spherical trigonometry is the branch of mathematics which concerns the measurement of spherical triangles and related figures on the surface of a sphere.


Also see

  • Results about trigonometry can be found here.


Historical Note

The earliest evidence of trigonometry dates from the records of Egypt and Mesopotamia.

There exists a Babylonian stone tablet dating from circa $\text {1900}$$\text { BCE}$ to $\text {1600}$$\text { BCE}$ on which ratios are listed which are equivalent to squares of the secant function.

In the Rhind Papyrus, dating from circa $\text {1650}$$\text { BCE}$, there exist problems where the ratios of the sides of a triangle are applied to pyramids.

However, neither the Egyptians nor the Babylonians had a concept of angular measure, and such ratios were considered as properties of triangles rather than angles.


The field of trigonometry emerged in ancient Greece from applications of geometry to astronomical studies.

The earliest such record comes from the time of Hippocrates of Chios's work Elements of Geometry, dating from circa $430$ BCE.

While the Greeks focused on the calculation of chords, mathematicians in India created the earliest-known tables of values for trigonometric functions such as sine.


An analytic approach to trigonometry was introduced by Leonhard Paul Euler.


Linguistic Note

The word trigonometry derives from the Greek trigōnon (triangle) and metron (measure), literally meaning measurement of triangles.


Sources

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