Chord (geometry)

A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc.

More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse.

The first known trigonometric table, compiled by Hipparchus in the 2nd century BC, is no longer extant but tabulated the value of the chord function for every ⁠7+1/2⁠ degrees.

Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part.

The chord function can be related to the modern sine function, by taking one of the points to be (1,0), and the other point to be (cos θ, sin θ), and then using the Pythagorean theorem to calculate the chord length:[2] The last step uses the half-angle formula.