What is a chord?
As used in mathematics, the word chord refers to a straight line drawn between two points on a
circle (or more generally, on any curve). The known first trigonometric table was a table of chords.
In modern times, the sine is used instead (sines and chords are closely related), but, perhaps,
chords are more intuitive.
For example, the angle AOB in the diagram shows the curve connecting A to B
to be an arc of a circle. The straight line AB is the chord. Of course, the length of the
chord depends on the radius of the circle, in fact, it is proportional to the radius of the circle.
Trigonometry began with chords
Hipparchus (190-120 B.C.E.) produced the first trigonometric table for use in astronomy. It was a
table of chords for angles in a circle of large fixed radius. Incidentally, his table was not in
terms of degrees, but "steps," each step being 1/24 of a circle. Later, Ptolemy (100-178 C.E.)
constructed a more complete table of chords. His table had chords for angles increasing from 1/2
degree to 180 degrees by steps of 1/2 degree. It also included aids for interpolating chords for
minutes of angle. Ptolemy used a different large fixed radius than Hipparchus. The advantage of a
large radius is that fractions can be avoided. In contrast, our present-day trigonometric functions
are based on a unit circle, that is, a circle of radius 1. Of course using a unit circle doesn't
avoid fractions, but we have decimal fractions which are easy to work with.
Although trigonometry was, and still could be, based on chords as the primary trigonometric
function, a slight modification of chords, called "sines," turns out to be more convenient. Sines
were first used in India a few centuries after chords were first used in ancient Greece. Sines are
described on the next page.
On to sines
© 1996, 1997.
David E. Joyce
Department of Mathematics and Computer Science
Worcester, MA 01610
Dave's Short Trig Course is located at http://www.clarku.edu/~djoyce/trig