Trigonometry in the Plane

Trigonometry allows one to systematically convert between measurements of angles and measurements of length, a topic that has interested mathematical astronomers from antiquity. Ancient Greeks also began to use angles to measure the height of buildings, in geography, and to construct sundials.

In the following centuries, study of angular measurement and related lengths moved to India, to the Arab world, and then to northern Europe. Related scales were incorporated on the back of instruments called astrolabes that showed the motion of the sun and the stars. Trigonometry, as the Bohemian-born scholar Piticus named the discipline in 1595, also found a place in gunnery, in surveying, and in the physical sciences. From the seventeenth century, scales of sines and tangents were found on a few rules and on drawing instruments called sectors. They also gained a place on calculating instruments called slide rules. Those carrying out more precise calculations consulted printed tables of trigonometric functions.

By the twentieth century, trigonometry was a routine part of high school teaching in the United States. Future mechanics, engineers, scientists, and mathematicians learned the subject. Special correspondence courses and standardized tests were available. Early electronic computers would produce more precise versions of trig tables. In the 1960s and 1970s, the introduction of desktop and then handheld electronic calculators that computed trigonometric functions replaced written tables and slide rules.

This group discusses objects associated with plane geometry. For a collection of materials relating to spherical trigonometry, see the web object group Trigonometry for the Sphere.