The Curious History of Trigonometry

Current trigonometry texts begin with trigonometric ratios, continue through the solution of right and other triangles, and go on to applications to the familiar problems on the height of a tree or the distance across a lake. The presentation leads one to believe that trigonometry developed out of the desire to solve such problems, or, more generally, to perform indirect measurements. One might further guess, given some knowledge of Euclidean geometry, that the subject simply developed as an outgrowth of the study of similar triangles as detailed in Euclid's Elements, Book VI. Surely, the Greeks needed to be able to measure heights of trees or buildings, or distances across rivers, and would have wanted to be able to simplify matters by using trigonometric methods. In fact, around 300 B.C.E. we find Euclid showing us in his Optics how to find heights, depths, and distances using similar triangles [Ver Eecke 19591 (see Figure 1).