Book review - Trigonometry: A Very Short Introduction, Glen Van Brummelen

★★★★

Today’s book is part of a very nice series by Oxford University Press which publishes very short introductions on different topics for a lay audience. Van Brummelen’s volume is devoted to Trigonometry, a branch of math that most of us had to deal with to at least some degree in high school and which we likely considered, back then, a useless mess of weirdly named object connected to even weirder lists of formulas that were employing in solving problems with triangles.

This volume is an attempt at giving the subject a second chance, with a heavy focus on historical aspects (how and why and where trigonometry was invented), all the way from ancient Greece and its attempts at measuring the heavens, though India and the use of taut strings to get the first trigonometric ratios, all through the composition o lengthy tables of sines and cosines in the Modern period to help with navigation, and through, calculus, complex numbers and non-Euclidean geometries. Along the way, we see how a discipline that was clearly geometric in its origins acquires an algebraic flavor and ends up being used in infinite processes and formulae. Besides the history we also get some of the math, some of the calculations, and many identities mostly in the service of solving relatively easy problems and to illuminate practical and mathematical uses of trig. The last, seventh chapter, delves a bit in a weird and little looked into branch of trigonometry which was very popular in the past but has now became a rarity: spherical trigonometry, the science used for understanding and predicting movements in the ‘celestial sphere’.

The book is, as its title promises, quite short (the reading part is a little more than a hundred, rather small, pages, and it’s chock-full of charts and pictures). I think it is quite accessible even for not overtly mathy people, although you do need to go back to the charts and think a bit from time to time. It is a noble effort, but I still feel only people already invested in curiosity towards the topic will end up picking this up and giving it a read.