Trigonometry, which developed out of the ancient Greeks’ yearning to comprehend how celestial bodies move, allowed them to foresee the future. The majority of what we learn about this topic in school is derived from these celestial sources; the astronomer Regiomontanus described it as “the foot of the stairway to the stars” in the 15th century.
In this Very Short Introduction, Glen Van Brummelen demonstrates how trigonometry bridges mathematics and science. Trigonometry is now crucial in forecasting cyclical phenomena like animal populations and ocean tides. It has traveled historically through significant cultures like medieval India and the Islamic World, as well as academic fields like geography and even religious activity. In addition, trigonometry has played a significant role in some of our most astounding mathematical breakthroughs. Its interactions with the idea of infinite produced the Taylor and Fourier series, two of contemporary science’s most useful instruments. Exponential and trigonometric functions were shockingly combined with the advent of complex numbers, giving rise to some of science’s most exquisite formulas and potent modeling tools. Van Brummelen concludes by demonstrating how trigonometry enables us to investigate the weird new worlds of non-Euclidean geometries, presenting absurd possibilities for the geometry of space. Indeed, one of those new geometries, the spherical one, brings us full circle back to the early European and Greek navigators who utilized it to map their routes through the skies and on the surface of the globe.
