古代の天体観測にはじまり、古典期インドの天文学や中世イスラム数学で研究され、15世紀ドイツの天文学者レギオモンタヌスによってほぼ今日の形式になった三角法。啓蒙時代にテイラー展開や一般角に対する三角関数を定義したオイラーの公式、フーリエ級数展開などへ発展したように三角法から派生した概念の応用分野は幅広く、現代文明の存立に欠かせない存在となっています。三角関数の性質やその応用を研究するこの一分野についてカナダ数学史学会長G・ヴァン・ブランメレンが解説します。
　　

• Draws together the full history of trigonometry, stretching across two millennia and several cultures
• Introduces the key concepts of trigonometry, drawing readers beyond the basic relationships first encountered in school to ideas such as curved space
• Explores connections with genuine modern applications, including navigation, the analysis of music, and computer graphics
• Shows how trigonometry has participated in big questions about the world, including the shape of the universe and the nature of infinity

                         
Born of the desire to understand the workings of motions of the heavenly bodies, trigonometry gave the ancient Greeks the ability to predict their futures. Most of what we see of the subject in school comes from these heavenly origins; 15th century astronomer Regiomontanus called it "the foot of the ladder to the stars".

In this Very Short Introduction Glen Van Brummelen shows how trigonometry connects mathematics to science, and has today become an indispensable tool in predicting cyclic patterns like animal populations and ocean tides. Its historical journey through major cultures such as medieval India and the Islamic World has taken it through disciplines such as geography and even religious practice. Trigonometry has also been a major player in the most startling mathematical developments of the modern world. Its interactions with the concept of infinity led to Taylor and Fourier series, some of the most practical tools of modern science. The birth of complex numbers led to a shocking union of exponential and trigonometric functions, creating the most beautiful formulas and powerful modelling tools in science. Finally, as Van Brummelen shows, trigonometry allows us to explore the strange new worlds of non-Euclidean geometries, opening up bizarre possibilities for the shape of space itself. And indeed, one of those new geometries - spherical - takes us full circle back to ancient Greek astronomers and European navigators, who first used it to chart their ways across the heavens and the earth.