The History of Trigonometry

Trigonometry did not begin as the subject most people learn today. It began as a table of chords, built so astronomers could say where a planet would be. This is the story of how that table became the sine, and how the sine became the wave.

Part I is eight chapters, following the idea from Mesopotamia and Egypt through Greek astronomy, the Indian half-chord that turned the chord into the sine, the six functions completed in the Islamic world, the road China and Japan took instead, the European printers who fixed the names we still use, and the moment a table of numbers became a function and then a wave.

Part II is a master timeline: 260 dated events across ten eras, from c. 3000 BCE to 2025, each one carrying what happened, who did it, where, and which source says so.

Part III is reference, in twelve appendices: a register of 194 people, the symbols and eponyms, a pronunciation guide, an accounting of whose name is on a theorem and who did the work, 93 historical calculations re-derived and checked in code, the disagreements between sources laid out side by side, the stories that check out and the stories that do not, and a 94-entry glossary.

It shows its work. 3,795 source pointers connect claims to 319 of the 338 sources in the bibliography. Where the sources genuinely disagree, the book says so on the page instead of quietly picking a winner: Appendix F lays out 84 conflicts and leaves 25 of them open, and 20 timeline entries carry a visible Dispute line that states the caveat and leaves it standing.

Accessibility is built in. All 1,508 mathematical expressions are real MathML carrying a spoken-English label, so VoiceOver reads a formula as a sentence rather than spelling it out symbol by symbol. All 170 images carry alternative text, and each of the 56 drawn figures comes with a full written description. Text is selectable and resizable, navigation is structural, and the book does not override your reading theme, so White, Sepia, Gray and Night all work as you set them.

For readers 14 and up, alongside any trigonometry course. The free web edition, with a reading voice and a hover glossary, is at historyoftrigonometry.megan-warren.com