About this site
The Unit Circle is a free interactive explanation of trigonometry built on one picture: a point going around a circle of radius 1. It has no ads and needs no sign-up.
Why it looks like this§
The diagrams follow Oliver Byrne’s 1847 edition of Euclid, which replaced the letters of geometry with colored lines[1]. Here each color has one meaning on every page: blue is cosine, vermilion is sine, yellow is tangent, green is arc length, purple is secant and cosecant. Text is set in Libre Caslon, after the Caslon type of Byrne’s book[2], with Libre Franklin for labels.
How the mathematics is checked§
Every figure draws from a small engine of pure functions: exact special-angle values, identity checks, triangle solving including the ambiguous case, polar curves, and the reconstructed historical tables. The engine has its own test suite of worked examples, invariants and edge cases. An independent reviewer then writes a second test suite from the published equations and reference values, without reading the engine’s code. Every factual and historical claim is recorded in a claims register with its source and checked by someone who did not write it. What each figure simplifies is stated next to the figure.
Found an error?§
Please open an issue on the source repository. Corrections are welcome and are credited.
Reuse§
Text and figures are licensed CC BY 4.0; code is MIT. Teachers may use and adapt any of it, including the printable chart, with attribution.
Sources
- (2021). Oliver Byrne, The First Six Books of the Elements of Euclid, in which coloured diagrams and symbols are used instead of letters (London: Pickering, 1847). Carleton College, Gould Library news. museum
- (1847). Byrne, The First Six Books of the Elements of Euclid (London: Pickering; Chiswick: C. Whittingham, 1847), catalogue record with notes ("Each proposition is set in Caslon italic"). Yale Center for British Art, Paul Mellon Collection. museum