A 19-year-old found a shape Euclid never knew could be built
For 2,000 years after Euclid, mathematicians assumed only a handful of regular polygons could ever be drawn using just a compass and an unmarked straightedge. In 1796, a 19-year-old worked out that one more regular polygon, with a number of sides nobody had ever managed before, could join that short list. Which polygon was it?
Reveal the answer
The regular 17-gon (heptadecagon). Carl Friedrich Gauss proved it constructible, and showed exactly which regular polygons are constructible at all. It was his first great discovery, reportedly tipping his career choice toward mathematics; he asked for a 17-gon on his tombstone, but the stonemason judged it would look indistinguishable from a circle and declined.
— Carl Friedrich Gauss, Disquisitiones Arithmeticae — result obtained 1796, published 1801