Gauss at 19 — The Heptadecagon

On March 30, 1796, the 19-year-old Carl Friedrich Gauss woke up and, before rising, worked out how to construct a regular 17-sided polygon using only a compass and straightedge. No one had known this was possible — it was the first new constructible polygon discovered in over 2,000 years. He was so excited that he decided then and there to devote his life to mathematics rather than languages. He later asked to have a heptadecagon engraved on his tombstone; the stonemason declined, saying it would look like a circle.