heptadecagon

He discovered a construction of the heptadecagon on 30 March.

See heptadecagon for the real part of a 17th root of unity.

In geometry, a heptadecagon (or 17-gon) is a seventeen-sided polygon.

The first explicit construction of a heptadecagon was given by Johannes Erchinger in 1825.

March 30 - He obtains conditions for the constructibility by ruler and compass of regular polygons, including the heptadecagon.

See heptadecagon.

His surprising result that had escaped his predecessors was that a regular heptadecagon (with 17 sides) could be so constructed.

Gauss was so pleased by this result that he requested that a regular heptadecagon be inscribed on his tombstone.

The regular heptadecagon is the Petrie polygon for one higher-dimensional polytope, projected in a skew orthogonal projection:

Constructing a regular heptadecagon thus involves finding the cosine of in terms of square roots, which involves an equation of degree 17-a Fermat prime.

A certain construction of the regular heptadecagon involving the Carlyle circles can be represented by the expression 8R + 4R + 22C + 11C and has simplicity 45.

The regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge), as was shown by Carl Friedrich Gauss in 1796 at the age of 19.

Entry 1, dated 1796, March 30, states "Principia quibus innititur sectio circuli, ac divisibilitus eiusdem geometrica in septemdecim partes etc.", which records Gauss's discovery of the construction of a heptadecagon by ruler and compass.