Gauss's diary

It was rediscovered in 1897 and published by Klein (1903), and reprinted in volume X1 of his collected works and in (Gauss 2005).

Entry 1, dated 1796, March 30, states "Principia quibus innititur sectio circuli, ac divisibilitas eiusdem geometrica in septemdecim partes etc.

", which records Gauss's discovery of the construction of a heptadecagon by ruler and compass.

Biermann (1997) found a manuscript by Gauss suggesting that GEGAN is a reversal of the acronym NAGEG standing for Nexum medii Arithmetico-Geometricum Expectationibus Generalibus and refers to the connection between the arithmetic geometric mean and elliptic functions.

More precisely, Gauss observed that if a+bi is a (Gaussian) prime and a–1+bi is divisible by 2+2i, then the number of solutions to the congruence 1=xx+yy+xxyy (mod a+bi), including x=∞, y=±i and x=±i, y=∞, is (a–1)2+b2.