If and only if n is one of the following two forms, a regular N polygon can be drawn with a ruler and compasses: k = 0, 1, 2 ... 1 7th century. The French mathematician Fermat thinks that this formula gives the prime numbers of k = 0,1,2,3 ...

Gauss solved geometric problems for more than 2000 years by algebraic method, and discovered the ruler method of regular heptagon. He was so excited that he decided to study mathematics all his life. It is said that he also expressed the hope that after his death, he could carve a regular heptagon on the tombstone to commemorate the most important mathematical discovery in his youth.

Gauss summed up the application of complex numbers.

It is strictly proved that every n-order algebraic equation must have n real solutions or complex solutions. In his first masterpiece, Arithmetic Research, he proved the law of quadratic reciprocity, which became an important basis for the continued development of number theory. The first chapter of this book deduces the concept of triangle congruence theorem. With the help of Gaussian survey adjustment theory based on least square method, the trajectory of celestial bodies is calculated. In this way, he calculated the trajectory of the asteroid Ceres.

Reference to the above content: Baidu Encyclopedia-Gauss