最美的数学定理

1988年，Springer-Verlag主持在Mathematical Intelligencer上评选10个最美数学定理，结果如下：


1. Euler’s identity, $e^{i\pi}=-1$.

2. Euler’s formula for a polyhedron, $V+F=E+2$.

3. There are infinitely many prime numbers.

4. There are only 5 regular polyhedra.

5. The sum of the reciprocals of the squares of the positive integers is $\pi^2/6$.

6. A continuous mapping of a closed unit disk into itself has a fixed point.

7. The square root of 2 is irrational.

8. $\pi$ is a transcendental number.

9. Every plane map can be colored with just 4 colors.

10. Every prime number of the form $4n+1$ is the sum of two square integers in only one way.

转载自: http://www.math.org.cn/forum.php?mod=viewthread&tid=36509