## Beautiful Mathematics Theorem

1988 poll of readers of the Mathematical Intelligencer ranked some of the most well-known theorems in mathematics, I like some.

(Of course, most of them I don’t understand)

1. Euler’s identity

$e^{i\pi} + 1 = 0$

$e^{i x} = \cos x + i \sin x$

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

3. There are infinitely many prime numbers.  Euclid had proven this!

4. There are only 5 regular polyhedra

5. The sum of the reciprocals of the squares of the positive integers is (π^2)/6. See the Basel problem.

$\displaystyle1 + \frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\cdots =\frac{\pi^2}{6}$

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

7. The square root of 2 is irrational number

8. π is a transcendental number

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

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

# References

• 1 David Wells, The Penguin Book of Curious and Interesting Mathematics. London: Penguin Books (1997): 126 – 127

(source website: http://planetmath.org/thetop10mostbeautifultheorems)

Another List about the beauty of mathematics (Maths is an art!):

http://www.livescience.com/26680-greatest-mathematical-equations.html

You will find common equations / formula there :-

Euler’s Equation
“It says that if you cut the surface of a sphere up into faces, edges and vertices, and let F be the number of faces, E the number of edges and V the number of vertices, you will always get V – E + F = 2,” said Colin Adams, a mathematician at Williams College in Massachusetts.

Euler line
“Start with any triangle,” Whitney explained. “Draw the smallest circle that contains the triangle and find its center. Find the center of mass of the triangle — the point where the triangle, if cut out of a piece of paper, would balance on a pin. Draw the three altitudes of the triangle (the lines from each corner perpendicular to the opposite side), and find the point where they all meet. The theorem is that all three of the points you just found always lie on a single straight line, called the ‘Euler line’ of the triangle.” Glen Whitney