Post your favorite theorem/equation!

Hi guys,

Let me know what your favorite theorem/equation is below and why! I have to go with a² + b² = c². An old classic, but useful in so many situations and fun to learn and understand. Not fancy, I know, but always good to have.

Best,

Squarehead314

 

I really like this equation that generates the sequence of numbers in the central column of Pascal's Triangle:
(2n)!/(n!)^2

 

I read your post on Pascal's triangle. Very interesting!

 

Sometime last year I came up with a different method for generating the sequence of numbers in the central column of Pascal's Triangle, but I've forgotten how I did it, so I've been trying like hell to redo it but I'm not having much luck. But I don't intend to stop trying!

 

For me that would be:

ed = 1 mod (P-1)(Q-1)

for the encryption exponent e and the decryption exponent d

and:

cyphertext c = p^e mod N
plaintext p = c^d mod N

for the actual encryption and decryption with RSA.

 

Here's another one that I like quite a bit:
Moser's Circle Theorem:
I can't seem to use the proper symbols, so I'll have to use what my calculator allows:
F=(x nCr 4) + (x nCr 2) + 1

 

Pythagorean theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Formulation in mathematical language: If a and b are the lengths of the legs, and c is the length of the hypotenuse, then: 2 = 2 + 2 c 2 =a 2 +b 2