crazy math blackboard

What is the most beautiful equation in mathematics?

1. Euler’s Identity. A very famous equation, Euler’s identity relates the seemingly random values of pi, e, and the square root of -1. It is considered by many to be the most beautiful equation in mathematics. When , the value of is -1, while is 0, resulting in Euler’s identity, as -1 + 1 = 0. 2.

Who discovered that the cardinality of real numbers is equal to the cardinality of all subsets of natural

This states that the cardinality of the real numbers is equal to the cardinality of all subsets of natural numbers. This was shown by Georg Cantor , the founder of set theory. It is remarkable in that it states a continuum is not countable, as .

Which theorem relates the sides of a right triangle?

Probably the most familiar equation on this list, the Pythagorean theorem relates the sides of a right triangle, where a and b are the lengths of the legs and c is the length of the hypotenuse. It also relates triangles to squares.

What is the factorial function?

The factorial function is commonly defined as n! = n (n-1) (n-2)…1, but this definition only “works” for positive integers. The integral equation makes factorial work for fractions and decimals as well. And negative numbers, and complex numbers…

Is the area under the curve the square root of pi?

The function in itself is a very ugly function to integrate, but when done across the entire real line, i.e. from minus infinity to infinity, it gives a bizarrely clean answer. It is certainly not obvious at first glance that the area under the curve is the square root of pi.

What happens if you square all the numbers?

This is somewhat unintuitive, because it says that if you add a bunch of numbers that keep getting smaller (and eventually become zero), they still reach infinity. Yet if you square all the numbers, it doesn’t add up to infinity (it adds up to pi squared over six).

Is the symbol on the left an infinite sum?

The symbol on the left is an infinite sum, while the one on the right is an infinite product. Theorized by Leonhard Euler once again, this equation relates the natural numbers (n = 1, 2, 3, 4, 5, etc.) on the left side to the prime numbers (p = 2, 3, 5, 7, 11, etc.) on the right side. Moreover, we can choose s to be any number greater than 1, and the equation is true.