## Mathematics / Theorems

##### "Odd numbers always produce odd results when squared."

It can be proven that if n is an odd number, then n^2 is also odd. This is because when an odd number is squared, the result is always an odd number.

55
Nov 13
##### Sum of Squares of First n Natural Numbers

This problem proves that the sum of the squares of the first n natural numbers is equal to n(n+1)(2n+1)/6. For example, when n = 4 , the sum of the squares of the first 4 natural numbers is 4(4+1)(2*4+1)/6.

60
Nov 13
##### Determine if set of points is convex.

This problem asks whether a given set of points is convex or not. A set of points is convex if, for any two points in the set, the line segment connecting them lies entirely within the set.

53
Nov 13
##### Isosceles Triangle Theorem

This theorem states that a triangle is isosceles if and only if the sum of the squares of its two shorter sides is equal to the square of its longest side.

53
Nov 12
##### Sum of Interior Angles of a Polygon

The sum of the interior angles of a polygon with n sides is (n-2)*180 degrees.

57
Nov 12
##### Infinitely Many Prime Numbers

There are infinitely many prime numbers.

46
Nov 12
##### Points on the Same Line

Given a set of n distinct points in the plane, the maximum number of points that lie on the same straight line is returned.

61
Nov 11
##### Determining if a line exists through all points in a plane

Given a set of points in the plane, this problem determines whether or not there exists a line that goes through all of the points. The input is a set of points in the plane, and the output is either "Yes" or "No" indicating whether or not such a line exists.

52
Nov 11