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.
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.
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.
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.
The sum of the interior angles of a polygon with n sides is (n-2)*180 degrees.
There are infinitely many prime numbers.
Given a set of n distinct points in the plane, the maximum number of points that lie on the same straight line is returned.
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.