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.

50

Nov 13
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.

55

Nov 13
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.

48

Nov 13
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.

49

Nov 12
The sum of the interior angles of a polygon with n sides is (n-2)*180 degrees.

51

Nov 12
Given a set of n distinct points in the plane, the maximum number of points that lie on the same straight line is returned.

53

Nov 11
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.

47

Nov 11