Polygonal numbers

   

Polygonal Numbers, as we said before , are the vertexes in a figure formed by a certain polygon. Normally , the first number in every group of polygonal numbers is 1 or a point ; and the second number is equal to the number of vertexes or sides of trial polygon ; the third one is made by extending 2 of the sides of the polygon from the second polygonal number, completing the larger polygon and placing vertexes and other point where necessary. There are 2 methods to find the polygonal number

• 1st method ( Shi-Cheung formula )

If x is even , then :

y = x/2 - 1 and the formula is n + y ( n2 - n )

If x is odd, then :

y = (x-1)/2 and the formula is (-(n2)+3n+2n2y-2ny)/2

• 2nd method ( Winton formula )

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