# More Centred Shape Relationships

Once you have explored some centred shapes, and taken a look at More to Explore, here are some more relationships you could try to prove if you're up for the challenge:

• 1½ of 3² - (1½ of 3) + 1 = 3rd Centred Triangle Number
{or One and a half of N² - (one and a half of N) + 1 = N th Centred Triangle Number }
• 3rd Hexagonal Pyramid Number = 3³
{or N th Hexagonal Pyramid Number = N³}
• 3rd Triangular Number + 2 of (2nd Triangular Number) +  1st Triangular Number = 3rd Centred Square Number
{or  N th Triangular Number + two of (N-1) th Triangular Number + (N-2) th Triangular Number = N th Centred Square Number}
• 6  of (3rd Square Based Pyramid Number) = Cuboid  3x4x7
{or 6 x N th Square Based Pyramid Number = N x (N+1) x (2N+1)}
• 3rd Centred Triangle Number + 2nd T = 3rd Centred Square Number
{or  N th Centred Triangle Number + (N-1) th T = N th Centred Square Number}
• 3rd Centred Triangle Number – 3rd T = 2nd Square Number
{or  N th Centred Triangle Number - N th T = (N-1) th Square Number}