Once you have got to grips with Centred Shapes, have a look for relationships between different centred shapes, triangular numbers and square numbers.
If you think you have found a relationship, try to find a diagram to explain why it works.
Here are some relationships you could try to prove:
- 6 x Nth Triangular Number + 1 = Nth Centred Hexagon
- N² + (2N – 2)th Triangular Number = Nth Centred Hexagon
- 3(N-1)th Triangular Number + Nth Centred Triangular Number = Nth Centred Hexagon
- N(N+1) + N² = (2N)th Triangular Number
- Nth Centred Pentagon = Nth Triangular Number + (2N-2)th Triangular Number
- Nth Centred Pentagon – N² + N = Nth Centred Triangle
- Nth Triangular Pyramid - N² = (N-2)th Triangular Pyramid
For some further challenges, have a look at More Centred Shape Relationships.