- The Difference of Two SquaresStand-up Maths
- Theorem 1:
- Every odd number can be written as the difference of two squares.
- Theorem 2:
- Every square number is the sum of consecutive odd numbers.
- Theorem 3 (Difference of squares):
- \(a^2 - b^2 = (a - b)(a + b)\)
- Theorem 4:
- A natural number \(n\) can be written as \(a^2 - b^2\) if and only if \(n\) is odd or a multiple of four.

- Algebraic proof of theorem 1
- Visual proof of theorem
- Visual proof of theorem 2
- Algebraic proof of theorem 2, using Gauss's trick
- Visual proof of theorem 3
- Visual proof of theorem 4
- Proof of theorem 4 by modular arithmetic
- Another visual proof of theorem 4

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- Worked example: average rate of change from table
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