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Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

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Proofs with Pictures

Some diagrammatic 'proofs' of algebraic identities and inequalities.

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For What?

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

Cosines Rule

Age 14 to 16 Challenge Level:

Why is the $60$ degree angle opposite the side of median length?

For the second part all you need is the cosine formula and some algebraic manipulation to get the required result.