Just because an idea has been around for centuries, it doesn't make it any less exciting when you discover it for yourself. In this feature, we share situations involving maths which may be new to you, to take you on a journey of discovery.

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Start with a triangle. Can you cut it up to make a rectangle?

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How much of the square is coloured blue? How will the pattern continue?

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Can you work out how to produce different shades of pink paint?

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Can you find an efficent way to mix paints in any ratio?

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Can you find a way to turn a rectangle into a square?

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How can visual patterns be used to prove sums of series?