Regular pentagon

The geometers of ancient Greece invented a peculiar game for themselves, a game called Construction, whose objective is to draw various geometric figures of interest. We are permitted to use just two instruments: an unmarked straightedge (a ‘ruler’), and a compass. Using these, we can draw a straight line through any given pair of points, and we can draw a circle with any given point as centre and passing through any other given point. (Oh yes, we also possess a pencil and an eraser, please do not feel worried about that!)

This series of articles will explore an amazing connection between three different objects in mathematics: the regular pentagon, the Golden Ratio and the icosahedron. Obviously, if the Golden Ratio is involved then the Fibonacci sequence can’t be far behind and, if the icosahedron is, so is its dual the dodecahedron!

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