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Mathematics

The Golden Ratio and Its Appearances in Geometry

Quick fact

The golden ratio is the only positive number that is exactly one more than its reciprocal: φ = 1 + 1/φ. Because of this, it appears as the ratio of consecutive Fibonacci numbers as they grow, and it emerges naturally in the diagonals of a regular pentagon.

Why this is interesting

You've likely seen this number in art and architecture, but did you know it hides inside a simple pentagon? What makes the golden ratio so special that it appears in so many geometric shapes?

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The Golden Ratio and Its Appearances in Geometry

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