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You know the Golden Ratio, but what is the Silver Ratio? Learn through active problem-solving at Brilliant:
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Polygons, Diagonals, and the Bronze Mean by Antonia Redondo
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Proving Brouwer's Fixed Point Theorem
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Cut a line segment into unequal pieces of lengths a and b such that the ratio a to b is the same as the ratio (a + b) to a --- that is, so that big over medium equals medium over small. This is how you construct the golden ratio Phi. If a rectangle has an aspect ratio of Phi, you can subdivide it forever into a square and another golden rectangle, and make fun logarithmic spirals by connecting the corners.
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