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A Curious Right Triangle Approximation

This sketch visualizes the following, found at Pat Ballew's always interesting math history blog: Hugh Worthington, “An essay on the Resolution of Plain Triangles, by Common Arithmetic.” appearing in “A Wealth of Numbers: An Anthology of 500 Years of Popular Mathematics Writing” by Benjamin Wardhaugh. “half the longer of the two legs added to the hypotenuse, is always in proportion to 86 as the shorter leg is to its opposite angle. ”