approximate of the length of the sides of a Golden Rectangle
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In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, {\displaystyle 1:{\tfrac {1+{\sqrt {5}}}{2}}} 1:{\tfrac {1+{\sqrt {5}}}{2}}, which is {\displaystyle 1:\varphi } 1:\varphi (the Greek letter phi), where {\displaystyle \varphi } \varphi is approximately 1.618.
Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well.
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A method to construct a golden rectangle. Owing to the Pythagorean theorem,[a] the diagonal dividing one half of a square equals the radius of a circle whose outermost point is also the corner of a golden rectangle added to the square.[1]