Construction of a golden rectangle

1. Construct a simple square
2. Draw a line from the midpoint of one side of the square to an opposite corner
3. Use that line as the radius to draw an arc that defines the height of the rectangle
4. Use the endpoints of the arc to complete the rectangle
5. The proportions of the resulting rectangle is φ or

${\displaystyle \varphi ={\frac {1}{2}}(1+{\sqrt {5}})\approx \ 1.618033989}$

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