Golden Rhombus

Author

Eric W. Weisstein
February 16, 2025

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polygons/GoldenRhombus.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GoldenRhombus.html.

©2025 Wolfram Research, Inc. except for portions noted otherwise

Figure

LaminaData

LaminaData["GoldenRhombus"]

LaminaData["FilledRhombus","Diagram"]

Straightedge and compass construction

Pegg

From Ed Pegg, Jr.
Dec 11, 2018

Sqrt[5]  comes from the (1,2)  rectangle.  With the above code 4 unit squares are drawn, then a circle is drawn in a (1,2) rectangle.   That leads to a diagonal of the Golden rhomb.

Graphics[{EdgeForm[Black],White,Rectangle/@Tuples[{0,1},{2}],Black,Circle[{1,0},Sqrt[5]],Line[{{0,2},{2 GoldenRatio,0},{1,0},{2,2}}]}]

John Molokach (cut-the-knot)

http://www.cut-the-knot.org/do_you_know/GoldenRatioMolokach.shtml