Simple Construction of the Golden Ratio and its Reciprocal

Simple Construction of τ and ρ

Click the buttons to show steps of the construction.

Erase the drawing

Step 1

Draw a right triangle ABC with perpendicular sides AB = 1 and BC = 1/2.

Step 2

Draw an arc, centered at C, with radius BC, to cut AC at P and the extension of AC beyond C at Q.

Step 3

Draw arcs centered at A with radii AP and AQ, meeting AB extended at R and T.

Then AR = ρ and AT = τ, so that R divides AB in the golden ratio, and B divides AT in the golden ratio.

Why this construction is valid

Last modified on $Date: 2015-04-23 17:26:33 -0400 (Thu, 23 Apr 2015) $

Christopher J. Henrich