Hans Walser, [20060526a] [20111205a]
The construction of the golden section using a compass only
We try to construct the golden section using only a compass, no ruler.
Step by step:
Step 1
Step 2
Step 3
Step 4
The golden section arises
The distances between the black point and the two red points are in the ratio of the golden section.
Proof 1:
Proof Figure
Let the first circle be the unit circle with radius 1. Then we have:
The number is the golden section (see [Walser 2001], p. 4)
Proof 2:
Embedding in the Figure of Odom (see [Walser 2001], p. 123)
Figure of Odom
See [Hofstetter 2002]. Step by step:
Step 1
Step 2
Step 3
The distances between the black point and the two red points are in the ratio of the golden section. The proof is left to the reader.
Reference
[Hofstetter 2002] Hofstetter,
Kurt: A Simple Construction of the Golden Section. Forum Geometricorum, 2
(2002), p. 65-66.
[Walser 2001] Walser, Hans: The Golden Section. Translated by Peter Hilton and Jean Pedersen. The Mathematical Association of America 2001. ISBN 0-88385-534-8