Geogebra gives me the golden ratio $\Phi$ to fifteen decimal places for this simple construction illustrated below wherein the ratio of the blue line i to the red line h is $\Phi$ or 1.6180....
The golden ratio construction is made in the following manner:
- Draw a circle resting on a line.
- Draw a segment (segment f) equal to the diameter of the circle from the center of the circle to the line at point C.
- Draw a second segment of the same length as the diameter of the circle (segment g) from point D where segment f intersects with the circle so that it also touches the line at point F.
The ratio of the blue segment i to the red segment h will then be the golden ratio $\Phi=1.6180\cdots.$
Has anyone seen any prior art relating to this construct? And again, both geometric and trigonometric proofs are welcome! :)