Lesson 13 of 20 · 7 moves
The Golden Cut
Divide AB at G so that AB : AG = AG : GB.
Euclid called it "extreme and mean ratio": cut a line so the whole is to the larger part as the larger is to the smaller. The answer is φ = 1.618…, the golden ratio.
Raise a post at B half as tall as AB, join its top to A, and use the post’s height to trim that diagonal. Then swing what is left down onto AB.
The app snaps to every crossing, checks your construction exactly, and offers hints one move at a time.
Step by step
Bisect draws the perpendicular bisector of two points in one move: it stands for the circles and line of the perpendicular bisector.
Bisect AB: the midpoint M.
Extend AB into a line.
Circle centred on B through M.
Bisect M and the far crossing: an upright at B. Its crossing with the circle is D.
Join A to D.
Circle centred on D through B: it trims AD at E.
Circle centred on A through E: it meets AB at the golden cut.
Point tool: mark the crossing on AB. That is G.
What it shows
AB : AG = AG : GB = φ. The same ratio will return in the rectangle, the pentagon and the pentagram.
