Lesson 14 of 20 · 6 moves
Golden Rectangle
Extend the square into a golden rectangle.
From the midpoint of the square’s base, the distance to a far corner is √5 / 2. Swing it down and the base grows to φ.
Cut a square from a golden rectangle and what remains is golden again, forever. Its corners trace the golden spiral.
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. Compass carries a length to a new centre. Euclid showed in his second proposition that a collapsing compass can always do the same.
Bisect AB to find its midpoint M.
Extend the base into a line.
Circle centred on M through C: it lands on the base at E.
Extend the top DC into a line.
Compass: take the length BE and set it down on C. It finds F.
Join E to F.
What it shows
Its sides are 1 and φ. Remove the square and the leftover sliver is another golden rectangle.
