Lesson 8 of 20 · 18 moves
The Dodecagon
Inscribe a regular twelve-sided polygon, starting at P.
Twelve is where three and four meet: the corners of the square and of the hexagon, woven around one circle. It counts the months, the hours and the signs of the zodiac.
Two diameters at right angles give four corners. A circle through the centre from each of those finds two more.
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.
Line through P and O: it finds the opposite corner.
Bisect P and the opposite corner: the diameter across marks two more.
Circle centred on P through O: a corner either side of P.
The same from the next quarter corner, through O (3 times).
Join the corners: all 12 sides.
What it shows
Twelve notes make the octave. Walk the corners seven at a time and you visit every one before coming home: the circle of fifths.