Lesson 12 of 20 · 14 moves
The Sacred Cut
Swing an arc from each corner through the centre, and join the cuts into an octagon.
Set the compass on a corner of the square and open it to the centre. Swing it, and the arc cuts both sides that meet at that corner.
The Danish engineer Tons Brunés called it the Sacred Cut, and believed the builders of antiquity laid out their temples with it. From all four corners, the eight cuts are the corners of a perfect octagon.
The app snaps to every crossing, checks your construction exactly, and offers hints one move at a time.
Step by step
Draw the diagonal AC.
Draw the diagonal BD: the two cross at the centre.
Circle centred on A through the centre: it cuts AB and AD.
The same from B.
From C.
And from D: eight cuts in all.
Join the two cuts on AB: side 1 of 8.
Join the cuts going round: sides 2 to 8.
What it shows
Every side of the square is cut as 1 : √2 : 1, and every side of the octagon is √2 − 1 of the square’s. Half a diagonal, swung down, is all it takes.
