Geometry: using only compasses and straightedge
How to divide a square into nine equal squares.
Draw a square. Mark half way across each side. (See how)
Join each corner to each opposite corner.
Join each corner to each half point.
Join each corner to each half point.
If you look closely you will see you have made a perfect octagon inside your square.
Draw lines through corners of the octagon as shown on right.
These lines divide the square in nine.
These lines divide the square in nine.