An octagon is a geometric design with eight sides of equal length. Most familiar as the distinctive shape of a stop sign, octagons are also popular in arts and crafts projects and are regularly seen as wall tiles, paving stones and pieces of furniture. The following method of converting a square to an octagon uses the principles of Pythagoras but does not require any advanced mathematical knowledge.
Things You'll Need
 Ruler
 Pencil
 Compass
 Cutting implement

Draw two lines connecting the opposite corners of the square, forming a large "X."

Set the point of the compass on one of the corners of the square and open it to the center of the "X."

Use the compass to draw an imaginary semicircle. Carefully mark the two points where the circle crosses the edge of the square.

Move the point of the compass to the next corner and repeat the process. Continue until there are a total of eight marks on the edge of the square.

Use the ruler to connect the two marks at each corner of the square with a straight line to form a triangle. Using the appropriate cutting implement for the material the square is made of, cut away the corners along the lines. The resulting shape will be a regular octagon.