Divide a paper into equal parts

A piece of paper can easily be divided into equal parts. As for 2, 4, or 8 parts, this is very straightforward. But you can also divide a paper into 3, 5, 6, or 7 parts without using a ruler. It is also quite simple to prove the correctness of the resulting partition:

Divide paper into thirds Coordinate system

The intersection of f and g can be calculated by solving the equation f(x) = g(x) ⟷ 2x = -x + ½ ⟷ x = ⅙

Folding instructions

Diagram 1 — Fold the paper in half, then unfold.

Diagram 2 — Fold the paper along the diagonal, then unfold.

Diagram 3 — Fold the line between the encircled points.

Diagram 4 — Fold a line through the intersection

Diagram 5 — Fold the left edge to the line made in step 4.

Divide a paper into fifths and sevenths

Divide paper into fifths Coordinate system

Divide paper into sevenths Coordinate system

To divide a paper into seven rectangles of equal size, the paper is divided into thirds first.