Dissection of 3 Equal Squares into One Square

Problem

Dissect $3$ equal squares and use the pieces to make $1$ large square.

Solution

Bisect $2$ of the squares along their diagonals.

Arrange the right triangles so generated around the outside of the $3$rd square as shown.

Join the $4$ right angles of the $4$ right triangles.

The overlapping bits fit into the gaps.

$\blacksquare$

Tessellation

This dissection can be used as the basis for a tessellation:

Historical Note

This dissection problem was discussed by Abu'l-Wafa Al-Buzjani in a work of his from the $10$th century.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Abul Wafa ($\text {940}$ – $\text {998}$): $39$