A “rusty” compass
A compass locked at one opening can still solve many construction problems when used with a straightedge.
23 / ANTIQUITY TO THE RENAISSANCE
Abu’l-Wafa al-Buzjani
A tiler has three equal square tiles and wants one bigger square. Two cuts on the diagonals and four small trims are enough.
Explore the mathematics ↓
01 / CUTTING AND REARRANGING
Three tiles. One square.
Cut two tiles along their diagonals and wrap the four triangles around the third tile.
Join the outer corners. The pieces that stick out fit exactly into the notches.
=
=
THE IDEAThree unit tiles make a square of side √3 ≈ 1.73. Nothing is measured: the tiles’ own diagonals and corners fix every cut.
The person behind the ideas
- Moved from Buzjan to Baghdad.
- Wrote a book of geometric constructions for craftspeople.
- Also developed trigonometric methods and accurate tables.
More of the mathematics
Mathematics for making
His geometric work connected the concerns of artisans with geometric reasoning.