Math in… Stone Walls

Before concrete and asphalt provided a cheap and easy way to make smooth surfaces, many roads and walls were built from stone blocks that fit together like jigsaw puzzles.

In this Incan stone wall, blocks were cut so precisely that they fit together with no visible gaps! (Photo by Welly Huang from Pexels.)

In this wall, on the other hand, blocks were cut more roughly, with mortar filling in the gaps. (Photo by M. M. from Pexels)

Imagine the time, creativity, and patience it would take to choose the right stones, then measure, break, and chisel them down into blocks of just the right fit!

If you want to build faster, it’s better if your blocks are uniform so that you can make a repeating pattern.

Uniform-width rectangular blocks are great for big projects, because they can be lain in rows. (Photo by Simon Berger from Pexels)

To give streets more character, many European cities use a bogen pattern of overlapping arcs or a fan/peacock’s tail pattern. (Photo by Diana ✨ from Pexels)

Ignoring the slight gaps filled with mortar or sand, these are all examples of tessellations: tilings with no gaps or overlaps.

While people still build stone roads and walls today, they’re often used to preserve historical character, since more newly discovered materials are cheaper and easier to work with.

Bricks and pavers remain common construction materials for their repeating pattern charm. Since most of them are molded instead of cut, they are uniform by default and designed to tessellate easily.

What other ways have you seen geometric tilings in the surfaces of roads, walls, and other structures?