Subpaving

High school (ages 12+)
Making & Design

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/subpaving

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the mathematical domain?Geometry, Discrete Mathematics, Combinatorics
2. What is the key historical figures?Johannes Kepler, Roger Penrose, Albrecht Dürer
3. Which shapes can tile the whole plane by themselves?Only three regular shapes can tile the plane by themselves: equilateral triangles, squares, and regular hexagons.
4. Who discovered that some patterns never repeat?In the 1970s, mathematician Roger Penrose showed that a set of tiles can cover a surface in a pattern that never repeats.

Aperiodic Tiling: A tiling that does not have translational symmetry; it never repeats exactly.
Vertex Configuration: The specific arrangement of polygons around a single point in a tiling.
Quasicrystal: A material with ordered atomic structure but lacking translational symmetry, often exhibiting aperiodic tiling patterns.