Tilings and Escher: a maths EPQ idea
A title to start from
Which shapes can tile the plane, and how can symmetry be used to design an original Escher-style tiling?
Why it works as an EPQ
Angle arguments and symmetry give a clear theory; the artefact is your own tiling, built from it.
Scope and difficulty
Accessible. Accessible. Regular and semi-regular tilings, then one designed tiling.
The maths
Builds on these A Level topics: Trigonometry · Vectors · Proof.
You would learn:
- Angle conditions at a vertex
- Translations, rotations and reflections
- Wallpaper groups (overview)
One possible plan
- Prove which regular polygons tile the plane.
- Find the semi-regular tilings by an angle argument.
- Design an original tiling by modifying a tile under symmetries.
- Evaluate it against your design brief.
Pitfalls
- Copying an existing design.
- Pictures without proofs.
Where to start reading
- Search for: semiregular tilings vertex angle condition
- Search for: wallpaper groups 17 explained
Making something? Read the artefact guide first: an artefact still needs a research-based written report.
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