Algebra and abstract structures · Maths EE idea · Solid

Classifying frieze patterns

A research question to start from

Why are there exactly seven types of frieze pattern, and how can a pattern's type be identified from its symmetries?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

A finite classification with a proof you can write yourself, and examples from art and architecture you collect.

Mathematics you would need

Isometries of the plane
Composition of transformations
Symmetry groups
Case analysis

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Describe the possible isometries that preserve a strip.
Show which combinations can occur together and prove there are seven.
Build an identification flowchart and test it on patterns you photograph or draw.

Scope and difficulty

Solid. Solid; the wallpaper groups (17) are too big for full proof but can be mentioned.

Pitfalls

Catalogue of photos without the proof.
Gaps in the case analysis.

Where to start reading

Search a library catalogue or a university's open lecture notes for: seven frieze groups classification proof; isometries of the strip. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.