History and philosophy of maths · Ambitious · Dissertation

Why you cannot trisect an angle: a maths EPQ idea

Why it works as an EPQ

A 2,000-year-old problem solved by algebra, with a proof you can follow and explain.

Scope and difficulty

Ambitious. Ambitious. Constructible numbers and one cubic equation are the core.

The maths

Builds on these A Level topics: Algebra and functions · Trigonometry · Proof.

You would learn:

• Constructible numbers
• Field extensions (informally)
• Irreducible cubics

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Show which numbers can be constructed with straight edge and compass.
2. Turn trisecting 60° into a cubic equation using a triple-angle identity.
3. Show the cubic has no constructible root.
4. Discuss constructions that cheat (marked rulers) and why they work.

Pitfalls

• Hand-waving at 'field theory'.
• Confusing approximate and exact construction.

Where to start reading

• What Is Mathematics? (Courant and Robbins)
• Search for: Wantzel 1837 angle trisection impossible

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All history and philosophy of maths ideas · all 93 ideas

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.