Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
7–14 weeks (4–6 hrs/week)
Take Euclidean plane and its relatives for free and do the exercises on the metric approach to the plane, congruence, parallel lines, inversion and hyperbolic geometry. Write every solution up in LaTeX and keep the source and the PDF in one public repo as you go.
Proof required
Link your public repo with the LaTeX source and the PDF of the exercises on the metric approach to the plane, congruence, parallel lines, inversion and hyperbolic geometry, and show your self-check (The book's hints).
What gets checked
- Every proof is complete and correct.
- Hints used are noted honestly.
- Figures match the proofs.
Common mistakes
- Copying posted solutions: verifiers read the reasoning and the history.
- A proof that skips the hard step.
- Asking for review before the self-check.
Powstik Guide
A public repo with your LaTeX write-ups of the exercises on the metric approach to the plane, congruence, parallel lines, inversion and hyperbolic geometry.
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: The book has hints for its exercises. Use a hint only after a real try, and note where you used one.
- Fix what the self-check shows, and say what you fixed.
- Ask three people who know the topic to check it.
Template
README Course: Euclidean plane and its relatives (Anton Petrunin (free book on arXiv)) What is here (problem sets, PDF): Self-check result: The hardest proof and why:
What gets sent back
- Answers with no reasoning.
- Photos of handwriting instead of typeset work.
- Self-check not shown.
Resources
Foundationstart here
Depthgo deeper
What a verifier looks for
- Every proof is complete and correct.
- Hints used are noted honestly.
- Figures match the proofs.
- Pick two proofs and check every step: each argument must be correct and complete, not just present.
- Ask about one step; the answer should be clear.
You'll sign in first, then come straight back here.
Prove a classic theorem from the axioms
1–3 weeks (5–8 hrs/week)
Use what you learned. Make an expository write-up that proves one classic theorem (the angle sum of a triangle, or that inversion maps circles to circles or lines) from the book's axioms, with a figure for each step. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link an expository write-up that proves one classic theorem (the angle sum of a triangle, or that inversion maps circles to circles or lines) from the book's axioms, with a figure for each step, in your public repo.
What gets checked
- Only the axioms and earlier results are used.
- Every step is correct and complete.
- Figures are drawn accurately (for example in GeoGebra).
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
An expository write-up that proves one classic theorem (the angle sum of a triangle, or that inversion maps circles to circles or lines) from the book's axioms, with a figure for each step.
Steps
- Write one line: what you will prove or show.
- Draft it, then read it cold the next day.
- Ask someone to read it and mark the first step they doubt.
- Fix it and typeset the final version.
- Ask three people to check it.
Template
Title: What this shows: Main result (statement): Proof: What I would look at next:
What gets sent back
- A main step left unproved.
- Not clearly the person's own work.
- Claims more than it proves.
Resources
Foundationstart here
Depthgo deeper
What a verifier looks for
- Only the axioms and earlier results are used.
- Every step is correct and complete.
- Figures are drawn accurately (for example in GeoGebra).
- Every argument must be correct and complete; mark the first gap you find.
- Check that the work is the person's own.
You'll sign in first, then come straight back here.