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For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/

124 votes
37 answers
12k views

One-step problems in geometry

I'm collecting advanced exercises in geometry. Ideally, each exercise should be solved by one trick and this trick should be useful elsewhere (say it gives an essential idea in some theory). If you ha …
106 votes
83 answers
19k views

Elementary + short + useful

Imagine your-self in front of a class with very good undergraduates who plan to do mathematics (professionally) in the future. You have 30 minutes after that you do not see these students again. You n …
35 votes
4 answers
3k views

Psychological test for Euclidean geometry [closed]

There is the so-called FCI test. It contains a list of questions such that anyone who can speak will have an opinion. Based on the answers one can determine if the answerer knows elementary mechanics. …
Anton Petrunin's user avatar
30 votes
6 answers
5k views

Euclid with Birkhoff

I'm looking for a short and elementary book which does Euclidean geometry with Birkhoff's axioms. It would be best if it would also include some topics in projective (and/or) hyperbolic geometry. Abou …
Anton Petrunin's user avatar
9 votes
1 answer
616 views

Problems which use S₄ → S₃

I need examples of problems which use, directly or indirectly, the homomorphism $S_4\to S_3$ in the solution (its kernel is $\mathbb{Z}_2\oplus\mathbb{Z}_2$). Obvious candidates: Lagrange resolvent …
Anton Petrunin's user avatar
7 votes
1 answer
243 views

Five cubes, Hadamard and Shklyarskiy

Here is my(=bad) translation of from the paper about Shklyarskiy by Golovina: ... in 1937/38 Dodik presented to school students a complete proof of Abel's theorem about equations of degree 5. He m …
Anton Petrunin's user avatar
3 votes
1 answer
188 views

Geometric construction exercises

Many of you know dynamic geometry exercises in Euclidea; if not, here is one example. It lets you do a geometric construction and sends a message once you achieve the result. I am looking for a way to …
Anton Petrunin's user avatar