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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
5
votes
Important open exposition problems?
This is an interesting question.
Responding sideways, I can give a closed exposition problem, namely the Kepler conjecture. Here is a talk by Thomas Hales:
Lessons learned from the Formal Proof of t …
1
vote
Excellent uses of induction and recursion
I came across this one browsing old questions under the logic tag.
Here's proof of the Principle of Induction:
https://openmathematics.org/#induction
The GitHub repository URL is available in the …
2
votes
What is Realistic Mathematics?
Update: Having read below a second time, I think you should change your usage from 'realistic mathematics' to 'empirical mathematics'. I think this is much more apt, plus it has the advantage that …
3
votes
An example of a beautiful proof that would be accessible at the high school level?
The most success I have ever had teaching proofs at secondary school level is with the Peaucellier–Lipkin linkage. The proof relies on nothing more than basic geometry, namely similar triangles, but t …