Solution to a problem of Erdős
The Endeavour 2024-12-09
How many ways can you select six points in the plane so that every subset of three points forms the vertices of an isosceles triangle?
One solution is to choose the five vertices of a regular pentagon and the center.
It’s easy to verify that this is a solution. The much harder part is to show that this is the only solution.
A uniqueness proof was published on arXiv last Friday: A note on Erdős’s mysterious remark by Zoltán Kovács.
More Erdős-related posts
- Six degrees of Paul Erdős
- Anti-calculus proposition of Erdős
- The sum-product conjecture
- Numbers don’t typically have many prime factors
- Spectra of random graphs