Solution to a problem of Erdős
by John from John D. Cook on (#6ST67)
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? This is a question asked by Erds and recently resolved.
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 Erds's mysterious remark by Zoltan Kovacs.
More Erds-related posts- Six degrees of Paul Erds
- Anti-calculus proposition of Erds
- The sum-product conjecture
- Numbers don't typically have many prime factors
- Spectra of random graphs