Erdős Problem 1086

### What is the conjecture

https://www.erdosproblems.com/1086

Let $g(n)$ be minimal such that any set of $n$ points in $\mathbb{R}^2$ contains the vertices of at most $g(n)$ many triangles with the same area. Estimate $g(n)$.

Status:open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Read the conjecture statement and status at https://www.erdosproblems.com/1086, then inspect existing formalized conjecture entries in the formal-conjectures repository. Determine how this project represents an Erdős problem and formalize Problem 1086 in the corresponding style; done means the conjecture is added and the project checks it successfully.

Written by the indexing model from the issue text.