The Biggest Smallest Triangle Just Got Smaller | Quanta Magazine
A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.
Hasnain says:
“Some believe the true answer to Heilbronn’s triangle problem won’t be a whole lot bigger than his original guess of 1/n2. “If I put points in a structured way, I fail; if I put points in a random way, then I fail. It can’t be too structured, it can’t be too random, therefore it probably doesn’t exist,” Bloom said. But Zakharov is hoping for a different answer. The intuitions that support an answer of 1/n2 are “kind of boring,” he said. “I would very much prefer if it was n3/2.””
Posted on 2023-09-13T04:55:26+0000