{"id":"palomar/PALOMAR-2026-11-02-000007","url":"https://github.com/veljjanoski/erdos657-palomar/tree/e44e1eb1d4a525f66a7a297235c956a29f56a535","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-02-000007-v1.json","repo":"https://github.com/veljjanoski/erdos657-palomar","tags":["math.CO","math.MG","msc:52C10"],"score":0,"title":"Erdős Problem 657: Straus's observation on isosceles-free point sets with few distances","trust":"high","domain":"math.CO","source":"palomar","authors":["Daniel Veljjanoski"],"reviews":0,"subject":"math.CO","summary":"Erdős asked whether a set of n points in the plane with no isosceles triangle must determine at least f(n)n distinct distances for some f(n) tending to infinity, and asked the same in R^k for each fixed k. Straus observed that no such bound holds uniformly in the dimension. In the form stated in formal-conjectures: for every k there are 2^k points in R^k with no isosceles triangle and at most 2^k - 1 distinct distances. This formalization proves that statement, using the points whose i-th coordinate is 0 or sqrt(2^i); the sources consulted do not record Straus's own construction.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-02","reactions":{},"formalized":true,"formalizes":[{"title":"Erdős Problem 657","identifier":"","relationship":"formalizes"}]}