Timeline for Sum of squared nearest-neighbor distances between points in a square

9 events

when toggle format	what		by	license	comment
Jan 24, 2019 at 0:47	vote	accept	T. Amdeberhan
Jan 18, 2019 at 8:41	answer	added	RaphaelB4		timeline score: 0
Jan 17, 2019 at 0:11	comment	added	Joseph O'Rourke		Perhaps this answer by @achillehui will help: Average distance between $n$ randomly distributed points on a square with their nearest neighbors.
S Jan 16, 2019 at 21:03	history	suggested	David G. Stork	CC BY-SA 4.0	Related to nearest-neighbor concept
Jan 16, 2019 at 20:17	comment	added	Fedor Petrov		A close result: any $n$ points in a right triangle $ABC$, $\angle ABC=\pi/2$, may be enumerated by $P_1,\dots,P_n$ so that $AP_1^2+P_1P_2^2+\dots+P_{n-1}P_n^2+P_nC^2\leqslant AB^2$. The proof is similar to Iosif Pinelis's idea: take a height $BH$ and apply the induction proposition to triangles $AHB,CHB$ (if all point lie in the same triangle, proceed partitioning.)
Jan 16, 2019 at 19:47	review	Suggested edits
S Jan 16, 2019 at 21:03
Jan 16, 2019 at 19:43	comment	added	David G. Stork		...and tight when $n= 4$ (points at corners).
Jan 16, 2019 at 19:35	answer	added	Iosif Pinelis		timeline score: 4
Jan 16, 2019 at 17:15	history	asked	T. Amdeberhan	CC BY-SA 4.0