311 citations · 1.2k across the 55 of their papers we have counts for
6 papers · 1 filter
A modern solution to the Gion shrine problem
Juan Arias de Reyna, David Clark
We give a new solution to the famous Gion shrine geometry problem from eighteenth-century Japan. Like the classical Japanese solution, ours is given in the form of a degree ten equ…
Point configurations that are asymmetric yet balanced
Henry Cohn, Noam D. Elkies, Abhinav Kumar +1
A configuration of particles confined to a sphere is balanced if it is in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function…
On some points-and-lines problems and configurations
Noam D. Elkies
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
The D_4 root system is not universally optimal
Henry Cohn, John H. Conway, Noam D. Elkies +1
We prove that the D_4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no uni…
Sylvester-Gallai Theorems for Complex Numbers and Quaternions
Noam Elkies, Lou M. Pretorius, Konrad J. Swanepoel
A Sylvester-Gallai (SG) configuration is a finite set S of points such that the line through any two points in S contains a third point of S. According to the Sylvester-Gallai Theo…
New upper bounds on sphere packings I
Henry Cohn, Noam Elkies
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which ar…