Geometry & Packing · 5 problems
Open problems in Geometry & Packing
Every Geometry & Packing problem in the Math Lab index — 5 in all. Each carries a precise statement, an honest status (open means open), and a concrete plan for throwing compute or tokens at it.
Borsuk's problem in low dimensionsGeometry & Packinguntouched
Can every bounded set of diameter 1 in R^d be partitioned into d + 1 pieces of strictly smaller diameter?
Hadamard's maximal determinant problemGeometry & Packinguntouched
What is the largest possible determinant of an n×n matrix with entries ±1? Hadamard's bound n^(n/2) is attained only at Hadamard orders; other orders are subtler.
Kissing numbers in higher dimensionsGeometry & Packinguntouched
How many unit spheres can simultaneously touch a central unit sphere in dimension d without overlapping?
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