Discrete geometry

Finite point configurations and their distances, polytopes and polyhedra, dissections and tilings, lattice points and extremal shape problems.

Part 1 of 2

• Blumenthal's minimax angle problem
• Continuous Turán numbers of planar patterns
• Dehn invariant
• Distinct and unit distances
• Convex and general position of point sets
• Equiangular lines
• Equilateral triangles in planar point sets
• Kakeya sets in finite fields
• Lattice points in dilated regions
• Moving sofa problem
• Pancake cutting with exotic knives
• Pick's theorem
• Platonic solids and regular polytopes
• Points and spanned hyperplanes
• Point–line incidences
• Steiner ratio
• A discrete subgroup is a lattice iff it has full rank
• Erdős–Anning theorem
• Euler's polyhedron formula
• Monsky's theorem

Part 2 of 2

• Squaring the square with distinct squares
• Sylvester–Gallai theorem

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