Lagrange multipliers: follow the constraint
Explore the method of Lagrange multipliers for constrained optimization, with a visual perspective.
calculusoptimizationinformation theory
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Problems to solve and ideas to explore.
A set that shifts into its complement
Can arbitrarily small translations turn a subset of the real line into its complement?
real analysislinear algebraset theory
From planar graphs to the five Platonic solids
Count vertices, edges, and faces; add a point at infinity; then discover why there are exactly five regular convex polyhedra.
geometrygraph theorytopology
Cutting a cube
How many straight cuts does it take to separate a cube into 27 unit cubes, even if you can rearrange the pieces?
geometrypuzzles
Four equal regions: two bisections and a turn
Two easy bisections leave one imbalance. A quarter-turn suggests how to remove it—but we must account for the jumps in a point count.
geometrycountingpuzzles