Solving problems by adding a dimension

Summary by Krater

A video exploring five geometry and topology puzzles in two dimensions that can be solved using higher-dimensional insights, including tilings, circle strips, circle tangents, tetrahedra volumes, and hypercubes.

From the video

Answers: How can higher-dimensional math solve two-dimensional geometry puzzles?

• geometry puzzles
• higher dimensions
• tiling patterns
• sphere packing
• determinants
• quaternions

What it concludes

• The 2D rombus tiling problem can be solved by viewing the tilings as projections of 3D cube stacks, where each move corresponds to adding or removing a cube.
• The minimum sum of widths for strips covering a unit disk is 2, proven by projecting the problem to a hemisphere.
• Monge's theorem for three circles can be proved by elevating the circles to spheres and finding intersecting planes.
• The volume of a 3D tetrahedron can be determined using a 4x4 matrix determinant.
• The 2D rombus tiling puzzle can be scaled up to a 4D hypercube stack where the maximum number of moves is N^4.