3D Math - Always a Single Plane to Cut Three 3D Objects in Half with Borsuk-Ulam Theorem - by Zach Star
June 28, 2021 Borsuk-Ulam Theorem 3D Math Title: A surprising topological proof - Why you can always cut three objects in half with a single plane By: Zach Star Youtube - Information Description: Proving that any set of n n-dimensional objects can be cut in half by n-1 dimensional object (i.e. 3 3D objects can be cut in half by a 2D plane). Overview This was just a fun and interesting mathematical proof I came across. Using the Borsuk-Ulam Theorem at its core, it proves how any set of 3 3D objects can be cut in half (by volume) by some 2D plane. It then expands that to show that this works for any n amount of n-dimensional objects, which are then divided by an object with n-1 dimensions. Borsuk-Ulam Theorem This can be read up on here at the corresponding wikipedia page: Wikipedia - Borsuk-Ulam Theorem This states: "every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point". ...