Math says you can perfectly split a bunch of random shapes in half using just a few straight, 90-degree cuts.
March 20, 2026
Original Paper
Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions
arXiv · 2603.18550
The Takeaway
This result is a powerful expansion of the 'Ham Sandwich Theorem.' It proves that no matter how messy or oddly shaped several objects (like masses of food or materials) are, there always exists a set of mutually perpendicular slices that will partition every single one of them into equal portions simultaneously.
From the abstract
A generalization of the Borsuk-Ulam theorem to Stiefel manifolds is considered. This theorem is applied to derive bounds on $d$ that guarantee--for a given set of $m$ measures in $\mathbb{R}^d$--the existence of $k$ mutually orthogonal hyperplanes, any $n$ of which partition each of the measures into $2^n$ equal parts. If $n=k$, the result corresponds to the bound obtained in [11], but with the stronger conclusion that the hyperplanes are mutually orthogonal.