The worst suitcases shape, according to math
Mathematicians Thomas Hales and Koundinya Vajjha have advanced packing theory, focusing on convex shapes, and conjectured the rounded octagon as the least efficient shape, pending peer review of their findings.
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Two mathematicians, Thomas Hales and Koundinya Vajjha, have made significant progress in identifying the worst shape for packing in a plane, a problem that has intrigued mathematicians since the 1920s. While hexagons are known to be the most efficient shape for packing, the quest for the least efficient shape has been more complex. Hales and Vajjha focused on convex and centrally symmetric shapes, ultimately proving a crucial intermediate conjecture related to the rounded octagon, which was previously conjectured by Karl Reinhardt to be the worst shape with a packing density of about 90.24%. Their work builds on Hales' earlier achievements, including the proof of Kepler's conjecture regarding sphere packing. The duo's research involved ruling out numerous potential shapes and utilizing advanced mathematical techniques, including optimal control theory. After years of collaboration, they have produced a comprehensive 260-page document detailing their findings, which is pending peer review. While they have not definitively proven that the rounded octagon is the worst shape, their work has opened new avenues for exploration in packing theory.
- Hales and Vajjha have advanced the study of packing shapes, focusing on convex and centrally symmetric forms.
- The rounded octagon is conjectured to have the worst packing efficiency, with a density of 90.24%.
- Their research builds on previous work by mathematicians like Karl Reinhardt and Kurt Mahler.
- The proof is extensive, spanning 260 pages, and is currently awaiting peer review.
- The problem remains open-ended, with further exploration needed to confirm the worst packing shape.
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