Mathematician Unveils Most Efficient Method for Origami Donut Construction
Mathematician solves origami donut efficiency challenge with fewest folds

Image: Phys.org
Mathematician Richard Evan Schwartz has proven that the most efficient origami torus, or donut shape, can be created using just eight vertices. His findings, published in the Proceedings of the National Academy of Sciences, could have implications for design in various fields, including architecture and materials science.
- 01Richard Evan Schwartz's research demonstrates that an origami torus can be constructed with a minimum of eight vertices, making it the most efficient design.
- 02Schwartz's work involved mathematical analysis and computer experiments to prove that seven vertices are insufficient for constructing a torus.
- 03The concept of vertices serves as a measure of efficiency in origami designs, akin to optimizing the number of triangles used.
- 04Schwartz refers to the eight-vertex origami torus as a 'pup tent' and provides a template for those interested in folding it.
- 05This research could enhance understanding of efficient design principles in architecture, materials science, and educational geometry.
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In a groundbreaking study published in the Proceedings of the National Academy of Sciences, mathematician Richard Evan Schwartz has determined that the most efficient way to create an origami torus, resembling a donut, requires only eight vertices. This conclusion stems from rigorous mathematical proof and computer experiments that show constructing a torus with fewer than eight vertices is impossible. Schwartz emphasizes that the number of vertices serves as a critical metric for efficiency in origami, paralleling the optimization of triangle counts in geometric constructions. His findings challenge earlier methods that utilized thousands of vertices and demonstrate that origami tori can be created with significantly fewer components. Schwartz has also provided a template for those interested in attempting to fold the eight-vertex design, which he playfully refers to as a 'pup tent.' The implications of this research extend beyond mathematics, offering insights into efficient design strategies in fields such as architecture and materials science, as well as serving as a valuable educational tool for teaching geometry.
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