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Higher-dimensional
origami constructions
Deveena R. Banerjee, Sara Chari and Adriana Salerno |
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Vol. 16 (2023), No. 2, 297–312
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Abstract |
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Origami is an ancient art that continues to yield both artistic and scientific insights to this day. In 2012, Buhler, Butler, de Launey, and Graham extended these ideas even further by developing a mathematical construction inspired by origami — one in which we iteratively construct points on the complex plane (the “paper”) from a set of starting points (or “seed points”) and lines through those points with prescribed angles (or the allowable “folds” on our paper). Any two lines with these prescribed angles through the seed points that intersect generate a new point, and by iterating this process for each pair of points formed, we generate a subset of the complex plane. We extend previously known results about the algebraic and geometric structure of these sets to higher dimensions. In the case when the set obtained is a lattice, we explore the relationship between the set of angles and the generators of the lattice and determine how introducing a new angle alters the lattice. |
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Keywords
origami construction, lattice
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Mathematical Subject Classification
Primary: 06B99
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Milestones
Received: 1 February 2022
Revised: 26 May 2022
Accepted: 31 May 2022
Published: 26 May 2023
Communicated by Vadim Ponomarenko
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Authors |
| Deveena R. Banerjee | |
| Department of Molecular Physiology
and Biophysics Vanderbilt University Nashville, TN United States |
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| Sara Chari | |
| Department of Mathematics Bates College Lewiston, ME United States |
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| Adriana Salerno | |
| Department of Mathematics Bates College Lewiston, ME United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
