Choe's Hexagon and Cairo Tiling

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

What is the minimum perimeter for a tile on the unit square lattice? A unit square has perimeter 4, but this is not minimal. In 1989, Jaigyoung Choe determined the minimal perimeter to be [1]. In this Demonstration, the Choe irregular hexagons are shown in blue (or orange). It turns out that this tile was already well known for hexagons within an optimized Cairo tessellation.

Contributed by: Ed Pegg Jr (June 13)
Open content licensed under CC BY-NC-SA


Details

References

[1] J. Choe, "On the Existence and Regularity of Fundamental Domains with Least Boundary Area," Journal of Differential Geometry, 29(3), 1989 pp. 623–663. 10.4310/jdg/1214443065.

[2] J. Cepelewicz, "Mathematicians Complete Quest to Build 'Spherical Cubes'," Quanta Magazine (Feb 28, 2023). www.quantamagazine.org/mathematicians-complete-quest-to-build-spherical-cubes-20230210/#0.

[3] E. Pegg. "Choe's Irregular Hexagon" from Wolfram Community–A Wolfram Web Resource. community.wolfram.com/groups/-/m/t/2840845.


Snapshots



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send