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Spheres are one of the most fundamental shapes that make up the universe. A sphere can easily be defined mathematically as the three dimensional set of points equidistant from a given center point. Because of this simplicity, many common objects can be approximated by a sphere, from apples to the Earth itself. Digging a little deeper into the universe, one could observe that atoms themselves can be considered spheres; spheres make up everything. A natural question arises: “how do spheres interact?” If atoms make up the universe, it would certainly seem useful to understand what kinds of plausible structures they could form. This brings about the sphere packing problem; “what is the most dense packing of regular spheres possible, without any sort of overlap?” This problem seems like it could be solved easily, but it took mathematicians centuries to come up with an indisputable answer. In the following pages, the history, intuition, interesting properties, and uses of the solution to the sphere packing problem will be explored. | Spheres are one of the most fundamental shapes that make up the universe. A sphere can easily be defined mathematically as the three dimensional set of points equidistant from a given center point. Because of this simplicity, many common objects can be approximated by a sphere, from apples to the Earth itself. Digging a little deeper into the universe, one could observe that atoms themselves can be considered spheres; spheres make up everything. A natural question arises: “how do spheres interact?” If atoms make up the universe, it would certainly seem useful to understand what kinds of plausible structures they could form. This brings about the sphere packing problem; “what is the most dense packing of regular spheres possible, without any sort of overlap?” This problem seems like it could be solved easily, but it took mathematicians centuries to come up with an indisputable answer. In the following pages, the history, intuition, interesting properties, and uses of the solution to the sphere packing problem will be explored. | ||
Latest revision as of 02:43, 6 December 2020
Introduction to Sphere Packing
Author: Eli LeChien
Spheres are one of the most fundamental shapes that make up the universe. A sphere can easily be defined mathematically as the three dimensional set of points equidistant from a given center point. Because of this simplicity, many common objects can be approximated by a sphere, from apples to the Earth itself. Digging a little deeper into the universe, one could observe that atoms themselves can be considered spheres; spheres make up everything. A natural question arises: “how do spheres interact?” If atoms make up the universe, it would certainly seem useful to understand what kinds of plausible structures they could form. This brings about the sphere packing problem; “what is the most dense packing of regular spheres possible, without any sort of overlap?” This problem seems like it could be solved easily, but it took mathematicians centuries to come up with an indisputable answer. In the following pages, the history, intuition, interesting properties, and uses of the solution to the sphere packing problem will be explored.
