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An Intro to Group Theory, and the Rubik’s Cube
Math is full of abstractions. Group theory is the pulling out of certain useful structures (or relations) from sets (or groups) of objects. These sets of objects can be composed of anything you could think of, such as rabbits, solar systems, colors, etc. Once we have a particular set in mind, we can identify or…
4-Dimensional Knots
Knots are 1-dimensional objects embedded in 3-dimensional space. So generalizing in an n-dimensional space, a knot would be an embedded (n-2)-dimensional object. Therefore in a 4-dimensional space we would embed a (4-2)-dimensional object, or a 2-dimensional object. Now when trying to visualize a 2-dimensional knot we need to come up with a fourth dimension. This…
What are Knots?
Knot so humble beginnings Knot Theory is a relatively new field of mathematics, and an active realm of contemporary research. It all began from a misconception in the early 1800s. Lord Kelvin theorized that different types of matter corresponded with different knots of ether. Ether was theorized to be a substance which pervaded all space…
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