FINAL PROJECT: Abstract and Reader's Reponse > The Relationship Between Group Theory and the Rubik's Cube
A, good description. Watch your its! Also, if you explain or review what permutations and combinations are in the cognitive wedge -- both text and formula definition -- you might help a reluctant reader to see this activity -- the algorithm of turnings -- as truly an embodiment of math theory.
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May 12, 2019 |
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ABSTRACT: Group theory is a very well-studied part of mathematics that is crucial for abstract algebra. It has been used to define several well-known and important algebraic concepts, like rings, fields, and vector spaces. Not only can group theory be used for understanding other mathematical concepts, it can also be used to define everyday objects, like a Rubik’s cube. If each of the non-center facets of the Rubik’s cube were to be labelled with a number from 1 to 48, then each unique configuration of the Rubik’s cube could be represented as a different permutation. For the sake of making the Rubik’s cube easier to solve, the case where the all of the facets are in the correct location would be considered the identity permutation. The rotation of each face of the cube is considered an element, and any composition of those 6 types of rotations can be used to generate all of the other elements of the group. Being able to set up the Rubik’s cube as a group, with the binary operator being composition, is what allows for group theory to be effectively used to solve the Rubik’s cube.
WC = 190
READER’S PROFILE: I imagine a reader who is more experienced in mathematics than me may doubt that I am properly applying the properties of groups to the Rubik’s cube.
READER’S RESPONSE: Majority of the information in this document comes from previous research articles that focus on the relationship between the Rubik’s cube and group theory. In addition, these research articles were written by mathematics professors from prestigious universities, such as Harvard, MIT, and UC Berkeley. In addition, even though I am just an undergraduate student, I have taken abstract algebra, which is a class heavily focused on group theory. As a result, I have a fairly good understanding of majority of the content in the research articles, and thus, can properly interpret their meaning.