Rubik’s Cube and Magic Square
Mathematical techniques involve the representation of essential elements of a given system using precise language. However, it requires a well detailed mathematical model that will offer a solution to a particular problem. There are different mathematical techniques that an individual may prefer to use as long as the problem is solved in mathematics. Where these techniques have the set rules that one follows to have the solution. At the same time, there are professional techniques that are maintained and developed for better results. Therefore, this paper is analyzing the Rubik’s cube and the magic square. The discussion over their set rules, and mathematical and problem-solving techniques that every model will represent. Also, the consideration of how professional mathematicians apply these models in analyzing their problems. Where magic square involves a square grid whereby the numbers are arranged in a particular format, and the Rubik’s cube is where the arrangement of numbers is in a three-D form.
Erno Rubik introduced the Rubik’s cube in 1974. Erno Rubik is a Hungarian architecture. The purpose of introducing this model is that he is trying to solve the three-dimensional geometry problem. The cube did not start as a toy, thus being successful since it achieves its purpose. The Rubik’s cube is initially known as the magic cube. The Rubik cubes have districting characteristics that attract human beings; hence it’s widespread. It continues to spread in the market since different professionals have been using it to solve their diverse needs in various fields. The principles of Rubik’s Cube are contained in numerous scientific systems that involve permutations and combinations, symmetries, and cyclicality.
Benjamin Franklin introduces the magic square at around 1736-1737. Whereby he is working as a clerk in the Pennsylvania assembly, he develops eight square where each square changes to another.
In the Rubik’s cube, there are legal moves that one can make where it’s only one in twelve chances for an issue to be solved. In every legal step, the cubes can only be represented by even the number of the swamp, and at the same time, an old name cannot describe it at any swamp. Also though the cube has old numbers, they cannot represent any legal move in the swap. It’s because in every legal step will always represent an equivalent of even number. Hence despite all the progress that one can make, the name of the accumulated swaps will remain as an even. Thus the set rule of Rubik’s is that even numbers should be maintained in every legal move (Books, LLC, 78). However, in the magic square, every play has his deck to play the game. Where each pack consists of sixty minimum cards. Every player is responsible for shifting their deck without being helped. There is a mutual agreement between the players as the game starts. To form the starting hand, the player draws seven cards from their decks, known as the library. Therefore the player should have the following to win the game; should have a negative life, the player should draw the card, and no card should be left in his library.
Mathematically Rubik’s cube is under the permutation group. The cube has six different colors, where each color is repeated nine times. Hence the cube is considered to have fifty-four elements that have numbers ranging from one to six. The order list can be rearranged by rotating the six faces of the cube. Through repetition and combination of the factors, the numbers are rearranged and hence a new permutation. While in mathematics, a permutation group is a group where its elements are part of an ordered list, and its operations rearrange the items in a particular order. The mathematical concepts that are used in Rubik’s cubes are that the elements in the same row or column can be arranged together. Still, there are elements that are neutral since their position does not rearrange the set. Also, in every presentation, there are inverse elements. It also includes the degree of permutation, which determines how many times can rotate the cube to go back to the original position of the cube. However, every transposition has a finite degree. At the same time, in Rubik’s cube, the algorithm technic can be used to solve the problem.
One of the amazing this is to create a mathematical magic square. It involves a grid of either three by three or four by four, where the numbers in the same row and column must add up to the same name. For instance, it can be used to solve a problem where one may engage his friends or family members to play the game. It’s where one will introduce the game and state all the rules of the game where every column and row should add up to the same number. For instance, you may request them to give you two or three names that may end up to fifteen. The repetition of this arrangement of numbers will provide you with different solutions for different problems.
Most of the mathematician professionals use the Rubik’s cube to change the attitude of the students towards mathematics. Some of the high school teachers have been experiencing low grades in their subjects since the student have a negative attitude towards mathematics. Therefore, most of the teachers will decide to use the Rubik’s cube to involve students and increase participation of students towards mathematics class (the United States International Trade Commission, 108). After the teacher introduced the use of Rubik’s cube, most of the students were able to come up with a mosaic historical figure, famous landmarks, and different animals from the cube. Therefore, the teacher is in a position to promote critical thinking to the student as well as introducing algorithm problem-solving. Most of the professional mathematicians use it to teach the following mathematical concepts; to determine volume and surface areas as well as helping in solving the three-dimensional problems, and fractions, ratios, and proportional reasoning. For instance, the Rubik’s cubes have different colors, and the teacher may ask the students to determine the portion of a specific color from the cubes
. Therefore, the mathematician professional uses the cubes to promote the creativity of the students as well as their critical thinking.
Still, the magical square is used by the mathematical professional through different techniques. Still, it can be used by the teachers to teach their students math. It’s applied to help the students to improve in their multiplication concepts. It helps them to think critically where they can rearrange the numbers in three orders: the vertical, horizontal, and diagonal to get the equal one magic number for all of them. Therefore the magic skills help the students to develop additional skills using the addition of whole numbers in every equation. The magic squares also help the students understand the subtraction concepts in the class, where they may give a total of two or three numbers where one number was missing, and the other number is requested. Hence the magic square cubes help the mathematical professional to help students to develop skills of problem-solving.
The variation between the Rubik’s cube and the magic squares on their existing activities may include the following; the Sudoku rule which under the magic square. It’s a single puzzle square that contains numbers ranging from one to nine. The Sudoku ensures that the sum of the numbers in the column and row end up o one magic number. Where most of the Sudoku can be found in the newspapers and even in textbooks. The other game is the hex game, which is under the Rubik’s cube. Involves where every player has been allocated a specific color that they play with. In this game, every player ensures that they place their stones in the position of their colors before their opponents.
In conclusion, the game arts helps in the improvement of critical thinking and being creative. It’s through the Rubik’s cube and magical squares that professional mathematician teachers use to help their students to love and participate in mathematics. The Rubik’s cubes help the student solve problems with volume, surface areas, fractions, and ratios while the magic squares help them solve the addition and subtraction problems.
Works Cited
Books, LLC. Mechanical Puzzles: Soma Cube, Tower of Hanoi, Flexagon, Rubik’s Cube, Jigsaw Puzzle, Peg Solitaire, Combination Puzzle, Speedcubing, Mechanical Puzzle, Rubik’s Revenge, Fifteen Puzzle, Professor’s Cube, Klotski, Square One, V-Cube 6, V-Cube 7, Pyramorphix. Books LLC, Wiki Series, 2011.
United States International Trade Commission. In the matter of certain cube puzzles: investigation no. 337-TA-112. DIANE Publishing, 1983.