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Mathemagic: Exploring Sudoku and Other Magic Squares

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Author: Judee Shipman

Grade Level: 6th & up; Type: Math

Objective:

This project explores the properties and uses of “magic squares.”

The goals of this project are:

  1. To experiment with magic square design.
  2. To find new uses for magic squares.

Research Questions:

  1. What is the history of magic squares?
  2. What are their applications, other than Sudoku puzzles?

A magic square is a mathematical construct in which symbols (usually numbers) are arranged in a square, so that the numbers in all rows, columns and diagonals add up to the same amount. No symbol can appear more than once in any row, column or diagonal. Magic squares have been known to mankind for thousands of years, and are sometimes associated with ceremonial magic. In contemporary culture, they most commonly appear in those form of those ever-so popular puzzles known as Sudoku. In this project we explore other uses for magic squares.

Materials:

  1. Computer with Internet access
  2. Color printer
  3. Digital camera
  4. Typical office/hobby/hardware/craft supplies (paper, poster board, glue, wood, etc.)

All materials can be found in your home, at local stores, or on ebay.

Experimental Procedure:

  • Read overview of relevant topics (see bibliography below and terms listed above)
  • Search and print out interesting images that seem appropriate to this project.
  • Address all of the above terms and research questions.
  • Take your own photographs throughout the course of the experiment.
  • Create your own Sudoku puzzle variations, using colors, shapes, or whatever you like.
  • Fill a 3x3 or 4x4 grid with letters. Try to create a magic square poem or anagram.
  • Design your own magic square art forms.
  • Think of a new way to use magic squares (optional).
  • Carefully record your experiences.
  • Analyze your data.
  • Interpret your findings in a detailed report.
  • Include interesting photos, diagrams and art in your science fair display.

Terms/Concepts: Magic Square; Mathematical constant

References:

  1. http://en.wikipedia.org/wiki/Magic_square (Wiki topic: Magic Square)
  2. http://www.jcu.edu/math/vignettes/magicsquares.htm (About magic squares)
  3. Internet searches of your choosing. Search words or terms listed here, or make up your own phrases. Click on any results you find interesting. Have fun surfing the net!  
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