# Pure Mathematics Project Ideas

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Showing 1 - 5 of 20 Project Ideas
Bet You Can’t Hit Me! The Science of Catapult Statistics
Bet You Can’t Hit Me! The Science of Catapult Statistics
 Difficulty Time Required Average (6-10 days) Prerequisites An introductory-level understanding of statistics (mean, standard deviation, and the normal distribution) is helpful, but not required for completing this project. Material Availability Requires catapult kit. See the Materials and Equipment list for details. Cost Average (\$40 - \$80) Safety Do not aim the catapult at people or breakable objects; minor injury possible.

If you have ever tried to hit a target (such as a trash can) with a wad of paper, you know that aim is everything. But it is not always easy to get it right every time! Missing is not that big a deal with a wad of paper, but what if you were in an invading army in the Middle Ages, using a catapult to hurl huge stones and knock down castle walls? For a successful invasion, it would be important to know exactly how far, and how reliably, a… Read more
Magic Squares *
Magic Squares
 Difficulty Time Required Average (6-10 days) Prerequisites Material Availability Cost Safety

A magic square is an arrangement of numbers from 1 to n2 in an n x n matrix. In a magic square each number occurs exactly once such that the sum of the entries of any row, column, or main diagonal is the same. You can make several magic squares and investigate the different properties of the square. Can you make an algorithm for constructing a Magic Square? Can you show that the sum of the entries of any row, column, or main diagonal must be… Read more
Making Patterns with Rubik's Cube
Making Patterns with Rubik's Cube
 Difficulty Time Required Long (2-4 weeks) Prerequisites To do this project you should enjoy solving puzzles and thinking in three dimensions. This project requires starting with Rubik's Cube in the solved position, so you will need to know how to solve the puzzle in order to do this project. Material Availability Readily available Cost Very Low (under \$20) Safety No issues

This project challenges you to figure out how to make geometric patterns with Rubik's Cube. Leaving your cube in one of these positions makes it much more tempting to pick it up and 'fix' it. Can you figure out how to make a checkerboard, or a cube-within-a-cube? Can you make only the center piece a different color from the rest? Can you figure out how to solve the cube from these positions? Read more
Playing Music *
Playing Music
 Difficulty Time Required Average (6-10 days) Prerequisites Material Availability Cost Safety

Music has many mathematical elements in it: rhythm, pitch, scale, frequency, interval, and ratio. There are many ways to turn these elements into a science fair project. You can investigate how the scale is based upon a special type of number sequence called a Harmonic Series. Another scale used by Bach, called the "Well-Tempered-Scale" or the "Equal-Tempered-Scale", is based upon a series. How are these mathematical series and ratios related to… Read more
Relationships Between Variables: Using Correlation and Linear Regression *
Relationships Between Variables: Using Correlation and Linear Regression
 Difficulty Time Required Short (2-5 days) Prerequisites Material Availability Cost Safety

Here's a project that combines sports and math. You'll learn how to use correlation analysis to choose the best team batting statistic for predicting run-scoring ability (Albert, 2003). You'll also learn how to use a spreadsheet to measure correlations between two variables. Which Team Batting Statistic Predicts Run Production Best? Read more