# Pure Mathematics Project Ideas

Science Fair Project Idea
 If you've ever played or watched basketball, you might already know that your chances of successfully banking a shot on the backboard are higher in certain positions on the basketball court, even when keeping the distance from the hoop the same. Ever wondered what would account for this? Do you think you could actually explain this using geometry? This science project will put your knowledge of geometry and algebra to good use. You will calculate and quantify how much more difficult it is to… Read more
Sports_p064
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 Time Required Short (2-5 days) Prerequisites You should have a familiarity with basic algebra. Material Availability Readily available Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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 catapult could launch a projectile. In this project you… Read more
Math_p046
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 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.
Science Fair Project Idea
 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 n(n2+1)/2? Are there any other hidden properties of a… Read more
Math_p036
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 Time Required Average (6-10 days) Prerequisites Material Availability Cost Safety
Science Fair Project Idea
 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
Math_p024
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 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
Science Fair Project Idea
 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 notes, chords, intervals, and octaves? You can… Read more
Math_p034
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 Time Required Average (6-10 days) Prerequisites Material Availability Cost Safety
Science Fair Project Idea
 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. Read more
Math_p041
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 Time Required Short (2-5 days) Prerequisites Material Availability Cost Safety
Science Fair Project Idea
 You may know Lewis Carroll as the author of Alice in Wonderland, but did you know that in real life he was a mathematician who studied symbolic logic and logical reasoning? How can math help you solve Lewis Carroll's Logic Game? (Bogomolny, 2006) How are algorithms for solving the game Sudoku similar to solving a logic problem? (Hayes, 2006) For the super-advanced mathematical genius, try to evaluate currently available, logic-based computational tools, or design a better one!… Read more
Math_p035
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 Time Required Average (6-10 days) Prerequisites Material Availability Cost Safety
Science Fair Project Idea
 Do you like to play cards? Here's a project that will get you thinking about strategy in card games and help you become a better card player. Read more
Math_p044
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 Time Required Short (2-5 days) Prerequisites Some very basic computer programming experience Material Availability Readily Available Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 This is a great science fair project for someone who is interested in both mathematics and art. Spidrons are geometric forms made from alternating sequences of equilateral and isosceles (30°, 30°, 120°) triangles. Spidrons were discovered and named by Daniel Erdély in the early 1970's, and have since been studied by mathematicians and artists alike. This project is a great way to learn about the mathematics and art of tiling patterns. Read more
Math_p043
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 Time Required Long (2-4 weeks) Prerequisites To do this science fair project, you should have at least one year of geometry. Material Availability Readily available Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 What do knots, maps, mazes, driving directions, and doughnuts have in common? The answer is topology, a branch of mathematics that studies the spatial properties and connections of an object. Topology has sometimes been called rubber-sheet geometry because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without… Read more
Math_p030
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 Time Required Average (6-10 days) Prerequisites Material Availability Cost Safety
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