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Pure Mathematics Project Ideas (42 results)

Wikipedia defines mathematics as "the study of quantity, structure, space and change." With a definition like that, it's easy to see why math is often called "the language of science." Math is essential for analyzing and communicating scientific results, and for stating scientific theories in a way that is clear, succinct, and testable. Start your science adventure by choosing a project from our collection of mathematics experiments.

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Science Fair Project Idea
Almost all of the games we play are based on math in some way or another. Card games, board games, and computer games are designed using statistics, probabilities, and algorithms. Begin by reading about games and game theory. Then you can choose your favorite game and investigate the mathematical principles behind how it works. Can combinatorial game theory help you to win two-player games of perfect knowledge such as go, chess, or checkers? (Weisstein, 2006; Watkins, 2004) In a multi-player… Read more
Math_p033
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Time Required Average (6-10 days)
Science Fair Project Idea
If you like solving challenging puzzles, this could be a good project for you. In this project you will research different methods for solving a Rubik's cube, and then do an experiment to compare them to each other. Which method works fastest? Read more
Math_p023
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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.
Material Availability Readily available
Cost Very Low (under $20)
Safety No issues
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 A kit is available from our partner . See the Materials tab 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)
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)
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. The project description provides the details. Read more
Math_p041
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Time Required Short (2-5 days)
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)
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
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