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Pure Mathematics Project Ideas

  Difficulty Level 6-10  

Throwing You Some Curves: Is Red or Blue Longer?

This a straightforward, but interesting, project in geometry. It is a good first proof to try on your own. You should be able to figure it out by yourself, and you'll gain insight into a basic property of circles.   Read more...
Difficulty =   5  –  6      Add to favorites     Show others like this

Around the World: The Geometry of Shooting Baskets *

Take shots at a set distance from the basket, but systematically vary the angle to the backboard. For a basic project: How do you think your success rate will vary with angle? Draw a conclusion...   Read more...
Difficulty =   5  –  7      Add to favorites     Show others like this

Geometry of Goal-Scoring *

Block off one-third of a soccer net with a cone, 5-gallon bucket or some other suitable object. Shoot into the smaller side from a set distance, but systematically varying the angle to the goal...   Read more...
Difficulty =   5  –  7      Add to favorites     Show others like this

Frequency Histograms *

Can you remember what the weather was like last week? Last year? Here's a project that looks at what the weather was like for over a hundred years. You'll use historical climate data to look at...   Read more...
Difficulty =   5  –  8      Add to favorites     Show others like this

Playing Games *

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...   Read more...
Difficulty =   6  –  9      Add to favorites     Show others like this

Thinking in (Semi-)Circles: The Area of the Arbelos

The arbelos is the white-shaded region between the three semicircles in the illustration at right. In this project, you'll prove an interesting method for determining the area of the arbelos.   Read more...
Difficulty =   6  –  7      Add to favorites     Show others like this

What's the Fastest Way to Solve Rubik's Cube?

If you like solving challenging puzzles, this could be a good project for you. In this project you'll learn one method for solving Rubik's Cube. Then you'll do your own background research to find other methods for solving the puzzle. Which method works fastest?   Read more...
Difficulty =   6      Add to favorites     Show others like this

Topologies *

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....   Read more...
Difficulty =   7  –  9      Add to favorites     Show others like this

Playing Music *

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...   Read more...
Difficulty =   7  –  9      Add to favorites     Show others like this

Solving Logic Problems *

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...   Read more...
Difficulty =   7  –  10      Add to favorites     Show others like this



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Index of Pure Mathematics Project Ideas
Pick a Card, Any Card | Play-Doh Math | Shape Changing with the CyberSquad | Juice Box Geometry | Estimation and Population Size | Measuring Up | M&M Math | M&M Geometry | Scale Models | Frequency of Outcomes in a Small Number of Trials | The Birthday Paradox | Money Problems | Gigantic, Invisible Triangles: Measuring Height (or Altitude) with an Inclinometer | Dice Probabilities | Divide and Conquer: Proving Pick's Theorem for Lattice Polygons | Throwing You Some Curves: Is Red or Blue Longer? | Around the World: The Geometry of Shooting Baskets | Geometry of Goal-Scoring | Frequency Histograms | Playing Games | Thinking in (Semi-)Circles: The Area of the Arbelos | Topologies | Playing Music | Solving Logic Problems | Magic Squares | Making Patterns with Rubik's Cube | The Effects of Card Counting on a Simple Card Game | Tiling with Spidrons | Statistical Significance: Using a t-Test | Relationships Between Variables: Using Correlation and Linear Regression | Data Models | Fractals | Origami | How do Baseball Stadium Dimensions Affect Batting Statistics? | Is There Such a Thing as Streakiness in Baseball? | What Makes a Team's Winning Percentage Deviate from the Pythagorean Relationship? | Taking Off on a Tangent | Devising an Algorithm for Solving Rubik's Cube | Exploring Fractals | Chain Reaction: Inversion and the Pappus Chain Theorem |