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Pure Mathematics Project Ideas

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  Difficulty Level 4-7  

Scale Models *

Many industries rely on scale models to develop new products and designs. Architects, industrial designers, artists, clothing designers, and car manufacturers all use scale models. Each model is...   Read more...
Difficulty =   4      Add to favorites     Show others like this

Frequency of Outcomes in a Small Number of Trials

People often draw conclusions from a small number of observations, but how easy is it to draw the wrong conclusion? Here is a simple project that shows the importance of making enough observations before making a prediction.   Read more...
Difficulty =   4      Add to favorites     Show others like this

The Birthday Paradox

This project shows how mathematical probability sometimes contradicts our intuition. Despite the fact that there are 365 days in a year, if you survey a random group of just 23 people there is a 50:50 chance that two of them will have the same birthday. Don't believe it? Try this project and see for yourself.   Read more...
Difficulty =   4      Add to favorites     Show others like this

Money Problems *

Math can make you money! If you understand some basic math, you can make good decisions about how to keep, spend, and use your hard earned dollars. Try an experiment comparing the same balance in...   Read more...
Difficulty =   5      Add to favorites     Show others like this

Gigantic, Invisible Triangles: Measuring Height (or Altitude) with an Inclinometer

If you've ever wondered how tall that bridge is, or how high your kite was, then this could be a good project for you. You'll learn how you can use the mathematics of right triangles to measure the height of an object with two measurements that you can make on the ground.   Read more...
Difficulty =   5      Add to favorites     Show others like this

Dice Probabilities

You're playing Monopoly with a friend, and you've already got Park Place and you really, really want to get Boardwalk. If you're on Pacific Avenue, what are the chances you'll reach your goal? Here's an easy project that will show you how to find out.   Read more...
Difficulty =   5      Add to favorites     Show others like this

Divide and Conquer: Proving Pick's Theorem for Lattice Polygons

If you like to play Tetris then you might like this project. You'll learn something interesting about the mathematics of complex shapes.   Read more...
Difficulty =   5      Add to favorites     Show others like this

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



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