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High School, Pure Mathematics Projects, Lessons, Activities (24 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.

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Devising an Algorithm for Solving Rubik's Cube
Science Fair Project Idea
Scientific Method
If you're the kind of person who has taken apart your Rubik's cube in order to grease the inside parts so it will move more smoothly, this could be a great project for you. We'll show you three sets of move sequences that accomplish specific rearrangements of the cube. Can you devise a way to solve the cube using only these three move sequences? Read more
Basketball: The Geometry of Banking a Basket
Science Fair Project Idea
Scientific Method
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
Chain Reaction: Inversion and the Pappus Chain Theorem
Science Fair Project Idea
Scientific Method
Here is a challenging problem for anyone with an interest in geometry. This project requires background research to solve it, but it is an excellent illustration of visual thinking in mathematics. Figure 1 below shows a series of circles (iC₁, iC₂, iC₃, ..., iC₃₀), inscribed inside an arbelos. What is an arbelos? The arbelos is the white region in the figure, bounded by three semicircles. The diameters of the three semicircles are all on the same line segment, AC,… Read more
Design Your Own 3D Printed Optical Illusion
Science Fair Project Idea
Engineering Design Process
The "impossible arrow" is an amazing optical illusion: an arrow that always seems to point to the right, even when you rotate it 180°. If you place the arrow in front of a mirror, however, its reflection points to the left! How does this illusion work? Can you design your own "impossible" shapes? Try this project and find out! Read more
Hacking the Air Gap: Stealing Data from a Computer that isn't Connected to the Internet
Science Fair Project Idea
Scientific Method
You might think that one sure-fire way to keep your computer safe from hackers is to disconnect it from the internet entirely. But did you know that even without internet, a computer can transmit data using light, sound, vibrations, or even heat? In this project, you will investigate how a spy or hacker can steal data from an "air-gapped" computer that has no internet connection. You can even use a smartphone equipped with a sensor app to demonstrate how the data can be picked up by a nearby… Read more
Bet You Can't Hit Me! The Science of Catapult Statistics
Science Fair Project Idea
Scientific Method
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
Exploring Fractals
Science Fair Project Idea
Scientific Method
Although fractal images can be intriguingly complex, fractals are more than just pretty pictures. In this project, you'll explore the mathematical properties of the famous Mandelbrot (illustration on the Background tab) and Julia sets. You'll learn about how these images are generated, and about the relationship between the Mandelbrot set and the Julia sets. Read more
How Do Baseball Stadium Dimensions Affect Batting Statistics?
Science Fair Project Idea
Scientific Method
Have you ever wondered how playing in a certain stadium affects how well the athletes perform? Major League Baseball (MLB) is played in ballparks that have their own individual quirks when it comes to the exact layout of the field. How an individual ballpark affects player performance, which is known as ballpark effects, is heavily investigated in the field of baseball. To name just a few parks and their different traits, Fenway Park (the long-time home ballpark for the Boston Red Sox in… Read more
Tiling with Spidrons
Science Fair Project Idea
Scientific Method
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
What's the Fastest Way to Solve Rubik's Cube?
Science Fair Project Idea
Scientific Method
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
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