This is an interesting geometry project that goes back to the time of Archimedes, the famous Greek mathematician. You can combine this mathematical project with computer science and take this ancient problem into the twenty-first century with a dynamic diagram using the geometry applet.
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Math_p018

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Time Required

Short (2-5 days)

Prerequisites

You should either currently be taking or have already completed a first course in geometry. You must understand the concept and method of a mathematical proof.

Here is a project that combines Computer Science and Mathematics. Prove a method for inscribing a circle within a triangle (as shown). You'll also learn how to create an interactive diagram to illustrate your proof, using an applet that runs in your Web browser. If you like solving problems and thinking logically, you'll like this project.
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CompSci_p004

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Time Required

Short (2-5 days)

Prerequisites

Must understand the concept and method of a mathematical proof

Material Availability

Readily available (laptop computer helpful for live demonstration)

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.
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Math_p012

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Time Required

Short (2-5 days)

Prerequisites

Must understand the concept and method of a mathematical proof

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.
Figure 1 below shows a semicircle (AE, in red) with a series of smaller semicircles (AB, BC, CD, DE, in blue) constructed inside it. As you can see, the sum of the diameters of the four smaller semicircles is equal to the diameter of the large semicircle. The area of the larger…
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Math_p010

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Time Required

Very Short (≤ 1 day)

Prerequisites

Must understand the concept of a mathematical proof

Here is a project that combines Computer Science and Mathematics. The semicircle has two tangent lines that meet at point T. You need to prove that a line drawn from A to T bisects CD. You'll also learn how to create an interactive diagram to illustrate your proof, using an applet that runs in your Web browser. If you like solving problems and thinking logically, you'll like this project.
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CompSci_p009

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Time Required

Short (2-5 days)

Prerequisites

You should either currently be taking or have already completed a first course in geometry. You must understand the concept and method of a mathematical proof.

Material Availability

Readily available (laptop computer helpful for live demonstration)

Here is a project that combines Computer Science and Mathematics. Prove a method for circumscribing a circle about a triangle (as shown). You'll also learn how to create an interactive diagram to illustrate your proof, using an applet that runs in your Web browser. If you like solving problems and thinking logically, you'll like this project.
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CompSci_p007

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Time Required

Short (2-5 days)

Prerequisites

Must understand the concept and method of a mathematical proof

Material Availability

Readily available (laptop computer helpful for live demonstration)

Here is a project that combines Computer Science and Mathematics. The two circles are tangent to one another at point A. Their diameters are parallel. Prove that points A, D and F are co-linear. You'll also learn how to create an interactive diagram to illustrate your proof, using an applet that runs in your Web browser. If you like solving problems and thinking logically, you'll like this project.
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CompSci_p008

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Time Required

Short (2-5 days)

Prerequisites

You should either currently be taking or have already completed a first course in geometry. You must understand the concept and method of a mathematical proof.

Material Availability

Readily available (laptop computer helpful for live demonstration)

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…
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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.
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Math_p013

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Time Required

Average (6-10 days)

Prerequisites

Good understanding of algebra, excellent computer skills

Have you ever wanted to analyze data from a NASA spacecraft? In this science project you will use data from NASA's MESSENGER mission to measure the diameter and calculate the depth of impact craters on Mercury. You will then analyze that data for relationships between a crater's depth and diameter. This is your chance to
perform a science project as a NASA researcher would!
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Astro_p036

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Time Required

Very Short (≤ 1 day)

Prerequisites

Geometry: familiarity using sine, cosine, and tangent to solve right triangles