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)

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)

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)

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

How big a ruler would you need to measure the circumference of the Earth? Did you know that you can do it with a yardstick? (And you won't have to travel all the way around the world!)
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Astro_p018

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Time Required

Short (2-5 days)

Prerequisites

You will need to understand some basic principles of geometry for this project. You will need a friend or relative in a distant city to make a shadow measurement for you on the same day you make yours. Both of you will need clear weather.

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,…
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Math_p011

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Time Required

Average (6-10 days)

Prerequisites

Good grasp of Euclidean geometry, a firm understanding of how to construct a mathematical proof, determination

When an earthquake occurs, seismic shock waves travel out through the earth from the source of the event. The shock waves travel through the earth or along the Earth's surface, and can be recorded at remote monitoring stations. Some of the waves that travel through the earth are blocked or refracted by the Earth's liquid core, which means that monitoring stations located certain distances from the earthquake do not detect these waves. This creates a "seismic shadow" that you can use to…
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Geo_p022

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Time Required

Long (2-4 weeks)

Prerequisites

This project uses the Global Earthquake Explorer program to download and analyze data from a global seismic network. In order to do this project you will need to be comfortable installing and working with a new program on your computer. This project requires a computer with high speed Internet access. You will also need to understand some basic trigonometry. You should be comfortable with determining the lengths of the sides of right triangles when given an angle and the length of one side. Experience looking at seismograms is useful but not required.

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.
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Math_p043

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Time Required

Long (2-4 weeks)

Prerequisites

To do this science fair project, you should have at least one year of geometry.

If you've ever so much as watched a news clip about a hurricane, you probably know that hurricanes draw their power from warm ocean waters. If that is true, does it mean that hurricanes actually cool the ocean down when they pass through? Can the amount of cooling be measured? Is it proportional to the strength of the hurricane? Find out using data that you can collect yourself using online archives. This project shows you how.
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