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

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. 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)

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)

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

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

A fractal is, "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole" (Mandelbrot, 1982). There are many different fractal patterns, each with unique properties and typically named after the mathematician who discovered it. A fractal increases in complexity as it is generated through repeated sets of numbers called iterations. There are many interesting projects exploring fractal geometry that go beyond…
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Is your computer fast? How quickly do you think it can do 100 million arithmetic problems? Do you think it could beat your friend's computer or another one at school? Try this science project to discover an easy way to measure whether or not your computer is a math whiz.
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CompSci_p011

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Time Required

Very Short (≤ 1 day)

Prerequisites

None

Material Availability

Requires computer with Java-enabled web browser (Java Runtime Environment version 1.5 or later) and Internet access

In this project, you will make 2-dimensional templates, called nets, that fold up into 3-dimensional (3-D) shapes. By making shapes of different sizes, you will be able to see how 3-D shapes change with size. Which property (or aspect) will change the most: the length of an edge, the surface area, or the volume?
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