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.

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. 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

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.

Want to stretch your imagination? One good way is to try to imagine how far it is to a distant star. How much farther away is it than the moon is from the earth? How much farther away than the earth is from the sun? How long would it take to get there? In this project, you'll learn one way of measuring the distance without leaving Earth.
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Astro_p019

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Time Required

Short (2-5 days)

Prerequisites

You will need a telescope for this project. Experience with geometry is recommended for this project (you need to understand similar triangles).

You've probably noticed the colorful patterns "reflecting" from the shiny surface of a CD disk. What you are seeing is actually diffraction of white light, and the rainbows of color are diffraction patterns. In this project you'll learn about how diffraction patterns are generated, and you'll find out how you can use a laser pointer and a protractor to measure the microscopic spacing of data tracks on a CD.
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Phys_p011

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Time Required

Very Short (≤ 1 day)

Prerequisites

None

Material Availability

Readily available

Cost

Low ($20 - $50)

Safety

Adult supervision recommended. Even low-power lasers can cause permanent eye damage. Please carefully review and follow the [# ProjectGuide Name="Advanced.LaserSafetyGuide" Value="HtmlAnchor" #].

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