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)

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.

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…
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This is an interesting project that explores which geometrical shapes make the strongest bridge truss structures. It is a good introduction to the engineering design process. You'll design three different trusses, and use online simulation software to analyze the distribution of load-bearing forces in each design. Then you'll build and test prototypes of each design.
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CE_p006

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Time Required

Average (6-10 days)

Prerequisites

Excellent computer skills, high school physics course

Material Availability

Readily available

Cost

Low ($20 - $50)

Safety

Use caution with sharp tools when cutting wooden parts to size. Adult supervision recommended for bridge-testing phase.

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

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)

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 do you turn a 2-dimensional piece of paper into a 3-dimensional work of art? Origami, the classical art of Japanese paper folding, is loaded with mathematical themes and concepts. What are the common folds in origami, and how do they combine to create 3-dimensional structure? Can you classify different types of origami into classes based upon the types of folds they use? Can you show Kawasaki's Theorem, that if you add up the angle measurements of every other angle around a point, the sum…
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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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- Less Details

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)