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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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.

A tsunami is a series of waves made in a body of water, like the ocean, that can cause serious destruction when they hit the coastline. In deep water, a wave can be just a few feet high and travel very fast. As it nears the coastline, and moves into shallower water, tsunamis usually slow down, but the wave height can grow to 100 feet! In this ocean science project, you will model a tsunami and investigate how wave velocity (speed) depends on water depth. Does it match the mathematical equation…
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OceanSci_p014

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Time Required

Short (2-5 days)

Prerequisites

None

Material Availability

You will need an extra-long plastic storage box to use as a water tank. Plastic storage boxes that can slide under a bed work very well. See the Materials and Equipment list for details.

Cost

Low ($20 - $50)

Safety

Use caution when working with the lamp and the water tank. Make sure the two are far apart from each other at all times. Adult supervision required.

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 is a great project for someone interested in both stargazing and photography. Bright city lights and even the light of the full Moon obscure the dimmest stars, which can make identifying constellations more difficult. In this astronomy science project, you will calibrate a digital camera to measure the skyglow in different locations. This can be a great tool to comparing the quality of different star viewing locations.
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Astro_p022

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Time Required

Long (2-4 weeks)

Prerequisites

You should have already taken an algebra class and understand what a function is.

Material Availability

A digital camera with full manual control is essential for this project. If you cannot manually control the ISO, shutter speed, focus, and lens aperture of your camera, then your camera will not work for this project. See the Materials and Equipment list for details.

Cost

Very Low (under $20)

Safety

Take an adult with you when you take skyglow photos at night.

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. 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. 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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- 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)

What makes you notice someone in a crowd? Why do some things stand out, while others melt into the background? In this science project you can investigate the psychology of how things get noticed, by studying how our brains perform a visual search.
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