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

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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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).

If you've ever wondered how tall that bridge is, or how high your kite was, then this could be a good project for you. You'll learn how you can use the mathematics of right triangles to measure the height of an object with two measurements that you can make on the ground.
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Have you ever played a computer game in which a cartoon character, like a dog or a cat, moves or turns when you click on it? Have you ever wondered how characters know how far to move or how far to turn? In this computer science project, you will learn how with a simple (and free) program called Scratch, which will let you write your own computer program that tells a cartoon kitty how to draw shapes.
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CompSci_p035

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Time Required

Short (2-5 days)

Prerequisites

You should have access to a computer with the Internet and room for the Scratch program. Scratch can be downloaded for either Windows (2000 or later) or Mac (OSX 10.4 or later).

You can see examples of parabolic reflectors in flashlights, car headlights, satellite TV antennas, and even on the sidelines at football games. How do these "dish" antennas work to gather signals? What is the best position for placing the detector for these antennas? In this project, you can use an LED and a simple photodetector to find out for yourself.
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Can you imagine designing and building a space telescope the size of a tennis court? Believe it or not, that is someone's job! Engineers are hard at work on the James Webb Space Telescope, or JWST. This telescope has the potential to enable astronomers to see light from when the Universe was first formed. No one knows what amazing discoveries this might lead to. However, to make the telescope work properly, engineers have to overcome a lot of challenges. In this science project, you can…
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Phys_p082

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Time Required

Long (2-4 weeks)

Prerequisites

None

Material Availability

Most of the materials are available in hardware or craft stores.

Cost

Average ($50 - $100)

Safety

Adult supervision is required. Use caution when using the box cutter, heat lamp, and laser pointer.

Just one sheet of paper can lead to a whole lot of fun. How? Paper planes! All you have to know is how to fold and you can have a simple plane in a matter of minutes! But what design should you use to build the best plane? In this aerodynamics science project, you will change the basic design of a paper plane and see how this affects its flight. Specifically, you will increase how much drag the plane experiences and see if this changes how far the paper plane flies. There is a lot of cool…
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Aero_p046

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Time Required

Very Short (≤ 1 day)

Prerequisites

None

Material Availability

Readily available

Cost

Very Low (under $20)

Safety

Fly your planes in a large area, away from foot and vehicle traffic.