Although fractal images can be intriguingly complex, fractals are more than just pretty pictures. In this project, you'll explore the mathematical properties of the famous Mandelbrot (illustration on the Background tab) and Julia sets. You'll learn about how these images are generated, and about the relationship between the Mandelbrot set and the Julia sets.
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Math_p013

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Time Required

Average (6-10 days)

Prerequisites

Good understanding of algebra, excellent computer skills

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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How big a ruler would you need to measure the circumference of the Earth? Did you know that you can do it with a yardstick? (And you won't have to travel all the way around the world!)
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Astro_p018

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Time Required

Short (2-5 days)

Prerequisites

You will need to understand some basic principles of geometry for this project. You will need a friend or relative in a distant city to make a shadow measurement for you on the same day you make yours. Both of you will need clear weather.

A magic square is an arrangement of numbers from 1 to n2 in an n x n matrix. In a magic square each number occurs exactly once such that the sum of the entries of any row, column, or main diagonal is the same. You can make several magic squares and investigate the different properties of the square. Can you make an algorithm for constructing a Magic Square? Can you show that the sum of the entries of any row, column, or main diagonal must be n(n2+1)/2? Are there any other hidden properties of a…
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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.

Did you know that you can figure out how much sugar is in a liquid without ever tasting it? In this science fair project, you will learn how to measure the concentration of sugar dissolved in a liquid by using a laser pointer, a hollow prism, and some physics. You will discover how refraction, or the bending of light, is the key to measuring the sugar content of a liquid with a laser pointer.
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Phys_p028

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Time Required

Short (2-5 days)

Prerequisites

None

Material Availability

A kit containing specialty items needed for this project is available from the [# Link Name="Phys_p028.7" Value="HtmlAnchor" #].

Cost

Average ($40 - $80)

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" #].

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).

Block off one-third of a soccer net with a cone, 5-gallon bucket or some other suitable object. Shoot into the smaller side from a set distance, but systematically varying the angle to the goal line. Take enough shots at each angle to get a reliable sample. How does success vary with angle? For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to…
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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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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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