# Others Like “Taking Off on a Tangent”

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Science Fair Project Idea
 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. Read more
Math_p012
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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 Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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. Read more
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) Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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. Read more
CompSci_p008
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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) Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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. Read more
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) Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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. Read more
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) Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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,… Read more
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 Material Availability Readily available Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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… Read more
Math_p010
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 Time Required Very Short (≤ 1 day) Prerequisites Must understand the concept of a mathematical proof Material Availability Readily available Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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… Read more
Math_p031
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 Time Required Long (2-4 weeks) Prerequisites Material Availability Cost Safety
Science Fair Project Idea
 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. Read more
Math_p013
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 Time Required Average (6-10 days) Prerequisites Good understanding of algebra, excellent computer skills Material Availability Computer with Internet access required Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 Is your computer fast? How quickly do you think it can do 100 million arithmetic problems? Do you think it could beat your friend's computer or another one at school? Try this science project to discover an easy way to measure whether or not your computer is a math whiz. Read more
CompSci_p011
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 Time Required Very Short (≤ 1 day) Prerequisites None Material Availability Requires computer with Java-enabled web browser (Java Runtime Environment version 1.5 or later) and Internet access Cost Very Low (under \$20) Safety No issues
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