# Others Like “Circles, Tangent Lines and Triangles”

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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
 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. Read more
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. 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 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
 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
 When an earthquake happens, how are scientists able to determine the original location of the quake? In this project, you'll use archived data from a global network of seismometers to find out for yourself. You will make your own seismograms using the Global Earthquake Explorer program, and then use the seismograms to determine the location of earthquake epicenters. Read more
Geo_p021
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 Time Required Long (2-4 weeks) Prerequisites This project uses the Global Earthquake Explorer program to download and analyze data from a global seismic network. In order to do this project you will need to be comfortable installing and working with a new program on your computer. This project requires a computer with high speed Internet access Material Availability Readily available Cost Very Low (under \$20) Safety No issues
Science Fair Project Idea
 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. Read more
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). Material Availability Readily available Cost Very Low (under \$20) Safety No issues
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