Mathematical Sciences Institute 2008
July 21-23, 2008
Problems
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What is the exact value of sin(72)?
Solution -- PNG-file (should open in browser window) - The area of a square is 2 square units. What is the area of a circle inscribed in a triangle formed by two sides of the square and one of its diagonals?
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Let ABC be a triangle with no angle exceeding 120 degrees.
Find the point P so that AP + BP + CP is as small as possible.
Solution -- Webpage made with GeoGebra - Looking at the sequence s(n) = 1 + 1/2 + 1/3 + 1/4 + ... + 1/n, will s(n) be an integer for any n > 1?
- What's in a Name? The imaginary number i is defined as the square root of -1 (i = sqrt[-1]). i * i = sqrt[-1]*sqrt[-1] = -1, but i * i = sqrt[-1]*sqrt[-1]= sqrt[(-1)*(-1)] = sqrt[1] = 1 So it looks like -1 = 1. What happened?
- "Can a square wheel roll as smoothly as a round wheel?"
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How can I create a figure other than a circle that has a cross-section with a constant width?
Solution -- Word 2007 Format
For More Information
For more information or questions, you may contact Andrew Talmadge, Institute Director, at: 504/931 - 4781 or via email at msi@promotinglearning.com
Solutions to problems will be presented at the institute and handouts of solutions will be distributed to all participants.