pow:problem3
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| pow:problem3 [2020/03/15 16:55] – created mazur | pow:problem3 [2020/03/19 05:33] (current) – mazur | ||
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| + | <box 80% round orange|Problem 3 (due Monday, March 16)> | ||
| + | Recall that a $chord$ of a circle is a straight line segment whose endpoints both lie on the circle. | ||
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| + | Several chords are drawn in a circle of radius 1 so that any diameter of the circle intersects at most | ||
| + | $k$ of the chords. Prove that the sum of the lengths of all the chords drawn is less than $k\pi$. | ||
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| + | </ | ||
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| + | Ashton Keith, a freshman majoring in math, is the only person who submitted a complete solution. His solution | ||
| + | is very nice and different from our original solution. A solution along similar lines, but lacking sufficient | ||
| + | details, was also submitted by Yuqiao Huang. Both our solution and the solution by Ashton Keith are discussed | ||
| + | in the following link {{: | ||