pow:problem2f21
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pow:problem2f21 [2021/09/28 00:55] mazur |
pow:problem2f21 [2021/09/28 00:56] (current) mazur |
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| + | <box 80% round orange| Problem 2 (due Monday, September 27)> | ||
| + | a) Given three distinct parallel lines on the plane, prove that one can choose one point on each | ||
| + | line so that the 3 points are vertices of an equilateral triangle. | ||
| + | |||
| + | b) Given four distinct parallel planes in the space, prove that one can choose one point on each | ||
| + | plane so that the 4 points are vertices of a regular tetrahedron. | ||
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| + | </box> | ||
| + | The problem was solved by Ashton Keith and Pluto Wang. Pluto's solution to part a) is slightly | ||
| + | different from our solutions, while Ashton's solution is similar to our first solution. The provided solutions | ||
| + | to part b) are similar to our solution, except that Pluto's solution is a bit sketchy and Ashton's solution | ||
| + | is brave enough to provide explicit computation rather than just an existence argument. For details | ||
| + | see the following link {{:pow:2021fproblem2.pdf|Solution}}. | ||