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December 6th, 2010, 12:18 PM   #1
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u.U interesting problem

A point moves along the perimeter of a square with a constant speed, and another point on the diagonal at the same speed. If they leave simultaneously from the same point, do they meet again?
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December 6th, 2010, 12:33 PM   #2
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When the second point reaches the end of the diagonal, does it go back the way it came? If so, they might meet again.
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December 6th, 2010, 12:35 PM   #3
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Re: u.U interesting problem

No. In order for them to meet, we would require to be rational.
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December 7th, 2010, 12:53 AM   #4
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Re: u.U interesting problem

Yes, it turns back again.
So.. should I understand that there's not a(n) lcm between a rational and a non-rational number?
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December 7th, 2010, 02:20 AM   #5
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The fact that it turns back means that you hadn't fully specified its motion originally, which introduces the possibility that you hadn't originally fully specified the motion of the other point either. Hence you can change the problem again so that [color=#00AA00]MarkFL[/color]'s conclusion is correct, or you can change it slightly differently so that the points can meet again. If you do neither, the problem remains inadequately defined. I'm not sure what mcm stands for, but it doesn't alter my conclusion.
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December 7th, 2010, 08:21 AM   #6
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Re: u.U interesting problem

mcm :=
"maraschino cherry maker", or
"merry Christ mass"
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January 28th, 2011, 05:41 AM   #7
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Re: u.U interesting problem

mcm= least common multiple. I'm sorry it was a bad translation =)
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January 28th, 2011, 02:59 PM   #8
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Re: u.U interesting problem

Since they both move at equal speeds then it's more a question of distances.

The diagonal can be assumed to be long with side lengths of . In the distance Point A on the diagonal has traveled, Point B on the perimeter has traveled a distance . This is a fairly trivial result but can be easily extended to get Mark's answer since this means we effective have



where . Now you're asking when but this is impossible since while is in the set of irrationals.
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