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 December 6th, 2010, 12:18 PM #1 Newbie   Joined: Nov 2010 Posts: 20 Thanks: 0 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?
 December 6th, 2010, 12:33 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,820 Thanks: 2159 When the second point reaches the end of the diagonal, does it go back the way it came? If so, they might meet again.
 December 6th, 2010, 12:35 PM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: u.U interesting problem No. In order for them to meet, we would require $\sqrt{2}$ to be rational.
 December 7th, 2010, 12:53 AM #4 Newbie   Joined: Nov 2010 Posts: 20 Thanks: 0 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?
 December 7th, 2010, 02:20 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,820 Thanks: 2159 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.
 December 7th, 2010, 08:21 AM #6 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: u.U interesting problem mcm := "maraschino cherry maker", or "merry Christ mass"
 January 28th, 2011, 05:41 AM #7 Newbie   Joined: Nov 2010 Posts: 20 Thanks: 0 Re: u.U interesting problem mcm= least common multiple. I'm sorry it was a bad translation =)
 January 28th, 2011, 02:59 PM #8 Member   Joined: Jan 2011 Posts: 36 Thanks: 0 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 $\sqrt{2}$ long with side lengths of $1$. In the distance Point A on the diagonal has traveled, Point B on the perimeter has traveled a distance $\sqrt{2}$. This is a fairly trivial result but can be easily extended to get Mark's answer since this means we effective have $d_A = n, d_B = \sqrt{2}n$ where $n \in \N$. Now you're asking when $d_A= d_B$ but this is impossible since $d_A \in \N$ while $d_B$ is in the set of irrationals.

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