tag:blogger.com,1999:blog-10348701.post8715768105338775079..comments2024-03-13T21:26:03.011-07:00Comments on Right on the Left Coast: Views From a Conservative Teacher: How Would Someone Figure This Out?Darrenhttp://www.blogger.com/profile/15730642770935985796noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-10348701.post-40597430710300401502011-01-16T07:11:07.858-08:002011-01-16T07:11:07.858-08:00These constants are attractors in the phase space ...These constants are attractors in the phase space of arithmetic operations. These are significant in dynamical systems and chaos theory work. One of the most famous (and still unproven) ones is the 3x+1 problem: 1. pick any positive integer. 2. If it is even divide by two, and if it is odd, multiply by three and add 1. 3. Back to step 2. The claim is that this will result in the sequence 4,2,1 for any starting integer. For example, starting with 13 gives: 13, 40, 20 , 10, 5, 16, 8, 4, 2, 1, 4, 2, 1 (ad infinitum). There are LOTS of related problems to this - there's an entire paper about this by J Lagarias (http://www.math.lsa.umich.edu/~lagarias/3x+1.html)Joshua Sasmorhttp://people.setonhill.edu/sasmornoreply@blogger.comtag:blogger.com,1999:blog-10348701.post-89234966947942355312011-01-15T22:15:32.845-08:002011-01-15T22:15:32.845-08:00believe it or not when I was in my math classes I ...believe it or not when I was in my math classes I was always on my calculator taking numbers flipping them and subtracting them. I don't think I was ever aware of any patterns just screwing around in class I guess.<br /><br />I remember when I was in the 11th grade and I made an equilateral triangle and then took the midpoints of the sides and connected them. I did it again and was blown away by it. Of course, I later found out I was just copying Sierpinski's triangle.Mr. Whttps://www.blogger.com/profile/13282059797251178491noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-20709600149740876442011-01-15T15:22:28.546-08:002011-01-15T15:22:28.546-08:00"...trick that will win you a drink"
Go..."...trick that will win you a drink"<br /><br />Good enough for me! :)KauaiMarkhttps://www.blogger.com/profile/02581543514815246743noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-47353649791677065572011-01-15T04:15:42.136-08:002011-01-15T04:15:42.136-08:00Which leads us back to the musical question -- &qu...Which leads us back to the musical question -- <b>"This is significant because...?"</b><br /><br />I mean, other than a barroom trick that will win you a drink or three, what is the significance?<br /><br />So asks the Social Studies teacher.Rhymes With Righthttp://rhymeswithright.mu.nunoreply@blogger.comtag:blogger.com,1999:blog-10348701.post-27589123754893189642011-01-14T23:46:46.096-08:002011-01-14T23:46:46.096-08:00Now that is interesting AND weird.
(I'll be t...Now that is interesting AND weird.<br /><br />(I'll be trying it out for a couple of hours just to see if it's a prank or not)KauaiMarkhttps://www.blogger.com/profile/02581543514815246743noreply@blogger.com