tag:blogger.com,1999:blog-5303307482158922565.post2695815336418375268..comments2024-03-22T13:39:55.941-07:00Comments on Math Mama Writes...: Dots On a CircleSue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-5303307482158922565.post-9058547494909278292010-10-17T10:55:55.623-07:002010-10-17T10:55:55.623-07:00Jonathan, I feel too stressed for time to play rig...Jonathan, I feel too stressed for time to play right now. (Shame, isn't it?) But this looks fascinating. It seems that you're saying that you can use Pascal's triangle to predict the proper number of regions if you start leaving off numbers at the 5th row. <br /><br />I'll look forward to exploring this when I'm on vacation or something.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-64106893304062288622010-10-17T08:22:07.590-07:002010-10-17T08:22:07.590-07:00This problem was offered to me as an example of a ...This problem was offered to me as an example of a pattern that breaks. I recall playing some more, a few of us, and one of our number discovering something neat:<br /><br />1<br />1+1<br />1+2+1<br />1+3+3+1<br />1+4+6+4+1<br />5+10+10+5+1<br />15+20+15+6+1<br />35+35+21+7+1<br />...<br /><br />1. Do I remember correctly?<br />2. Is there a nice link to what is physically going on? (either in the Richeson book or the video)<br />3. Is this easier to understand as:<br />(k=0 to 4) Sum C(n,k)<br />or as:<br />2^n - (k = 0 to n - 3) Sum C(n,k)<br /><br />(Look at the regions? Look at the regions that fail to be formed?)<br /><br />Interesting. I haven't thought about this in a long time.<br /><br />JonathanAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-61776559480702644002010-10-04T13:42:53.347-07:002010-10-04T13:42:53.347-07:00Mary, how'd 42 get into the mix?Mary, how'd 42 get into the mix?Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-68380083957037426802010-10-04T13:12:51.597-07:002010-10-04T13:12:51.597-07:00I've read that book, and enjoyed the parts I u...I've read that book, and enjoyed the parts I understood. I would not have thought of it as being related to this problem. I'm obviously not seeing the big picture here. I like your post.<br /><br />I will think about this more after I take a nap. ;^)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-41738944402007411962010-10-04T09:08:35.889-07:002010-10-04T09:08:35.889-07:00Incredibly, Dave Richeson wrote an entire book abo...Incredibly, Dave Richeson wrote an entire book about this problem, ...<br /> http://pballew.blogspot.com/2009/04/eulers-theorem-of-planer-graphs.htmlPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-46739143926068684922010-10-04T06:27:00.970-07:002010-10-04T06:27:00.970-07:00I love this post, Sue! I just linked it on my fac...I love this post, Sue! I just linked it on my facebook, where I am posting something cool about powers of two, powers of ten, or 42 every day this month.<br /><br />This was perfect for today!<br /><br />And my word verification challenge on your blog is "taxess" which is an elision of my daughters' nickname for me ("tax goddess")<br /><br />How cool is that!Maryhttp://albanyareamathcircle.blogspot.com/noreply@blogger.com