tag:blogger.com,1999:blog-10235575.post698970334067753364..comments2017-04-20T02:32:13.974-04:00Comments on Adventures in Applied Math: Adventures in Fibonacci NumbersRebeccahttp://www.blogger.com/profile/06927630155994067676noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-10235575.post-77550127893575665482012-07-29T19:06:34.746-04:002012-07-29T19:06:34.746-04:00I was at a talk George Andrews gave to the math cl...I was at a talk George Andrews gave to the math club in Urbana around 1998 (plus or minus 2 years), and he introduced this. If I recall correctly, he took credit for it, and there may have been some inspiration on the back of a cereal box. Don't quote me on that last sentence, though.Kevinhttps://www.blogger.com/profile/13939749817050918113noreply@blogger.comtag:blogger.com,1999:blog-10235575.post-78325875707938348472012-07-19T22:26:08.573-04:002012-07-19T22:26:08.573-04:00Thanks for the correction! I knew you could write ...Thanks for the correction! I knew you could write any integer as the sum of Fibonacci numbers, but I obviously made up the part about it being only two ;)Rebeccahttps://www.blogger.com/profile/06927630155994067676noreply@blogger.comtag:blogger.com,1999:blog-10235575.post-84658997498770810012012-07-19T15:39:49.697-04:002012-07-19T15:39:49.697-04:00I've long loved this conversion, but have only...I've long loved this conversion, but have only just seen the extension to non-Fibonacci numbers.<br /><br />One correction, there isn't a theorem that says any number is the sum of two Fibonacci numbers. For example, 12 isn't.<br /><br />But the 'Zeckendorff representation' allows you to write any number in a unique way as the sum of non-adjacent Fibonacci numbers. So 12 = 8 + 3 + 1 (skips 5 & 2). Then you can use that if you want to be exact in your approximation.<br /><br />Eg. see here:<br />http://cameroncounts.wordpress.com/2012/06/21/fibonacci-numbers-2/outofthenormathshttp://outofthenormmaths.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-10235575.post-58658629834442320402012-07-16T09:32:00.136-04:002012-07-16T09:32:00.136-04:00This is new and interesting info to me about the F...This is new and interesting info to me about the Fibonacci series. Thanks!Common Household Momhttps://www.blogger.com/profile/03715969218648104267noreply@blogger.comtag:blogger.com,1999:blog-10235575.post-10115407254648258012012-07-01T13:18:31.188-04:002012-07-01T13:18:31.188-04:00I always found the mental conversion of KPH to MPH...I always found the mental conversion of KPH to MPH the hardest (how fast am I really going?) - probably because one must, of necessity, do it while driving. Handy trick!Jenny F. Scientist, PhDhttp://naturalscientist.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-10235575.post-44035278511436814982012-07-01T12:31:25.352-04:002012-07-01T12:31:25.352-04:00Holy Crud! This is probably the best thing I'...Holy Crud! This is probably the best thing I'll read all month. You may not know it, but the Fibonacci sequence is my most favorite sequence!<br /><br />I plan on using this whenever possible.Josh Lothianhttps://www.blogger.com/profile/12856170672689363559noreply@blogger.com