Channel: Mathologer

Category: Education

Description: Okay, as it says in the title of this video, today's mission is to figure out how many ways there are to make change for one googol, that is 10^100 dollars. The very strange patterns in the answer will surprise, as will the explanation for this phenomenon, promise. 0:00 Intro 1:15 Chapter 1: curious count 9:05 Chapter 2: googol 14:10 Chapter 3: infinite change 28:41 Acknowledgements A very nice Mathematica file created by Andrew Neitsch in 2005 covers pretty much every aspect of change making mathematics. andrew.neitsch.ca/publications/m496pres1.nb Here is a pdf version of this file: andrew.neitsch.ca/publications/m496pres1.nb.pdf What I cover in the last part of this video is pretty much fleshing out and animating the section "Coin change revisited". All this is part of to Andrew's answer to a post on math.stackoverflow stackoverflow.com/questions/1106929/how-to-find-all-combinations-of-coins-when-given-some-dollar-value The visual algebra approach to calculate the number of ways to make change at the very beginning of this video was inspired by this article G. Pólya, On Picture-Writing, Am Math Monthly 63 (1956), 689-697. jstor.org/stable/2309555 Concrete mathematics by Graham, Knuth and Patashnik, the book I mentioned at the end of the video does the whole analysis for the coin set 1, 5, 10, 25, 50 (so no dollar coins). A complete list of all the different ways to make change for a dollar appears in this post maa.org/frank-morgans-math-chat-293-ways-to-make-change-for-a-dollar The book "Generatingfunctionology" by Herbert Wilf, is a great intro to generating functions :) www2.math.upenn.edu/~wilf/DownldGF.html Ron Graham to who this video is dedicated did a couple of videos with Numberphile. So if you'd like to see him in action, check out those videos. A lot of other interesting articles about Ron Graham can be found on his wife's (also a math professor) website. math.ucsd.edu/~fan/ron As usual the music in the video is from the free YouTube audio library: No. 2 Remembering her by Ester Abrami, Morning Mandolin by Chris Haugen, First time experience and T'is the season by Nate Blaze Today's t-shirts: google "only half evil t-shirt". Enjoy! Burkard