Explaining the bizarre pattern in making change for a googol dollars (infinite generating functions)
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. http://andrew.neitsch.ca/publications/m496pres1.nb
Here is a pdf version of this file: https://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 https://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. https://www.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 https://www.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 :) https://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. http://www.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
Видео Explaining the bizarre pattern in making change for a googol dollars (infinite generating functions) канала Mathologer
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. http://andrew.neitsch.ca/publications/m496pres1.nb
Here is a pdf version of this file: https://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 https://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. https://www.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 https://www.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 :) https://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. http://www.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
Видео Explaining the bizarre pattern in making change for a googol dollars (infinite generating functions) канала Mathologer
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
The hardest "What comes next?" (Euler's pentagonal formula)Visualising irrationality with triangular squaresWhy do mirrors flip left and right but not up and down?Why don't they teach this simple visual solution? (Lill's method)A New Way to Look at Fibonacci NumbersIrrational Roots2000 years unsolved: Why is doubling cubes and squaring circles impossible?Toroflux paradox: making things (dis)appear with mathFermat's Christmas theorem: Visualising the hidden circle in pi/4 = 1-1/3+1/5-1/7+...New Reuleaux Triangle MagicWhat does this prove? Some of the most gorgeous visual "shrink" proofs ever inventedPower sum MASTER CLASS: How to sum quadrillions of powers ... by hand! (Euler-Maclaurin formula)Secret of row 10: a new visual key to ancient Pascalian puzzlesThe ARCTIC CIRCLE THEOREM or Why do physicists play dominoes?Times Tables, Mandelbrot and the Heart of MathematicsEuler's and Fermat's last theorems, the Simpsons and CDC6600The ultimate algorithmEuler's crazy pi formula generatorLiouville's number, the easiest transcendental and its clones (corrected reupload)