Secret of row 10: a new visual key to ancient Pascalian puzzles

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Today's video is about a recent chance discovery (2002) that provides a new beautiful visual key to some hidden self-similar patterns in Pascal's triangle and some naturally occurring patterns on snail shells. Featuring, Sierpinski's triangle, Pascal's triangle, some modular arithmetic and my giant pet snail shell. Thank you very much to Marty for all his help with finetuning the script for this video and to Steve Humble and Erhard Behrends for making some photos available to me. Enjoy! Burkard P.S.: The article I mentioned in this video is: Steve Humble, Erhard Behrends, ”Triangle Mysteries“, The Mathematical Intelligencer 35 (2), 2013, 10-15. There is also a followup article: ”Pyramid Mysteries“, The Mathematical Intelligencer 36 (3), 2014, 14 - 19. And there is a book by Erhard Behrends that has a couple of chapters dedicated to this topic: The Math Behind the Magic: Fascinating Card and Number Tricks and How They Work: https://bookstore.ams.org/mbk-122/ :) A Wolfram demonstration project that implements the 3-color game: http://demonstrations.wolfram.com/TriangleMysteries/ Philip Smolen contributed this animation https://www.trade-ideas.com/home/phil/Triangles/Circles.html Someone pointed out these links to some code wars problems: https://www.codewars.com/kata/coloured-triangles https://www.codewars.com/kata/5a331ea7ee1aae8f24000175 Juan Mir Pieras pointed out these earlier references: http://mathcentral.uregina.ca/mp/archives/previous2000/ (Problem of the month June 2001)(http://mathcentral.uregina.ca/mp/archives/previous2000/june01sol.html) The webpage says the problem is from "Crux Mathematicorum 27:3 (April 2001) pages 204-205 - it is problem 3 from the Ninth Annual Konhauser Problemfest (Carleton College, prepared by David Savitt and Russell Mann." https://www.macalester.edu/mscs/studentopportunities/competitions/konhauserproblemfest/kp2001/ https://cms.math.ca/crux/v27/n3/CRUXv27n3.pdf Today's t-shirt: https://www.teepublic.com/en-au/posters-and-art-prints/5475843-funny-math-i-cant-even

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Published 13 March 2015| Subscribed 527,000| Videos 85


Enter the world of the Mathologer in which beautiful math(s) rules. In real life the Mathologer is a maths professor at Monash University in Melbourne, Australia and goes by the name of Burkard Polster. Check out what other things Burkard is up to at http://www.qedcat.com (Burkard & Marty's Maths Masters site) and http://tinyurl.com/pr9qxgf (Burkard's page at Monash University). The Mathologer channel started out as a joint project of Burkard and video wiz Giuseppe (Gerachitano). In early videos you often hear Giuseppe commenting from behind the camera. Sadly Giuseppe had to leave Melbourne at the end of 2015 which ended his involvement with the channel. Check out Giuseppe's LinkedIn profile at http://goo.gl/O8TURb and his own channel "Peppe Nero Production" at https://www.youtube.com/watch?v=6kneT3RLBPU

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