number theory

The boys are back for season two! They try ramping Pascal's Triangle up a couple of dimensions, consider the physics of how we control volume and attempt to help out someone with a fishy problem. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Pascal's Pyramid Sound Quality Fish Tank Siphoning Show Notes Cuboctohedron Stacking (https://robertlovespi.net/2014/03/25/a-space-filling-pair-of-polyhedra-the-cuboctahedron-and-the-octahedron/) Sphere Packing Systems (https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres?fbclid=IwAR3pUsuDc8I0u-EK8WOeh0C5KgRdgH7XWd1_QoDRx3qTssLVqd9AQI7UPDA) Colouring in Pascal's Triangle in mod 3, 4 and 5 (https://www.maa.org/press/periodicals/loci/joma/patterns-in-pascals-triangle-with-a-twist-first-twist-what-is-it) Sierpinski's Pyramid (https://www.researchgate.net/figure/Ray-tracing-Figure-13-The-Sierpinski-Pyramid_fig2_260126327) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Quasi-analytic classes with respect to logarithmically convex sequences by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys help organise a rugby training scheme, set robots upon an infinite hotel and discover some lovely patterns in the probability of Snakes and Ladders. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Rugby Training Problem Busy Beavers Gamble Shambles Show Notes Articles written by Alaric on Langton's: * Loops (Introduction) (http://www.alaricstephen.com/main-featured/2017/6/27/langtons-loops) * Loops (Evolving) (http://www.alaricstephen.com/main-featured/2017/6/27/improvements-to-langtons-loops) * Ant (http://www.alaricstephen.com/main-featured/2016/12/13/langtons-ant) Busy Beaver on Wikipedia (https://en.wikipedia.org/wiki/Busy_beaver) Noether's Theorem (https://en.wikipedia.org/wiki/Noether%27s_theorem) The Music Episode (http://www.oddsandevenings.com/21) Maths Jam (that you should totally be attending) (https://mathsjam.com/find-a-jam/) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Appreciation of the phrase Busy Beavers by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys celebrate a year of the podcast, try to get a hold on some of the weirder polygonal numbers and debrief after big maths jam. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Trapezium Numbers Shamir's Shared Secrets Vampire and Werewolf Lies Show Notes Catriona Shearer's Geometry Puzzles on Twitter (https://twitter.com/Cshearer41) Mathigon's Tweet about Trapezium Numbers (https://twitter.com/MathigonOrg/status/1070302146632081409?s=09) An Article on Properties of Trapezium Numbers (https://www.hindawi.com/journals/ijmms/2017/4515249/#B4) Alaric's Lock Gates Article (http://www.alaricstephen.com/main-featured/2017/5/1/lock-gates?rq=key) A Good Quality Shamir's Shared Secrets Article (https://ericrafaloff.com/shamirs-secret-sharing-scheme/) The Vampire and Werewolf MAT Question (https://www.cs.ox.ac.uk/admissions/undergraduate/how_to_apply/MAT2015.pdf) The Answers to the MAT Question (https://www.maths.ox.ac.uk/system/files/attachments/websolutions15_1.pdf) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Silver Service at the Vampire-Werewolf Symposium by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys get to the bottom of a neat pattern that suddenly breaks, contort their limbs into strange shapes in the name of Plato and attempt a very satisfying problem involving some spiders and an ant. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Factorial Terminating Digits Making Polyhedra with your Limbs Spiders and an Ant Pursuit Puzzle Show Notes Nice PDF of the Solution to the Partitions Problem by André Malraux (https://ufile.io/twukd) Alaric's Puzzle from the Conference (https://twitter.com/OddsAndEvenings/status/1064153315280330752) Platonic Solids to Stare at during Sections 2 and 3 of the Show (https://upload.wikimedia.org/wikipedia/commons/d/d3/Platonic_solids.jpg) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Fervent attempts to keep on top of responding to emails for the show by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys get as spooky as they can with cellular automata, have a maths conversation about maths conversations and can't get past the fact that Brunnian and Borromean sound too similar. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Zombies and Vampires The Maths of Conversations Brunnian Pumpkin Carving Show Notes Follow Up Maths Jam Annual Gathering Page (https://www.solipsys.co.uk/cgi-bin/MJ_Wiki.py?FrontPage) The Shade (Alex's New Podcast) (https://hacking.finance/read/?c=the-shade) Maths From the Show SIR Model Introduction by Alaric (http://www.alaricstephen.com/main-featured/2016/9/24/modelling-a-pandemic) SIR Model You Can Play With (https://docs.google.com/spreadsheets/d/1HxS1GttDPT8eDOhTIfOYckueArSJjGb5VfOr1hgqLno/edit?usp=sharing) Borromean Rings (https://en.wikipedia.org/wiki/Borromean_rings) Brunnian Links (https://en.wikipedia.org/wiki/Brunnian_link)(more generalised) Pochhammer's Countour (https://en.wikipedia.org/wiki/Pochhammer_contour) A Classic Video on Brunnian Links (https://www.youtube.com/watch?v=heKK95DAKms&ab_channel=Vihart) (in the form of snakes), by Vi Hart Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Following of the brief: bring halloween problems by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys settle a dicussion about a bike that Alaric has been aching to talk about for a fortnight, Alex finally brings up music and then they both dive down the Gödel rabbit hole with some puzzles. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Bike Pedals Time Signatures Taking an Offer Puzzles Show Notes Follow Up Visualisation of the Codepad Solution from Tom Verduyn (https://bl.ocks.org/TVerduyn/raw/4935615ba55a2c0b73b2550e0eb8764d/) Maths Jam Annual Gathering Page (https://www.solipsys.co.uk/cgi-bin/MJ_Wiki.py?FrontPage) The Shade (Alex's New Podcast) (https://hacking.finance/read/?c=the-shade) Maths From the Show Visuals of the Two Cycloids Mentioned: Prolate (http://mathworld.wolfram.com/ProlateCycloid.html) and Curtate (http://mathworld.wolfram.com/CurtateCycloid.html) Video of the Bike Moving (https://twitter.com/SingMathsJam/status/1042057017148334080) Unusual Time Signatures (https://en.wikipedia.org/wiki/List_of_musical_works_in_unusual_time_signatures) Forever Undecided: A Puzzle Guide to Gödel (https://www.amazon.co.uk/Forever-Undecided-Puzzle-Guide-Godel/dp/0192801414) The book I talk about in the third part of the show. It's great. The Gödel Sentence on Wikipedia (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Truth_of_the_Gödel_sentence) (Related to the puzzle) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Incomplete knowledge of incompleteness theorems by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys move seemlessly between high philosophy and pirate jokes in this eclectic episode. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Keypad Code Guessing Platonism vs Formalism Pirate Plunder Puzzle Show Notes Pirate Plunder Puzzle (http://www.alaricstephen.com/main-featured/2017/4/10/the-pirate-puzzle) Prisoners in Rainbow Hats (http://www.alaricstephen.com/main-featured/2017/6/13/prisoners-in-rainbow-hats) Z-Order Curves (https://en.wikipedia.org/wiki/Z-order_curve) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Dreams of being a philosopher pirate by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys try their hands at problems provided by the listeners in today's special episode. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Prisoners in Hats Kaprekar's Constant Generalised Egg Dropping Show Notes Prisoners in Rainbow Hats (http://www.alaricstephen.com/main-featured/2017/6/13/prisoners-in-rainbow-hats) Islander Paradox (http://www.alaricstephen.com/main-featured/2017/4/10/the-islander-paradox) Kaprekar's Constant (https://en.wikipedia.org/wiki/6174_(number)) General Egg Problem Solution (https://stackoverflow.com/questions/11603218/three-egg-problem#) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Too many Hat Problem anecdotes by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys both have problems which involve complicating the process of adding. Also snakes. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed FRACTRAN Negative Bases Polycube Snakes Show Notes FRACTRAN (https://en.wikipedia.org/wiki/FRACTRAN) Adding in Negative Bases (https://en.wikipedia.org/wiki/Negative_base#Addition) Quarter-Imaginary Base (https://en.wikipedia.org/wiki/Quater-imaginary_base) Fascinating Turing Complete Magic the Gathering (https://www.toothycat.net/~hologram/Turing/HowItWorks.html) Article on Polycube Snakes (http://www.alaricstephen.com/main-featured/2017/5/20/polycube-snakes) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Knuth Pronunciation by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

We’re going to play a simple coin-flip game. We take turns flipping a fair coin. The first one to get “heads” wins. You go first. // What’s your chance of winning? // Spiciness: *** out of ****

(Errata alert! This episode was re-uploaded with a correction on Monday March 28 at 10am PST. The corrected version is 6m04s long; the old one is 6m02s. Visit http://www.buzzsprout.com/56982 if your feed contains the old version.) // Here's a game you can play with two fair dice, one red and one green. You throw both dice, and use the throw to generate an infinitely long sequence of numbers, like this: first, you write down the red number. Then you add in the green number, write down the result, add the green again, write down that result, and so on. // You decide to play the game once today. What’s the chance that the sequence made by your dice throw will contain a perfect square? // Spiciness: *** out of ****

John Conway is a prolific mathematician who researches the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Series: "UC Berkeley Graduate Lectures" [Science] [Show ID: 23320]

John Conway is a prolific mathematician who researches the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Series: "UC Berkeley Graduate Lectures" [Science] [Show ID: 23320]