https://www.unexpected-maths.com/blog daily 1.0 2020-07-15 https://www.unexpected-maths.com/blog/2019/6/12/2zldt2ppu9cw3zezr3li3ma0glf093 monthly 0.5 2019-07-31 https://www.unexpected-maths.com/blog/2018/9/11/taking-a-break monthly 0.5 2018-09-15 https://www.unexpected-maths.com/blog/2018/8/22/roll-for-initiative monthly 0.5 2019-01-22 https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534943903336-Q6R316KR4ECSPYHKF5Y8/upload.jpg Blog - Roll For Initiative Please don't sue me, Nintendo. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534945051137-9HFJ47UDJBFYJZD4LF8K/upload.jpg Blog - Roll For Initiative Don't judge my magic abilities or I'll turn you into a "Guess Who?" Character. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534944914292-70CGZ7A8XQKYD8G6101L/upload.jpg Blog - Roll For Initiative The main dice we'll be focusing on. These Wolf dice were a birthday gift from my best friend Lucy. I love this set so much. Note I wrote the d(10•10) the wrong way round- it is important to put the multiplier "inside" the dice indicator. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1535048572869-R45RGASTKDAHGKLMUEEW/Emerald+Dice.jpg Blog - Roll For Initiative As a reward for all this work, have a picture of my fanciest dice. They're made of Emeralds. https://www.unexpected-maths.com/blog/2018/8/22/addendum-code-for-bridging-numbers monthly 0.5 2019-01-22 https://www.unexpected-maths.com/blog/2018/8/9/lattice-embeddable-graphs-some-general-ideas monthly 0.5 2018-09-05 https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534936689734-740VLD9X6L35R5AHAN82/upload.jpg Blog - Lattice Embeddable Graphs- Some general ideas Examples of our current non-embedding criteria.  https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534936746612-GEZWWIAD06FWO2JZ9XJV/upload.jpg Blog - Lattice Embeddable Graphs- Some general ideas The graph 3L(1). Will it embed on L3H? https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534936817456-7NZTTKQ3G7KBR6ZSL8CU/upload.jpg Blog - Lattice Embeddable Graphs- Some general ideas The graph 6L(1{4³}). Does this embed on L3H?  https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534938989257-6D22AO2HJD0HDEQM1692/upload.jpg Blog - Lattice Embeddable Graphs- Some general ideas The Bridging Numbers B¹ₘ(L) for several lattices, calculated by computer code. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534939107874-PKT6MIY30KVL5LKHOVSF/upload.jpg Blog - Lattice Embeddable Graphs- Some general ideas A table of all the information we've discussed (and some we haven't), for various lattices, as well as some wrong avenues I took before arriving at these 4 conditions. Sorry about the quality of the photo. This was the best I could do. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534939181595-YCK2UY7KF5WY5WKCOCRW/upload.jpg Blog - Lattice Embeddable Graphs- Some general ideas Some lattices and their respective numbers of lattice graphs of vertex number n.  https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534936880842-CW6DU6X77S606EI5X5J0/upload.jpg Blog - Lattice Embeddable Graphs- Some general ideas 3 aperiodic, planar lattices of constant connectivity, and 3 periodic, planar lattices of differing connectivity. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1534936923678-W2J678RT3D8QVHXC6041/upload.jpg Blog - Lattice Embeddable Graphs- Some general ideas A lattice without the Planarity condition.  https://www.unexpected-maths.com/blog/2018/8/9/a-multidimensional-complexity-onion monthly 0.5 2018-11-20 https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533835882152-980CHVR83TWB6Z6EVL9I/upload.jpg Blog - A Multidimensional Complexity Onion Our example graph (in black) embedded on L3H (in yellow). Longest chain (graph backbone) coloured in red. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533835945241-T4NVCW5GTSR8LS40PR6H/upload.jpg Blog - A Multidimensional Complexity Onion Our fully labelled graph. While 6(4,5) is also a valid labelling, it is incorrect as 6(2,3) has lower branch numbers overall. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533837143351-FNEC6UUI5TEX1QWUXIXN/upload.png Blog - A Multidimensional Complexity Onion A fully labelled graph of the chemical compound Norbornane. Hopefully it is evident as to why its label is 6L(1{4²}). https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533844333792-4OJJ6WFYN6EVJABKXH7T/upload.jpg Blog - A Multidimensional Complexity Onion Constructing every embeddable graph up to N=6 on L3H (in yellow) by Induction. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533844361745-921ANTCWSSE34K4KZNU5/upload.jpg Blog - A Multidimensional Complexity Onion A table showing the number of lattice embeddable graphs on L3H  up to N=8. https://www.unexpected-maths.com/blog/2018/8/6/brute-force-and-hexes monthly 0.5 2018-08-22 https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533757336553-9Q8VHNARV0OFRMA9ER40/upload.jpg Blog - Brute Force and Hexes A graph in orange. A lattice cell in green. A question arrow in black. Don't worry about the written shorthand for now. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533558907818-1QSTS5IP124FGRB6G83M/upload.jpg Blog - Brute Force and Hexes Three examples of attempted embeddings. Only the top two graphs embed on this lattice (L3H). https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533757422533-8R4972QWJ043KFB2JYC1/upload.jpg Blog - Brute Force and Hexes https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533757499899-QCOPJ5I9GSOC1XUNEJT7/upload.jpg Blog - Brute Force and Hexes Is this an embedding? https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533757567680-TPO82DLD9NUU8U740AAH/upload.jpg Blog - Brute Force and Hexes How about now? https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533560019627-OOGV9MRZ10N1E548QWO7/upload.jpg Blog - Brute Force and Hexes A table of our results so far. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533757632700-P0C4SRGP04697KC6NXCD/upload.jpg Blog - Brute Force and Hexes Checking both 3-vertex graphs... https://www.unexpected-maths.com/blog/2018/8/5/gettin-griddy monthly 0.5 2018-08-16 https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533492882057-GWB66EY41HBVJ9I1JV7V/L4S.jpg Blog - Gettin' Griddy The Infinite Square Lattice, L4S. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533492900868-5OF808VX7O31ZB56VZ7H/L6T.jpg Blog - Gettin' Griddy The Infinite Triangular Lattice, L6T. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533492920927-QRDU6XUNBPE52TKMEJ2E/L5H.jpg Blog - Gettin' Griddy The Infinite Snub Trihexagonal Lattice, L5H. Colours are to show similar regions. I am never drawing this again. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533492969465-5L92TQHQLLP841OX2XJV/Cookie.jpg Blog - Gettin' Griddy That was some heavy maths. Have a cookie. https://www.unexpected-maths.com/blog/2018/8/4/a-numerical-chisel monthly 0.5 2018-08-08 https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533434067695-YTSTY3WJO13XGPCLW53K/upload.jpg Blog - A Numerical Chisel A Kakuro board in the process of being solved. My competed time is 9:35 total, and about 5:32 from this point forward. See if you can beat me! https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533439270701-E40Y3WKLX1LLJQ1OU2ZL/upload.jpg Blog - A Numerical Chisel A picture of Chiselling- breaking a number down into its nonsimilar component parts. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533439331743-R3BZQL8Y0D31NFI2NRRF/upload.jpg Blog - A Numerical Chisel The Chisel Numbers for 1 and 2 boxes. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533439352109-8SJ4ALWSLQOBE4274IV5/upload.jpg Blog - A Numerical Chisel The Completed puzzle from earlier, as I know some of you will want the solution! Also attached is my time to completion :3 https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533439372451-XRDT0Z08DBJTLI0G66AW/upload.jpg Blog - A Numerical Chisel A basic energy level diagram. Yes, I know real quantum particles rarely have 0 energy due to zero-point energy. We can set our energy 0 to be the zero-point energy in these cases, to get the same diagram. It's a common enough procedure that I feel justified doing it here. I'm not your physics teacher! :P https://www.unexpected-maths.com/blog/2018/7/26/the-strangest-construction-manager monthly 0.5 2018-08-23 https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1532726855571-X9DWDLYI5TGVAMUEEWMM/Manager.png Blog - The Strangest Construction Manager He might look something like this. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533001543476-5QVEG6HOO5CKZOJKLVXK/Layouts.png Blog - The Strangest Construction Manager Schematic of possible layouts illustrating the construction rules. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533002676249-CC2ZT6U0T67SQL04WIC3/Not+these+Graphs.png Blog - The Strangest Construction Manager ...Probably most of your reactions right about now. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533004926217-A453NSGYR03MW7CXPV6S/These+Graphs.png Blog - The Strangest Construction Manager 4 kinds of graphs (top left to bottom right): A 5-vertex, 7-edge graph; K4; P5; K3,3. https://images.squarespace-cdn.com/content/v1/5b59ba013c3a5389a263a2f6/1533440437823-6ON6F3STK16LVZEJN0AQ/Mappings.png Blog - The Strangest Construction Manager A couple of examples of our mapping. https://www.unexpected-maths.com/blog/2018/7/26/welcome-to-unexpected-maths monthly 0.5 2018-07-27 https://www.unexpected-maths.com/blog/category/Lattice+Graphs monthly 0.5 https://www.unexpected-maths.com/blog/category/Personal monthly 0.5 https://www.unexpected-maths.com/blog/category/Graph+Theory monthly 0.5 https://www.unexpected-maths.com/blog/category/Coding monthly 0.5 https://www.unexpected-maths.com/blog/category/Dice+Games monthly 0.5 https://www.unexpected-maths.com/blog/category/Probability monthly 0.5 https://www.unexpected-maths.com/blog/category/General monthly 0.5 https://www.unexpected-maths.com/blog/category/Random+Topics monthly 0.5 https://www.unexpected-maths.com/blog/category/Addendums monthly 0.5 https://www.unexpected-maths.com/blog/category/Roleplaying+Games monthly 0.5 https://www.unexpected-maths.com/blog/category/Update monthly 0.5 https://www.unexpected-maths.com/blog/tag/Lattice+Graphs monthly 0.5 https://www.unexpected-maths.com/blog/tag/Statistical+Mechanics monthly 0.5 https://www.unexpected-maths.com/blog/tag/Quantum+Mechanics monthly 0.5 https://www.unexpected-maths.com/blog/tag/Dice+Games monthly 0.5 https://www.unexpected-maths.com/blog/tag/Probability monthly 0.5 https://www.unexpected-maths.com/blog/tag/update monthly 0.5 https://www.unexpected-maths.com/blog/tag/personal monthly 0.5 https://www.unexpected-maths.com/blog/tag/Addendum monthly 0.5 https://www.unexpected-maths.com/blog/tag/Chemistry monthly 0.5 https://www.unexpected-maths.com/blog/tag/Maths+Games monthly 0.5 https://www.unexpected-maths.com/blog/tag/Graph+Theory monthly 0.5 https://www.unexpected-maths.com/blog/tag/Coding monthly 0.5 https://www.unexpected-maths.com/blog/tag/intro monthly 0.5 https://www.unexpected-maths.com/blog/tag/Kakuro monthly 0.5 https://www.unexpected-maths.com/blog/tag/Roleplaying+Games monthly 0.5 https://www.unexpected-maths.com/archive daily 0.75 2018-08-09 https://www.unexpected-maths.com/contact daily 0.75 2018-08-09