2026-02-18T08:09:56Z https://njump.me Interesting Esoterica https://njump.me/npub17uhxgsq9cvkhtsnt2mj7uvgdux7r69djh04l9r6svth4lapjnusqsefv3h https://media.mathstodon.xyz/accounts/avatars/000/000/556/original/09c5f35c36501799.png https://media.mathstodon.xyz/accounts/avatars/000/000/556/original/09c5f35c36501799.png https://njump.me/nevent1qqsz3lr2s8cy5uc3sjkpksyvl6t28sr9m0vk8f05e2ulgd6jy4hkjvqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqldm468 On sphere-filling ropes<br/>Article by Gerlach, Henryk and von der Mosel, Heiko<br/>In collections: Easily explained, Geometry, Fun maths facts<br/>What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope&#39;s thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are...<br/>URL: <a href="http://arxiv.org/abs/1005.4609">http://arxiv.org/abs/1005.4609</a><br/>PDF: <a href="http://arxiv.org/pdf/1005.4609v1">http://arxiv.org/pdf/1005.4609v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Gerlach2010">https://read.somethingorotherwhatever.com/entry/Gerlach2010</a> 2026-02-18T07:58:10Z https://njump.me/nevent1qqsfhlsdglxzpgahvkpxffcuf0mxwnm0dvhc0nn9fz3r9zknlfa7ysqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqj95r0e Music: a Mathematical Offering<br/>Book by Dave Benson<br/>In collection: Music<br/>URL: <a href="https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html">https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/item46">https://read.somethingorotherwhatever.com/entry/item46</a> 2026-02-10T07:58:03Z https://njump.me/nevent1qqs2vf2n4gqj84eesuzjpr5zx7fkty979psaeg2zzcdgkgjy2uesv3szyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq6rhy0y The top ten prime numbers<br/>Article by Dubner, H<br/>In collections: Easily explained, Lists and catalogues, Integerology<br/>URL: <a href="http://primes.utm.edu/lists/top_ten/topten.pdf">http://primes.utm.edu/lists/top_ten/topten.pdf</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Dubner2001">https://read.somethingorotherwhatever.com/entry/Dubner2001</a> 2026-02-08T07:58:06Z https://njump.me/nevent1qqs0l04m3zgrvcswg7y0664gp57emkk3y0xwztr3fvnmqs7gp5950fgzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqlqfl9s New entry!<br/>The Extraordinary Power of Division in Straight Line Programs<br/>Article by Peter Borwein and Joe Hobart<br/>In collections: Fun maths facts, Integerology<br/>A lovely circle of ideas due primarily to Shub, Smale and Shamir says that if it is possible to divide quickly, then it is possible to factor quickly. Here, dividing quickly means modular division over a straight line program. In this context, quickly means actual computations...<br/>URL: <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.119.07.584?seq=3">https://www.jstor.org/stable/10.4169/amer.math.monthly.119.07.584?seq=3</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/TheExtraordinaryPowerofDivisioninStraightLinePrograms">https://read.somethingorotherwhatever.com/entry/TheExtraordinaryPowerofDivisioninStraightLinePrograms</a> 2026-02-06T14:14:02Z https://njump.me/nevent1qqspc3jar04shypqz2e94ht70r8c8v5et6grf6j2zfsa27c9cyhf4sgzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqnpg8z0 New entry!<br/>A formula for any real number, maybe<br/>Article by James E. Hanson and Connor Watson<br/>In collections: Animals, Attention-grabbing titles, Fun maths facts<br/>We discuss how to write down three specific natural numbers \(A\), \(B\), \(C\) such that for any real number \(r\) you&#39;ve probably ever thought of, it is consistent with \(\mathsf{ZFC}\) set theory that...<br/>URL: <a href="https://arxiv.org/abs/2602.02384v1">https://arxiv.org/abs/2602.02384v1</a><br/>PDF: <a href="https://arxiv.org/pdf/2602.02384v1">https://arxiv.org/pdf/2602.02384v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Aformulaforanyrealnumbermaybe">https://read.somethingorotherwhatever.com/entry/Aformulaforanyrealnumbermaybe</a> 2026-02-05T14:30:14Z https://njump.me/nevent1qqsqrh6zlk6pj5wms562nyphpjmkczcfvrfcgltauut8ucve2l6mq3czyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqk4uy7f New entry!<br/>Optimal play in &#39;Guess Who?&#39;<br/>Article by David Cushing and Stuart Gipp and Ezra Levick and Em Rickinson and David I. Stewart<br/>In collections: Games to play with friends, Protocols and strategies<br/>We prove an optimal strategy for the children&#39;s game Guess Who? assuming the official rules are in use and that both players ask `classical&#39; questions with a bipartite response. Applying a technique...<br/>URL: <a href="https://arxiv.org/abs/2508.00799v3">https://arxiv.org/abs/2508.00799v3</a><br/>PDF: <a href="https://arxiv.org/pdf/2508.00799v3">https://arxiv.org/pdf/2508.00799v3</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/OptimalplayinGuessWho">https://read.somethingorotherwhatever.com/entry/OptimalplayinGuessWho</a> 2026-01-28T14:19:20Z https://njump.me/nevent1qqs2xvudey8ykype0n8wdat3k6c0urzw7qxkh7x5na96tn6ufx6sstqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqvs2z34 New entry!<br/>Classical billiards can compute<br/>Article by Eva Miranda and Isaac Ramos<br/>In collection: Unusual computers<br/>We show that two-dimensional billiard systems are Turing complete by encoding their dynamics within the framework of Topological Kleene Field Theory. Billiards serve as idealized models of particle motion with elastic reflections and arise naturally as limits of smooth Hamiltonian systems...<br/>URL: <a href="https://arxiv.org/abs/2512.19156v2">https://arxiv.org/abs/2512.19156v2</a><br/>PDF: <a href="https://arxiv.org/pdf/2512.19156v2">https://arxiv.org/pdf/2512.19156v2</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Classicalbilliardscancompute">https://read.somethingorotherwhatever.com/entry/Classicalbilliardscancompute</a> 2026-01-12T14:51:05Z https://njump.me/nevent1qqsq2eq092kvdu7hd4cffu5wpsawpp3n0584269u7dvgmehpdjt5c2czyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqdet8nr Every natural number is the sum of forty-nine palindromes<br/>Article by William D. Banks<br/>In collections: Fun maths facts, Integerology<br/>It is shown that the set of decimal palindromes is an additive basis for the natural numbers. Specifically, we prove that every natural number can be expressed as the sum of forty-nine (possibly zero) decimal palindromes.<br/>URL: <a href="http://arxiv.org/abs/1508.04721v1">http://arxiv.org/abs/1508.04721v1</a><br/>PDF: <a href="http://arxiv.org/pdf/1508.04721v1">http://arxiv.org/pdf/1508.04721v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Everynaturalnumberisthesumoffortyninepalindromes">https://read.somethingorotherwhatever.com/entry/Everynaturalnumberisthesumoffortyninepalindromes</a> 2026-01-05T07:58:04Z https://njump.me/nevent1qqs92smjxpz0n59yklyz2tr0tj2s5930pay99zeuep7yt8uhzdcqsaszyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqxlrqva Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers<br/>Article by Martin Erik Horn<br/>In collections: Attention-grabbing titles, Fibonaccinalia<br/>The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal...<br/>URL: <a href="http://arxiv.org/abs/0711.4030v1">http://arxiv.org/abs/0711.4030v1</a><br/>PDF: <a href="http://arxiv.org/pdf/0711.4030v1">http://arxiv.org/pdf/0711.4030v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/PauliPascalPyramidsPauliFibonacciNumbersandPauliJacobsthalNumbers">https://read.somethingorotherwhatever.com/entry/PauliPascalPyramidsPauliFibonacciNumbersandPauliJacobsthalNumbers</a> 2025-12-30T07:58:05Z https://njump.me/nevent1qqsx6q3p4autggtc4gndqyqeq5nj4l49nq5er5jxwh28kpsx2dtzyxqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq3390ay Pancake Flipping is Hard<br/>Article by Bulteau, Laurent and Fertin, Guillaume and Rusu, Irena<br/>In collections: Attention-grabbing titles, Puzzles, Basically computer science, Easily explained, Food<br/>Pancake Flipping is the problem of sorting a stack of pancakes of different sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to flip the pancakes...<br/>URL: <a href="http://arxiv.org/abs/1111.0434">http://arxiv.org/abs/1111.0434</a><br/>PDF: <a href="http://arxiv.org/pdf/1111.0434v2">http://arxiv.org/pdf/1111.0434v2</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Bulteau2011">https://read.somethingorotherwhatever.com/entry/Bulteau2011</a> 2025-12-24T07:58:04Z https://njump.me/nevent1qqs0vyy4xw2mhkjjsj5aw9hjd063t0d5kl48c9fq7p8narlq7jz7dpszyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqeg0z9n New entry!<br/>The Census of Mathematical Notations<br/>Article by Abdelshafi Bekhit and Paul Libbrecht<br/>In collections: Lists and catalogues, Notation and conventions<br/>This is the home of the notation census which aims at a list of mathematical notations around the world.<br/>URL: <a href="https://notations.hoplahup.net/Census/">https://notations.hoplahup.net/Census/</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/TheCensusofMathematicalNotations">https://read.somethingorotherwhatever.com/entry/TheCensusofMathematicalNotations</a> 2025-12-10T16:01:38Z https://njump.me/nevent1qqsvl2xhgxy7h8ujyewt8n0n52dt0kjmzxy3ffe083432p6dw6zurrqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqkzvpkf Any Monotone Boolean Function Can Be Realized by Interlocked Polygons<br/>Article by Erik D. Demaine and Martin L. Demaine and Ryuhei Uehara<br/>In collections: Basically computer science, Easily explained, Geometry, Fun maths facts<br/>We show how to construct interlocked collections of simple polygons in the plane that fall apart upon removing certain combinations of pieces. Precisely, interior-disjoint simple...<br/>URL: <a href="http://erikdemaine.org/papers/InterlockedPolygons_CCCG2010/">http://erikdemaine.org/papers/InterlockedPolygons_CCCG2010/</a><br/>PDF: <a href="http://erikdemaine.org/papers/InterlockedPolygons_CCCG2010/paper.pdf">http://erikdemaine.org/papers/InterlockedPolygons_CCCG2010/paper.pdf</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/AnyMonotoneBooleanFunctionCanBeRealizedByInterlockedPolygons">https://read.somethingorotherwhatever.com/entry/AnyMonotoneBooleanFunctionCanBeRealizedByInterlockedPolygons</a> 2025-12-03T06:25:10Z https://njump.me/nevent1qqsdxurmjxtega4gvp3s60crh8ytz0x0nr5rpph6w20fcjdzxd73k9qzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq94j29e New entry!<br/>Notation as a Tool of Thought<br/>Article by Kenneth E. Iverson<br/>In collection: Notation and conventions<br/>The thesis of the present paper is that the advantages of executability and universality found in programming languages can be effectively combined, in a single coherent language, with the advantages offered by mathematical notation. <br/>URL: <a href="https://www.jsoftware.com/papers/tot.htm">https://www.jsoftware.com/papers/tot.htm</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/NotationasaToolofThought">https://read.somethingorotherwhatever.com/entry/NotationasaToolofThought</a> 2025-11-26T14:59:30Z https://njump.me/nevent1qqsqkcgt45ea0wnv90gu0wrm60dra7ty6006nyedu68ffqflwfvepsczyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq6q4lz8 On a curious property of 3435<br/>Article by Berkel, Daan Van<br/>In collections: Easily explained, Fun maths facts, Integerology<br/>Folklore tells us that there are no uninteresting natural numbers. But some natural numbers are more interesting then others. In this article we will explain why 3435 is one of the more interesting natural numbers around. We will show that 3435 is a Munchausen number in base 10, and...<br/>URL: <a href="http://arxiv.org/abs/0911.3038">http://arxiv.org/abs/0911.3038</a><br/>PDF: <a href="http://arxiv.org/pdf/0911.3038v2">http://arxiv.org/pdf/0911.3038v2</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Berkel2009">https://read.somethingorotherwhatever.com/entry/Berkel2009</a> 2025-11-22T06:25:09Z https://njump.me/nevent1qqsyasrpswlvdsydp80n9c2dpszxlagdsknluncu3ujpahxz08qxv8gzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqgdfu08 Сетунь ВС (Setun Web Simulator)<br/>Software by Trinarygroup<br/>In collections: Basically computer science, History, Unusual computers<br/>URL: <a href="http://trinary.ru/projects/setunws/">http://trinary.ru/projects/setunws/</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/SetunSimulator">https://read.somethingorotherwhatever.com/entry/SetunSimulator</a> 2025-11-11T06:25:10Z https://njump.me/nevent1qqs8dmq66dkjg8ja6ealnkdtgd7e6yz6tn8zmfacsmj3hp0gdsh9fmqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqhkpezm There are not Exactly Five Objects<br/>Article by Andreas Blass<br/>In collection: Attention-grabbing titles<br/>The purpose of this note is to present a solution to a problem posed informally by A. Wilkie at the 1977 ASL meeting in Wrocław: Formulate &#34;the cardinality of the universe is not exactly five&#34; as a Horn sentence. Although this solution is not new -- I found it and M. Morley found another solution during the same meeting -- continuing...<br/>URL: <a href="https://www.jstor.org/stable/2274177?seq=1#metadata_info_tab_contents">https://www.jstor.org/stable/2274177?seq=1#metadata_info_tab_contents</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/TherearenotExactlyFiveObjects">https://read.somethingorotherwhatever.com/entry/TherearenotExactlyFiveObjects</a> 2025-11-06T06:25:06Z https://njump.me/nevent1qqsfa0cuw5mq0wh7nffnd9rlhmuz3lv2mp0g4gck4l49p3xhrgvdv6gzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqyrjj6n Quotients Homophones des Groupes Libres Homophonic Quotients of Free Groups<br/>Article by Washington, Lawrence and Zagier, Don<br/>In collections: Easily explained, The groups group<br/>URL: <a href="http://people.mpim-bonn.mpg.de/zagier/files/exp-math-2/fulltext.pdf">http://people.mpim-bonn.mpg.de/zagier/files/exp-math-2/fulltext.pdf</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Washington1986">https://read.somethingorotherwhatever.com/entry/Washington1986</a> 2025-11-03T06:25:09Z https://njump.me/nevent1qqs867vwqwtmdwaep6e0tnkun59s9u0v9kmpwz27d0ue4a09q6yfwtczyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq5n3u7g Tiling with Three Polygons is Undecidable<br/>Article by Erik D. Demaine and Stefan Langerman<br/>In collections: Basically computer science, Easily explained, Fun maths facts, Geometry<br/>We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding...<br/>URL: <a href="http://arxiv.org/abs/2409.11582v1">http://arxiv.org/abs/2409.11582v1</a><br/>PDF: <a href="http://arxiv.org/pdf/2409.11582v1">http://arxiv.org/pdf/2409.11582v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/TilingwithThreePolygonsisUndecidable">https://read.somethingorotherwhatever.com/entry/TilingwithThreePolygonsisUndecidable</a> 2025-11-01T06:25:09Z https://njump.me/nevent1qqsrmwv5xdv04e5k3tcuhrtc7dcj30pslfkfpt7grp90te0w685s6pszyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqpj80lh Actegories for the Working Amthematician<br/>Article by Matteo Capucci and Bruno Gavranović<br/>In collection: Attention-grabbing titles<br/>Actions of monoidal categories on categories, also known as actegories, have been familiar to category theorists for a long time, and yet a comprehensive overview of this topic seems to be missing from the literature. Recently, actegories have been increasingly employed in...<br/>URL: <a href="http://arxiv.org/abs/2203.16351v3">http://arxiv.org/abs/2203.16351v3</a><br/>PDF: <a href="http://arxiv.org/pdf/2203.16351v3">http://arxiv.org/pdf/2203.16351v3</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/ActegoriesfortheWorkingAmthematician">https://read.somethingorotherwhatever.com/entry/ActegoriesfortheWorkingAmthematician</a> 2025-10-27T06:25:14Z https://njump.me/nevent1qqswks4z4ecf0zpu5yyr00xswrltrk28g8zpujzvtpecd236jxmce6szyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq84ev9w An unusual cubic representation problem<br/>Article by Andrew Bremner and Allan Macleod<br/>In collection: Puzzles<br/>For a non-zero integer \(N\), we consider the problem of finding \(3\) integers \( (a, b, c) \) such that \[ N = \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}. \] We show that the existence of solutions is related to points of infinite order on a family of elliptic curves. We discuss strictly positive solutions and prove the...<br/>URL: <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_43_from29to41.pdf">http://ami.ektf.hu/uploads/papers/finalpdf/AMI_43_from29to41.pdf</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/AnUnusualCubicRepresentationProblem">https://read.somethingorotherwhatever.com/entry/AnUnusualCubicRepresentationProblem</a> 2025-10-26T06:25:09Z https://njump.me/nevent1qqstm9q5lv76kqklzgc4ujwjrmdkutkuhuk4xs60jamahfa5xezgulszyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqw2y09p Every natural number is the sum of forty-nine palindromes<br/>Article by William D. Banks<br/>In collections: Fun maths facts, Integerology<br/>It is shown that the set of decimal palindromes is an additive basis for the natural numbers. Specifically, we prove that every natural number can be expressed as the sum of forty-nine (possibly zero) decimal palindromes.<br/>URL: <a href="http://arxiv.org/abs/1508.04721v1">http://arxiv.org/abs/1508.04721v1</a><br/>PDF: <a href="http://arxiv.org/pdf/1508.04721v1">http://arxiv.org/pdf/1508.04721v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Everynaturalnumberisthesumoffortyninepalindromes">https://read.somethingorotherwhatever.com/entry/Everynaturalnumberisthesumoffortyninepalindromes</a> 2025-10-15T05:25:09Z https://njump.me/nevent1qqs0dchdry3yc7mr08yc9r4m9sy0en4azwryms2q9743dwla3re0aagzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqtc8rgf Look, There&#39;s More to Say about Conway&#39;s Look and Say Sequence<br/>Article by Greg Dresden and Jacob Siehler<br/>In collections: Easily explained, Fun maths facts<br/>We take Conway&#39;s Look and Say Sequence into a base-3 world, and we discover that there are only 24 interesting and irreducible sequences in base 3.<br/>URL: <a href="http://arxiv.org/abs/2405.11103v1">http://arxiv.org/abs/2405.11103v1</a><br/>PDF: <a href="http://arxiv.org/pdf/2405.11103v1">http://arxiv.org/pdf/2405.11103v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/LookTheresMoretoSayaboutConwaysLookandSaySequence">https://read.somethingorotherwhatever.com/entry/LookTheresMoretoSayaboutConwaysLookandSaySequence</a> 2025-10-10T05:25:12Z https://njump.me/nevent1qqspfsqg2pd5gg2ptj0yjzcvm28xnjynvf9gf4dk4na7k98q7pprstczyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq7jj2hd Fibbinary Zippers in a Monoid of Toroidal Hamiltonian Cycles that Generate Hilbert-Style Square-Filling Curves<br/>Article by Douglas M. McKenna<br/>In collections: Art, Combinatorics, Fibonaccinalia, Things to make and do<br/>Within the recursive subdivision of the \(n \times n\) square, what characterizes a Hilbert-style space-filling curve motif of length \(n^2\) when—under iterated, self-similar, pure edge-replacement—a sequence of always...<br/>URL: <a href="http://ecajournal.haifa.ac.il/Volume2022/ECA2022_S2A13.pdf">http://ecajournal.haifa.ac.il/Volume2022/ECA2022_S2A13.pdf</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/FibbinaryZippers">https://read.somethingorotherwhatever.com/entry/FibbinaryZippers</a> 2025-10-04T05:25:37Z https://njump.me/nevent1qqsfvk7y9gexyqfh7n7rw5knsxvz5al6smsrurefatu258kem3hd5lszyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqqd85lg The Bulgarian solitaire and the mathematics around it<br/>Article by Vesselin Drensky<br/>In collections: Easily explained, Games to play with friends, History, Puzzles<br/>The Bulgarian solitaire is a mathematical card game played by one person. A pack of \(n\) cards is divided into several decks (or &#34;piles&#34;). Each move consists of the removing of one card from each deck and collecting the removed cards to form a...<br/>URL: <a href="http://arxiv.org/abs/1503.00885v1">http://arxiv.org/abs/1503.00885v1</a><br/>PDF: <a href="http://arxiv.org/pdf/1503.00885v1">http://arxiv.org/pdf/1503.00885v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/TheBulgariansolitaireandthemathematicsaroundit">https://read.somethingorotherwhatever.com/entry/TheBulgariansolitaireandthemathematicsaroundit</a> 2025-09-30T05:25:06Z https://njump.me/nevent1qqstwnhrc3hzgthh42gh580c8m4k0zkx0z8ufaxql6gl66dqs93w4rgzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqvl34z9 New entry!<br/>The Rubik&#39;s Cube Perfect Scramble<br/>Article by Bryan Wolf<br/>In collections: Fun maths facts, The groups group<br/>I was playing with my son’s Rubik’s Cubes and tried to scramble a cube randomly so that no two squares with the same color were side by side. But I wanted a scramble that looked like a random scramble.<br/>URL: <a href="https://www.solutionslookingforproblems.com/post/the-rubik-s-cube-perfect-scramble">https://www.solutionslookingforproblems.com/post/the-rubik-s-cube-perfect-scramble</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/TheRubiksCubePerfectScramble">https://read.somethingorotherwhatever.com/entry/TheRubiksCubePerfectScramble</a> 2025-08-20T07:55:05Z https://njump.me/nevent1qqszm84wm988ejnxlr9c36l6yezczed28azahhj7uktufujuuwjfyfczyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq40j2q5 ‘Knowable&#39; As ‘Known After an Announcement&#39;<br/>Article by Balbiani, Philippe and Baltag, Alexandru and Ditmarsch, Hans Van and Herzig, Andreas and Hoshi, Tomohiro and De Lima, Tiago<br/>URL: <a href="http://www.journals.cambridge.org/abstract_S1755020308080210">http://www.journals.cambridge.org/abstract_S1755020308080210</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Balbiani2008">https://read.somethingorotherwhatever.com/entry/Balbiani2008</a> 2025-08-18T05:25:13Z https://njump.me/nevent1qqsyhlqa2v8h2x5d7hymj4k5jumg97vcwa2d68942jnw36nj0nqq5wgzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqc695lh The Amazing \(3^n\) Theorem and its even more Amazing Proof [Discovered by Xavier G. Viennot and his École Bordelaise gang]<br/>Article by Doron Zeilberger<br/>In collections: Attention-grabbing titles, Combinatorics, Fun maths facts, Things to make and do<br/>The most amazing (at least to me) result in Enumerative Combinatorics is Dominique Gouyou-Beauchamps and Xavier Viennot&#39;s theorem that states that the...<br/>URL: <a href="http://arxiv.org/abs/1208.2258v1">http://arxiv.org/abs/1208.2258v1</a><br/>PDF: <a href="http://arxiv.org/pdf/1208.2258v1">http://arxiv.org/pdf/1208.2258v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/TheAmazing3nTheoremanditsevenmoreAmazingProofDiscoveredbyXavierGViennotandhiscoleBordelaisegang">https://read.somethingorotherwhatever.com/entry/TheAmazing3nTheoremanditsevenmoreAmazingProofDiscoveredbyXavierGViennotandhiscoleBordelaisegang</a> 2025-08-17T05:25:06Z https://njump.me/nevent1qqsd8cxns9dt8yn97wq4urzxcxzzr6xltdgvlxhareds9acq3m9ekmczyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqmz2uec Neumbering<br/>Article by O.G. Cassani and John H. Conway<br/>In collections: Easily explained, Notation and conventions<br/>The importance of starting at 0 when counting has not often been discussed, nor has the incompatibility between this way of numbering and the usual adjectives first, second, third ... In fact, if the first number is zero, then the fifth is four and the ninth is eight, which is perfectly coherent with the traditional...<br/>URL: <a href="https://link.springer.com/article/10.1007/s00283-017-9720-3">https://link.springer.com/article/10.1007/s00283-017-9720-3</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Neumbering">https://read.somethingorotherwhatever.com/entry/Neumbering</a> 2025-08-14T05:25:07Z https://njump.me/nevent1qqspe2kt9q5qqsv9yap6u69s2az0sarx4zu5zg6zdjqtdledusx86gqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqja82af Markets are efficient if and only if P = NP<br/>Article by Maymin, PZ<br/>In collection: Computational complexity of games<br/> I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse...<br/>URL: <a href="https://arxiv.org/abs/1002.2284">https://arxiv.org/abs/1002.2284</a><br/>PDF: <a href="https://arxiv.org/pdf/1002.2284">https://arxiv.org/pdf/1002.2284</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Maymin2011">https://read.somethingorotherwhatever.com/entry/Maymin2011</a> 2025-08-09T05:25:06Z https://njump.me/nevent1qqsr9ke4f4489wswyh8c9xmtwm938zx0kest39l6vvnhmuphcx6kl7gzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqpn8rcc The paramagnetic and glass transitions in sudoku<br/>Article by Williams, Alex and Ackland, Graeme . J.<br/>In collection: Basically physics<br/>We study the statistical mechanics of a model glassy system based on a familiar and popular mathematical puzzle. Sudoku puzzles provide a very rare example of a class of frustrated systems with a unique groundstate without symmetry. Here, the puzzle is recast as...<br/>URL: <a href="http://arxiv.org/abs/1212.1649">http://arxiv.org/abs/1212.1649</a><br/>PDF: <a href="http://arxiv.org/pdf/1212.1649v1">http://arxiv.org/pdf/1212.1649v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Williams2012">https://read.somethingorotherwhatever.com/entry/Williams2012</a> 2025-08-05T05:25:06Z https://njump.me/nevent1qqsg0k6yep8q80cenm3kp9ep9e840jv206rcmtmkplm5vlquw99ue9szyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqu5tss4 Check Digits<br/>Web page by Jonathan Mohr<br/>In collections: Basically computer science, Easily explained, Fun maths facts, Unusual arithmetic<br/>A decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.<br/>URL: <a href="https://web.archive.org/web/20230204135539/http://www.augustana.ualberta.ca/~mohrj/algorithms/checkdigit.html">https://web.archive.org/web/20230204135539/http://www.augustana.ualberta.ca/~mohrj/algorithms/checkdigit.html</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/CheckDigits">https://read.somethingorotherwhatever.com/entry/CheckDigits</a> 2025-07-26T05:25:08Z https://njump.me/nevent1qqs8xv6ayww7pm4dnac3txzg6xh8nsnvpv36k98xf7n8e5tz0alq46qzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqs78jny How Not to Compute a Fourier Transform<br/>Article by J. A. Grzesik<br/>In collections: Attention-grabbing titles, The act of doing maths<br/>We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate second order differential equation, one of...<br/>URL: <a href="http://arxiv.org/abs/2001.11987v3">http://arxiv.org/abs/2001.11987v3</a><br/>PDF: <a href="http://arxiv.org/pdf/2001.11987v3">http://arxiv.org/pdf/2001.11987v3</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/HowNottoComputeaFourierTransform">https://read.somethingorotherwhatever.com/entry/HowNottoComputeaFourierTransform</a> 2025-07-13T05:25:07Z https://njump.me/nevent1qqs02sta32rqz3vr0cwxwj3zhjk9gp8klxrtdljqljkyp2n8fyksgqqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqyl08sa London Calling Philosophy and Engineering: WPE 2008<br/>Article by Glen Miller<br/>URL: <a href="http://www.ncbi.nlm.nih.gov/pubmed/19543813">http://www.ncbi.nlm.nih.gov/pubmed/19543813</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/item13">https://read.somethingorotherwhatever.com/entry/item13</a> 2025-06-25T05:25:11Z https://njump.me/nevent1qqsznddgv37s68lq82xzf8nc6xptwtwkgafgtmv0xrc69cvc93c402szyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqxt6lr7 Solving Differential Equations by Symmetry Groups<br/>Article by John Starret<br/>URL: <a href="https://www.jstor.org/stable/27642331">https://www.jstor.org/stable/27642331</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/item36">https://read.somethingorotherwhatever.com/entry/item36</a> 2025-06-18T05:25:04Z https://njump.me/nevent1qqs07tmqef06ufl9zv5t60yexuz5cgm4tcfqed234tae6s5dadde7wgzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqhy2lls Mathematical proofs with cardboard and paper<br/>Article by Arnaldo Gunzi and Ernée Kozyroff Filho<br/>In collections: About proof, Things to make and do<br/>In this tutorial, we&#39;ll show visual mathematical proofs using cardboard and paper. This ludic technique is especially good for children. These math proofs are like puzzles, and, best of all, you can do it yourself, at home.<br/>URL: <a href="https://github.com/asgunzi/Math_proofs_cardboard_paper">https://github.com/asgunzi/Math_proofs_cardboard_paper</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/asgunziMathproofscardboardpaperMathematicalartwithpaperandcardboard">https://read.somethingorotherwhatever.com/entry/asgunziMathproofscardboardpaperMathematicalartwithpaperandcardboard</a> 2025-06-12T05:25:17Z https://njump.me/nevent1qqsqlszvl8e5k0t886rlscenc24uz75upmrnh63dzmdd2m2n0wclttqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqdf3ptg The Amazing \(3^n\) Theorem and its even more Amazing Proof [Discovered by Xavier G. Viennot and his École Bordelaise gang]<br/>Article by Doron Zeilberger<br/>In collections: Attention-grabbing titles, Combinatorics, Fun maths facts, Things to make and do<br/>The most amazing (at least to me) result in Enumerative Combinatorics is Dominique Gouyou-Beauchamps and Xavier Viennot&#39;s theorem that states that the...<br/>URL: <a href="http://arxiv.org/abs/1208.2258v1">http://arxiv.org/abs/1208.2258v1</a><br/>PDF: <a href="http://arxiv.org/pdf/1208.2258v1">http://arxiv.org/pdf/1208.2258v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/TheAmazing3nTheoremanditsevenmoreAmazingProofDiscoveredbyXavierGViennotandhiscoleBordelaisegang">https://read.somethingorotherwhatever.com/entry/TheAmazing3nTheoremanditsevenmoreAmazingProofDiscoveredbyXavierGViennotandhiscoleBordelaisegang</a> 2025-06-10T05:25:04Z https://njump.me/nevent1qqs23z23yxzz0mzc7qkvwn2xtd8067mkzmep0ulrfjdwqqzmx607hxczyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqlyq0j6 Wolstenholme&#39;s theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862--2012)<br/>Article by Mestrovic, Romeo<br/>In collections: History, Integerology<br/>In 1862 Wolstenholme proved that for any prime \(p\ge 5\) the numerator of the fraction \(\) 1+\frac 12 +\frac 13+...+\frac{1}{p-1} \(\) written in reduced form is divisible by \(p^2\), \((2)\) and the numerator of the fraction...<br/>URL: <a href="http://arxiv.org/abs/1111.3057">http://arxiv.org/abs/1111.3057</a><br/>PDF: <a href="http://arxiv.org/pdf/1111.3057v2">http://arxiv.org/pdf/1111.3057v2</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Mestrovic2011">https://read.somethingorotherwhatever.com/entry/Mestrovic2011</a> 2025-06-09T05:25:07Z https://njump.me/nevent1qqsrq8kelvgt5vdn8tc9hakpgwege89n6tnk0uhw48z03cx3sd8p6wczyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqujzxpp Lyons Taming<br/>Article by Wolfram Neutsch<br/>In collections: Animals, The groups group<br/>Based on Kantor&#39;s geometry, we give a new Highly symmetric construction of Lyons&#39; sporadic simple group \(Ly\) via its minimal representation over \(\mathbb F_5^{111}\), thus obtaining elementary existence proofs for both the group and the representation at one stroke.<br/>URL: <a href="http://arxiv.org/abs/2307.11399v1">http://arxiv.org/abs/2307.11399v1</a><br/>PDF: <a href="http://arxiv.org/pdf/2307.11399v1">http://arxiv.org/pdf/2307.11399v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/LyonsTaming">https://read.somethingorotherwhatever.com/entry/LyonsTaming</a> 2025-06-01T05:25:07Z https://njump.me/nevent1qqsxw0q29q4clzyka9v6hwg7jzkpudfeggm9ek6kwwfevpmrmxnz38gzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqrqwj8w Best Laid Plans of Lions and Men<br/>Article by Mikkel Abrahamsen and Jacob Holm and Eva Rotenberg and Christian Wulff-Nilsen<br/>In collections: Attention-grabbing titles, Protocols and strategies, Animals, Fun maths facts<br/>We answer the following question dating back to J.E. Littlewood (1885 - 1977): Can two lions catch a man in a bounded area with rectifiable lakes? The lions and the man are all assumed to...<br/>URL: <a href="http://arxiv.org/abs/1703.03687v1">http://arxiv.org/abs/1703.03687v1</a><br/>PDF: <a href="http://arxiv.org/pdf/1703.03687v1">http://arxiv.org/pdf/1703.03687v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/BestLaidPlansofLionsandMen">https://read.somethingorotherwhatever.com/entry/BestLaidPlansofLionsandMen</a> 2025-05-31T05:25:06Z https://njump.me/nevent1qqsy5w2ekxrztqx9mxacqud339lln57ml3qf9egsvwzuz6vqe6kpepczyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqysz5l8 World&#39;s shortest explanation of Gödel&#39;s theorem<br/>Article by Mark Dominus<br/>In collections: About proof, Attention-grabbing titles, Easily explained, Fun maths facts<br/>A while back I started writing up an article titled &#34;World&#39;s shortest explanation of Gödel&#39;s theorem&#34;. But I didn&#39;t finish it, and later I encountered Raymond Smullyan&#39;s version, which is much shorter anyway. So here, shamelessly stolen from Smullyan, is the World&#39;s...<br/>URL: <a href="https://blog.plover.com/math/Gdl-Smullyan.html">https://blog.plover.com/math/Gdl-Smullyan.html</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/WorldsshortestexplanationofGdelstheorem">https://read.somethingorotherwhatever.com/entry/WorldsshortestexplanationofGdelstheorem</a> 2025-05-19T05:25:09Z https://njump.me/nevent1qqs865yr6fn2ss4hguz775fdvtnx2ufqwy053stvx64dl06lq8gn8mszyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq3f0gq6 On Some two way Classifications of Integers<br/>Article by J. Lambek and L. Moser<br/>In collections: Fun maths facts, Integerology<br/>In this note we use the method of generating functions to show that there is a unique way of splitting the non-negative integers into two classes in such a way that the sums of pairs of distinct integers will be the same (with same multiplicities) for both classes. We prove a...<br/>URL: <a href="https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/on-some-two-way-classifications-of-integers/C36087ADE965C59BE843D73B9FA11A87#">https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/on-some-two-way-classifications-of-integers/C36087ADE965C59BE843D73B9FA11A87#</a><br/>PDF: <a href="https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C36087ADE965C59BE843D73B9FA11A87/S0008439559051116a.pdf/div-class-title-on-some-two-way-classifications-of-integers-div.pdf">https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C36087ADE965C59BE843D73B9FA11A87/S0008439559051116a.pdf/div-class-title-on-some-two-way-classifications-of-integers-div.pdf</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/OnSometwowayClassificationsofIntegers">https://read.somethingorotherwhatever.com/entry/OnSometwowayClassificationsofIntegers</a> 2025-05-10T05:25:08Z https://njump.me/nevent1qqs2rgly5hcaax9sxff9zkq6aymzw5lmu4thctm8kgal0yh4ah584pgzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqdwusha Circular orbits on a warped spandex fabric<br/>Article by Middleton, Chad A. and Langston, Michael<br/>In collections: Basically physics, Things to make and do, Geometry<br/>We present a theoretical and experimental analysis of circular-like orbits made by a marble rolling on a warped spandex fabric. We show that the mass of the fabric interior to the orbital path influences the motion of the marble in a nontrivial...<br/>URL: <a href="http://arxiv.org/abs/1312.3893">http://arxiv.org/abs/1312.3893</a><br/>PDF: <a href="http://arxiv.org/pdf/1312.3893v1">http://arxiv.org/pdf/1312.3893v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Middleton2013">https://read.somethingorotherwhatever.com/entry/Middleton2013</a> 2025-05-08T05:25:07Z https://njump.me/nevent1qqsfvpdxnds50223a74t0ut7cjl5zc32fsm8yl6r7w58lgkvq8tqdgszyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq2vsg7l Mechanical Computing Systems Using Only Links and Rotary Joints<br/>Article by Ralph C. Merkle and Robert A. Freitas Jr. and Tad Hogg and Thomas E. Moore and Matthew S. Moses and James Ryley<br/>In collections: Basically computer science, Things to make and do, Unusual computers<br/>A new paradigm for mechanical computing is demonstrated that requires only two basic parts, links and rotary joints. These basic parts...<br/>URL: <a href="http://arxiv.org/abs/1801.03534v1">http://arxiv.org/abs/1801.03534v1</a><br/>PDF: <a href="http://arxiv.org/pdf/1801.03534v1">http://arxiv.org/pdf/1801.03534v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/MechanicalComputingSystemsUsingOnlyLinksandRotaryJoints">https://read.somethingorotherwhatever.com/entry/MechanicalComputingSystemsUsingOnlyLinksandRotaryJoints</a> 2025-04-21T05:25:23Z https://njump.me/nevent1qqsvd435rq7cjpvtd0k4ngu7vvpywku70u4p9cqz8yndgc8qvlhjt3czyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqt9epyv Earliest Uses of Symbols of Calculus<br/>Web page by Jeff Miller<br/>In collections: Easily explained, History, Lists and catalogues, Notation and conventions<br/>URL: <a href="http://jeff560.tripod.com/calculus.html">http://jeff560.tripod.com/calculus.html</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/item26">https://read.somethingorotherwhatever.com/entry/item26</a> 2024-07-18T06:25:44Z https://njump.me/nevent1qqs0h5c8a6n3l8gmp0ncv465k36f5fdjll9dfq5pmah4pu7vrkp5vkqzyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jqwtumt0 Every natural number is the sum of forty-nine palindromes<br/>Article by William D. Banks<br/>In collections: Fun maths facts, Integerology<br/>It is shown that the set of decimal palindromes is an additive basis for the natural numbers. Specifically, we prove that every natural number can be expressed as the sum of forty-nine (possibly zero) decimal palindromes.<br/>URL: <a href="http://arxiv.org/abs/1508.04721v1">http://arxiv.org/abs/1508.04721v1</a><br/>PDF: <a href="http://arxiv.org/pdf/1508.04721v1">http://arxiv.org/pdf/1508.04721v1</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/Everynaturalnumberisthesumoffortyninepalindromes">https://read.somethingorotherwhatever.com/entry/Everynaturalnumberisthesumoffortyninepalindromes</a> 2024-03-25T06:25:08Z https://njump.me/nevent1qqs8p5tr2vwpmgrvnmnpnxjg9esyx07afnakp9thw8q4gm38jjd5tcszyrmjuezqqhpj6awzddtwtm33phsmc0g4k2a7hu502p3w7hl5x20jq0zl7se Poe, E.: Near A Raven<br/>Web page by Mike Keith<br/>In collections: Animals, Art<br/>At the time of its writing in 1995, this composition in Standard Pilish, a retelling of Edgar Allan Poe&#39;s &#34;The Raven&#34;, was one of the longest texts ever written using the π constraint, in which the number of letters in each successive word &#34;spells out&#34; the digits of π (740 digits in this example). For length this poem was subsequently outdone by the...<br/>URL: <a href="http://www.cadaeic.net/naraven.htm">http://www.cadaeic.net/naraven.htm</a><br/>Entry: <a href="https://read.somethingorotherwhatever.com/entry/item14">https://read.somethingorotherwhatever.com/entry/item14</a> 2023-09-15T06:25:09Z