Nim multiplication
Article by H. W. Lenstra, Jr.
In collections: Games to play with friends, Unusual arithmetic
URL: openaccess.leidenuniv.nl/bitst

A New Rose : The First Simple Symmetric 11-Venn Diagram
Article by Mamakani, Khalegh and Ruskey, Frank
In collections: Art, Easily explained
A symmetric Venn diagram is one that is invariant under rotation, up to a relabeling of curves. A simple Venn diagram is one in which at most two curves intersect at any point. In this paper we introduce a new...
URL: arxiv.org/abs/1207.6452
PDF: arxiv.org/pdf/1207.6452v1

New entry!
Duotone Truchet-like tilings
Article by Cameron Browne
In collections: Art, Easily explained, Geometry, Things to make and do
This paper explores methods for colouring Truchet-like tiles, with an emphasis on the resulting visual patterns and designs. The methods are extended to non-square tilings that...
URL: tandfonline.com/doi/full/10.10

Nim multiplication
Article by H. W. Lenstra, Jr.
In collections: Games to play with friends, Unusual arithmetic
URL: openaccess.leidenuniv.nl/bitst

New entry!
Prime Number Races
Article by Andrew Granville and Greg Martin
In collections: Attention-grabbing titles, Easily explained, Fun maths facts, Integerology
This is a survey article on prime number races. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more...
URL: arxiv.org/abs/math/0408319v1
PDF: arxiv.org/pdf/math/0408319v1

Rithmomachia
Web page by Daniel U. Thibault and Michel Boutin
In collections: Games to play with friends, History
This complex chess-like game appeared in the western world around the year 1000. The game knew a great burst of popularity in the 15th century, because of some rules changes. When chess also saw its rules change (particularly when the Queen started to move in its...
URL: gamecabinet.com/rules/Rithmoma

A history of mathematical notations
Book by Florian Cajori
In collections: History, Notation and conventions, Lists and catalogues
URL: maths.ed.ac.uk/~aar/papers/caj

Homotopy type theory: the logic of space
Article by Michael Shulman
This is an introduction to type theory, synthetic topology, and homotopy type theory from a category-theoretic and topological point of view, written as a chapter for the book "New Spaces for Mathematics and Physics" (ed. Gabriel Catren and Mathieu Anel).
URL: arxiv.org/abs/1703.03007v1
PDF: arxiv.org/pdf/1703.03007v1

An Invitation to Inverse Group Theory
Article by João Araújo and Peter J. Cameron and Francesco Matucci
In collection: Unusual arithmetic
In group theory there are many constructions which produce a new group from a given one. Often the result is a subgroup: the derived group, centre, socle, Frattini subgroup, Hall subgroup,...
URL: arxiv.org/abs/1803.10179v2
PDF: arxiv.org/pdf/1803.10179v2

Survey on fusible numbers
Article by Xu, Junyan
In collection: Easily explained
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties...
URL: arxiv.org/abs/1202.5614
PDF: arxiv.org/pdf/1202.5614v1

Maximum Matching and a Polyhedron With 0,1-Vertices
A matching in a graph $G$ is a subset of edges in $G$ such that no two meet the same node in $G$. The convex polyhedron $C$ is characterised, where the extreme points of $C$ correspond to the matchings in $G$. Where each edge of $G$ carries a real numerical weight, an efficient algorithm is...
URL: nvlpubs.nist.gov/nistpubs/jres

A categorical foundation for Bayesian probability
Article by Culbertson, Jared and Sturtz, Kirk
In collection: Probability and statistics
Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a prior probability measure $P_H$ on $H$ and a sampling distribution $\mcS:H \rightarrow D$, there is a corresponding...
URL: arxiv.org/abs/1205.1488
PDF: arxiv.org/pdf/1205.1488v3

Random Walks on Finite Groups
Article by Saloff-coste, Laurent
In collection: Probability and statistics
Markov chains on finite sets are used in a great variety of situations to approximate, understand and sample from their limit distribution. A familiar example is provided by card shuffling methods. From this viewpoint, one is interested in the “mixing time” of...
URL: statweb.stanford.edu/~cgates/P

New entry!
Conway's doughnuts
Article by Peter Doyle and Shikhin Sethi
In collections: Food, Fun maths facts, Geometry
Morley's Theorem about angle trisectors can be viewed as the statement that a certain diagram exists', meaning that triangles of prescribed shapes meet in a prescribed pattern. This diagram is the case n=3 of a class of...
URL: arxiv.org/abs/1804.04024v1
PDF: arxiv.org/pdf/1804.04024v1

Half of a coin: negative probabilities
Article by Székely, GJ
In collections: Probability and statistics, Unusual arithmetic, Fun maths facts
URL: citeseerx.ist.psu.edu/viewdoc/

A history of mathematical notations
Book by Florian Cajori
In collections: History, Notation and conventions, Lists and catalogues
URL: maths.ed.ac.uk/~aar/papers/caj

A note on paradoxical metric spaces
Article by Deuber, W A and Simonovits, M and Os, V T S
URL: renyi.hu/~miki/walter07.pdf

The Curling Number Conjecture
Article by Benjamin Chaffin and N. J. A. Sloane
In collections: Easily explained, Integerology
Given a finite nonempty sequence of integers S, by grouping adjacent terms it is always possible to write it, possibly in many ways, as S = X Y^k, where X and Y are sequences and Y is nonempty. Choose the version...
URL: arxiv.org/abs/0912.2382v5
PDF: arxiv.org/pdf/0912.2382v5

Random Triangles and Polygons in the Plane
Article by Jason Cantarella and Tom Needham and Clayton Shonkwiler and Gavin Stewart
In collections: Probability and statistics, Geometry
We consider the problem of finding the probability that a random triangle is obtuse, which was first raised by Lewis Caroll. Our investigation...
URL: arxiv.org/abs/1702.01027v1
PDF: arxiv.org/pdf/1702.01027v1
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