Remainder Wheels and Group Theory
Article by Brenton, Lawrence
In collections: Unusual arithmetic, Easily explained, The groups group
URL: maa.org/sites/default/files/pd

National Curve Bank
Article by Shirley B. Gray and Stewart Venit and Russ Abbott
In collections: Lists and catalogues, Geometry
The National Curve Bank is a resource for students of mathematics. We strive to provide features - for example, animation and interaction - that a printed page cannot offer. We also include geometrical, algebraic, and historical aspects of curves, the kinds of attributes that make the mathematics special...
URL: web.calstatela.edu/curvebank/h

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 of fusible numbers. We suggest some possible...
URL: arxiv.org/abs/1202.5614
PDF: arxiv.org/pdf/1202.5614v1

New entry!
Perimeter-minimizing pentagonal tilings
Article by Chung, Ping Ngai and Fernandez, Miguel and Shah, Niralee and Sordo Vieira, Luis and Wikner, Elena
In collections: Easily explained, Geometry, Things to make and do
We provide examples of perimeter-minimizing tilings of the plane by convex pentagons and examples of perimeter-minimizing tilings of certain small flat tori.
URL: msp.org/involve/2014/7-4/p02.x
PDF: msp.org/involve/2014/7-4/invol

This is the (co)end, my only (co)friend
Article by Loregian, Fosco
In collection: Attention-grabbing titles
The present note is a recollection of the most striking and useful applications of co/end calculus. We put a considerable effort in making arguments and constructions rather explicit: after having given a series of preliminary definitions, we characterize co/ends as particular co/limits; then we...
URL: arxiv.org/abs/1501.02503
PDF: arxiv.org/pdf/1501.02503v2

How to Hunt an Invisible Rabbit on a Graph
Article by Tatjana V. Abramovskaya and Fedor V. Fomin and Petr A. Golovach and Michał Pilipczuk
In collections: Animals, Attention-grabbing titles, Combinatorics, Easily explained, Protocols and strategies, Puzzles
We investigate Hunters & Rabbit game, where a set of hunters tries to catch an invisible rabbit that slides along the edges of a graph. We show...
URL: arxiv.org/abs/1502.05614v2
PDF: arxiv.org/pdf/1502.05614v2

Plane partitions in the work of Richard Stanley and his school
Article by C. Krattenthaler
In collections: Art, Combinatorics
These notes provide a survey of the theory of plane partitions, seen through the glasses of the work of Richard Stanley and his school.
URL: arxiv.org/abs/1503.05934v2
PDF: arxiv.org/pdf/1503.05934v2

Exact Enumeration of Garden of Eden Partitions
Article by Brian Hopkins and James A. Sellers
In collections: Attention-grabbing titles, Easily explained, Combinatorics
We give two proofs for a formula that counts the number of partitions of $$n$$ that have rank −2 or less (which we call Garden of Eden partitions). These partitions arise naturally in analyzing the game Bulgarian solitaire, summarized in...
URL: emis.de/journals/INTEGERS/pape
PDF: emis.de/journals/INTEGERS/pape

The Takagi Function and Its Properties
Article by Jeffrey C. Lagarias
In collections: Easily explained, Fun maths facts
The Takagi function is a continuous non-differentiable function on [0,1] introduced by Teiji Takagi in 1903. It has since appeared in a surprising number of different mathematical contexts, including mathematical analysis, probability theory and number theory. This paper surveys the...
URL: arxiv.org/abs/1112.4205v2
PDF: arxiv.org/pdf/1112.4205v2

The Namer-Claimer game
Article by Ben Barber
In collections: Easily explained, Games to play with friends
In each round of the Namer-Claimer game, Namer names a distance d, then Claimer claims a subset of [n] that does not contain two points that differ by d. Claimer wins once they have claimed sets covering [n]. I show that the length of this game is of order log log n with optimal play from each side.
URL: arxiv.org/abs/1808.10800v1
PDF: arxiv.org/pdf/1808.10800v1

Paperfolding morphisms, planefilling curves, and fractal tiles
Article by Michel Dekking
In collections: Geometry, Things to make and do
An interesting class of automatic sequences emerges from iterated paperfolding. The sequences generate curves in the plane with an almost periodic structure. We generalize the results obtained by Davis and Knuth on the self-avoiding and planefilling properties of these...
URL: arxiv.org/abs/1011.5788v2
PDF: arxiv.org/pdf/1011.5788v2

Ovals and Egg Curves
Article by Jürgen Köller
In collections: Art, Things to make and do, Food, Geometry
URL: mathematische-basteleien.de/eg

Sloane's Gap: Do Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS?
Article by Gauvrit, Nicolas and Delahaye, Jean-Paul and Zenil, Hector
In collections: Easily explained, Probability and statistics, The act of doing maths, Integerology
The Online Encyclopedia of Integer Sequences (OEIS) is made up of thousands of numerical sequences considered particularly interesting by...
URL: arxiv.org/abs/1101.4470
PDF: arxiv.org/pdf/1101.4470v2

Finding the Bandit in a Graph: Sequential Search-and-Stop
Article by Pierre Perrault and Vianney Perchet and Michal Valko
In collections: Attention-grabbing titles, Protocols and strategies
We consider the problem where an agent wants to find a hidden object that is randomly located in some vertex of a directed acyclic graph (DAG) according to a fixed but possibly unknown distribution. The agent can only...
URL: arxiv.org/abs/1806.02282v1
PDF: arxiv.org/pdf/1806.02282v1

Counting Cases in Marching Cubes: Towards a Generic Algorithm for Producing Substitopes
Article by David C. Banks and Stephen Linton
In collection: Basically computer science
We describe how to count the cases that arise in a family of visualization techniques, including marching cubes, sweeping simplices, contour meshing, interval volumes, and separating surfaces. Counting the cases is the first step toward developing a generic...
URL: evl.uic.edu/cavern/rg/20040525

Remainder Wheels and Group Theory
Article by Brenton, Lawrence
In collections: Unusual arithmetic, Easily explained, The groups group
URL: maa.org/sites/default/files/pd
The problem of finding small sets that block every line passing through a unit square was first considered by Mazurkiewicz in 1916. We call such a set {\em opaque} or a {\em barrier} for the square. The shortest known barrier has length $$\sqrt{2}+ \frac{\sqrt{6}}{2}= 2.6389\ldots$$. The current...