Article by Brenton, Lawrence

In collections: Unusual arithmetic, Easily explained, The groups group

URL: http://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/Brenton.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Brenton2008

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: http://web.calstatela.edu/curvebank/home/home.htm

Entry: https://read.somethingorotherwhatever.com/entry/NationalCurveBank

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: http://arxiv.org/abs/1202.5614

PDF: http://arxiv.org/pdf/1202.5614v1

Entry: https://read.somethingorotherwhatever.com/entry/Xu2012

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: https://msp.org/involve/2014/7-4/p02.xhtml

PDF: http://msp.org/involve/2014/7-4/involve-v7-n4-p02-s.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Perimeterminimizingpentagonaltilings

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: http://arxiv.org/abs/1501.02503

PDF: http://arxiv.org/pdf/1501.02503v2

Entry: https://read.somethingorotherwhatever.com/entry/Loregian2015

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: http://arxiv.org/abs/1502.05614v2

PDF: http://arxiv.org/pdf/1502.05614v2

Entry: https://read.somethingorotherwhatever.com/entry/HowtoHuntanInvisibleRabbitonaGraph

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: http://arxiv.org/abs/1503.05934v2

PDF: http://arxiv.org/pdf/1503.05934v2

Entry: https://read.somethingorotherwhatever.com/entry/PlanepartitionsintheworkofRichardStanleyandhisschool

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: https://www.emis.de/journals/INTEGERS/papers/a19int2005/a19int2005.Abstract.html

PDF: https://www.emis.de/journals/INTEGERS/papers/a19int2005/a19int2005.pdf

Entry: https://read.somethingorotherwhatever.com/entry/ExactEnumerationOfGardenOfEdenPartitions

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: http://arxiv.org/abs/1112.4205v2

PDF: http://arxiv.org/pdf/1112.4205v2

Entry: https://read.somethingorotherwhatever.com/entry/TheTakagiFunctionandItsProperties

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: http://arxiv.org/abs/1808.10800v1

PDF: http://arxiv.org/pdf/1808.10800v1

Entry: https://read.somethingorotherwhatever.com/entry/TheNamerClaimergame

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: http://arxiv.org/abs/1011.5788v2

PDF: http://arxiv.org/pdf/1011.5788v2

Entry: https://read.somethingorotherwhatever.com/entry/Paperfoldingmorphismsplanefillingcurvesandfractaltiles

Article by Jürgen Köller

In collections: Art, Things to make and do, Food, Geometry

URL: http://www.mathematische-basteleien.de/eggcurves.htm

Entry: https://read.somethingorotherwhatever.com/entry/OvalsandEggCurves

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: http://arxiv.org/abs/1101.4470

PDF: http://arxiv.org/pdf/1101.4470v2

Entry: https://read.somethingorotherwhatever.com/entry/Gauvrit2011

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: http://arxiv.org/abs/1806.02282v1

PDF: http://arxiv.org/pdf/1806.02282v1

Entry: https://read.somethingorotherwhatever.com/entry/FindingtheBanditinaGraphSequentialSearchandStop

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: https://www.evl.uic.edu/cavern/rg/20040525_renambot/Visualization-papers/papers/03/01250354.pdf

Entry: https://read.somethingorotherwhatever.com/entry/CountingCasesInMarchingCubes

Article by Mahadevan, L and Keller, JB

In collection: Geometry

URL: http://rspa.royalsocietypublishing.org/content/440/1908/149.short

PDF: http://www.seas.harvard.edu/softmat/downloads/pre2000-20.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Mahadevan1993

Article by Brenton, Lawrence

In collections: Unusual arithmetic, Easily explained, The groups group

URL: http://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/Brenton.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Brenton2008

Article by Adrian Dumitrescu and Minghui Jiang

In collections: Easily explained, Geometry

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...

URL: http://arxiv.org/abs/1311.3323v1

PDF: http://arxiv.org/pdf/1311.3323v1

Entry: https://read.somethingorotherwhatever.com/entry/Theopaquesquare

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@christianp's collection of interesting and unusual maths references.

Posts one interesting reference a day.

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Joined Apr 2017