Every positive integer is a sum of three palindromes

Article by Javier Cilleruelo and Florian Luca and Lewis Baxter

In collections: Easily explained, Fun maths facts

For integer \(g\ge 5\), we prove that any positive integer can be written as a sum of three palindromes in base \(g\).

URL: http://arxiv.org/abs/1602.06208v2

PDF: http://arxiv.org/pdf/1602.06208v2

Entry: http://read.somethingorotherwhatever.com/entry/Everypositiveintegerisasumofthreepalindromes

When are Multiples of Polygonal Numbers again Polygonal Numbers?

Article by Jasbir S. Chahal and Nathan Priddis

In collections: Easily explained, Fun maths facts, Integerology

Euler showed that there are infinitely many triangular numbers that are three times another triangular number. In general, as we...

URL: http://arxiv.org/abs/1806.07981v1

PDF: http://arxiv.org/pdf/1806.07981v1

Entry: http://read.somethingorotherwhatever.com/entry/WhenareMultiplesofPolygonalNumbersagainPolygonalNumbers

Swiss cheeses, rational approximation and universal plane curves

Article by Feinstein, JF and Heath, MJ

In collections: Attention-grabbing titles, Food, Geometry

URL: http://www.maths.nottingham.ac.uk/personal/jff/Papers/pdf/Swisscheeses2.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Feinstein2010

On subsets with intersections of even cardinality

Article by E.R. Berlekamp

In collection: Fun maths facts

This paper solves a question by Paul Erdős

URL: https://cms.math.ca/10.4153/CMB-1969-059-3

PDF: https://cms.math.ca/openaccess/cmb/v12/cmb1969v12.0471-0474.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Onsubsetswithintersectionsofevencardinality

Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence

Article by Luigi Moretti and Vito Mocella

In collections: Basically physics, Geometry

We investigate from a theoretical point of view the photonic properties of a two dimensional photonic aperiodic crystal. These structures are...

URL: https://www.osapublishing.org/oe/abstract.cfm?uri=oe-15-23-15314

Entry: http://read.somethingorotherwhatever.com/entry/TwodimensionalphotonicaperiodiccrystalsbasedonThueMorsesequence

The Nesting and Roosting Habits of The Laddered Parenthesis

Article by R. K. Guy and J. L. Selfridge

In collections: Attention-grabbing titles, Easily explained, Combinatorics

URL: http://www.jstor.org/stable/2319392

PDF: http://oeis.org/A003018/a003018.pdf

Entry: http://read.somethingorotherwhatever.com/entry/item43

Three-dimensional finite point groups and the symmetry of beaded beads

Article by Fisher, GL and Mellor, B.

In collections: Easily explained, Things to make and do

URL: http://www.tandfonline.com/doi/abs/10.1080/17513470701416264

PDF: http://myweb.lmu.edu/bmellor/beadedbeads.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Fisher2007

The elasto-plastic indentation of a half-space by a rigid sphere

Article by Hardy, C. and Baronet, C. N. and Tordion, G. V.

URL: http://doi.wiley.com/10.1002/nme.1620030402

Entry: http://read.somethingorotherwhatever.com/entry/Hardy1971

New entry!

Brazilian Primes Which Are Also Sophie Germain Primes

Article by Jon Grantham and Hester Graves

In collections: Attention-grabbing titles, Easily explained, Fun maths facts, Integerology

We disprove a conjecture of Schott that no Brazilian primes are Sophie Germain primes. We enumerate all...

URL: http://arxiv.org/abs/1903.04577v1

PDF: http://arxiv.org/pdf/1903.04577v1

Entry: http://read.somethingorotherwhatever.com/entry/BrazilianPrimesWhichAreAlsoSophieGermainPrimes

Picture-Hanging Puzzles

Article by Demaine, Erik D. and Demaine, Martin L. and Minsky, Yair N. and Mitchell, Joseph S. B. and Rivest, Ronald L. and Patrascu, Mihai

In collections: Puzzles, Easily explained

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out...

URL: http://arxiv.org/abs/1203.3602

PDF: http://arxiv.org/pdf/1203.3602v2

Entry: http://read.somethingorotherwhatever.com/entry/Demaine2012

The snail lemma

Article by Enrico M. Vitale

In collections: Attention-grabbing titles, Animals

The classical snake lemma produces a six terms exact sequence starting from a commutative square with one of the edge being a regular epimorphism. We establish a new diagram lemma, that we call snail lemma, removing...

URL: http://www.tac.mta.ca/tac/volumes/31/19/31-19abs.html

PDF: http://www.tac.mta.ca/tac/volumes/31/19/31-19.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Thesnaillemma

Gödel's Second Incompleteness Theorem Explained in Words of One Syllable

Article by Boolos, George

In collections: Easily explained, Fun maths facts

URL: http://mind.oxfordjournals.org/cgi/doi/10.1093/mind/103.409.1

Entry: http://read.somethingorotherwhatever.com/entry/Boolos1994

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...

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

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

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

2178 And All That

Article by Sloane, NJA

In collections: Easily explained, Integerology

For integers g >= 3, k >= 2, call a number N a (g,k)-reverse multiple if the reversal of N in base g is equal to k times N. The numbers 1089 and 2178 are the two smallest (10,k)-reverse multiples, their reversals being 9801 = 9x1089 and 8712 = 4x2178. In 1992, A. L....

URL: http://arxiv.org/abs/1307.0453

PDF: http://arxiv.org/pdf/1307.0453v4

Entry: http://read.somethingorotherwhatever.com/entry/Sloane2013

History-dependent random processes

Article by Clifford, P. and Stirzaker, D.

Ulam has defined a history-dependent random sequence by the recursion Xn+1=Xn+XU(n), where (U(n); n[≥]1) is a sequence of independent random variables with U(n) uniformly distributed on {1, ..., n} and X1=1. We introduce a new class of continuous-time history-dependent random...

URL: http://rspa.royalsocietypublishing.org/content/464/2093/1105

Entry: http://read.somethingorotherwhatever.com/entry/Clifford2008

Methods for studying coincidences

Book by Diaconis, P and Mosteller, Frederick

In collections: Easily explained, Probability and statistics

This article illustrates basic statistical techniques for studying coincidences. These include data-gathering methods (informal anecdotes, case studies, observational studies, and experiments) and methods of analysis...

URL: http://link.springer.com/chapter/10.1007/978-0-387-44956-2_39

Entry: http://read.somethingorotherwhatever.com/entry/Diaconis2006

What is a closed-form number?

Article by Timothy Y. Chow

In collections: Notation and conventions, The act of doing maths

If a student asks for an antiderivative of exp(x^2), there is a standard reply: the answer is not an elementary function. But if a student asks for a closed-form expression for the real root of x = cos(x), there...

URL: http://arxiv.org/abs/math/9805045v1

PDF: http://arxiv.org/pdf/math/9805045v1

Entry: http://read.somethingorotherwhatever.com/entry/Whatisaclosedformnumber

How to recognise a 4-ball when you see one

Article by Geiges, Hansjörg and Zehmisch, Kai

In collections: Attention-grabbing titles, Geometry

We apply the method of filling with holomorphic discs to a 4-dimensional symplectic cobordism with the standard contact 3-sphere as a convex boundary component. We establish the following dichotomy: either the...

URL: http://arxiv.org/abs/1104.1543

PDF: http://arxiv.org/pdf/1104.1543v3

Entry: http://read.somethingorotherwhatever.com/entry/Geiges2011

Haruspicy 3: The anisotropic generating function of directed bond-animals is not D-finite

Article by Rechnitzer, Andrew

In collections: Animals, Attention-grabbing titles

While directed site-animals have been solved on several lattices, directed bond-animals remain unsolved on any nontrivial lattice. In this paper we demonstrate that the anisotropic...

URL: http://www.sciencedirect.com/science/article/pii/S0097316505001883

Entry: http://read.somethingorotherwhatever.com/entry/Rechnitzer2006

Doubly-, triply-, quadruply- and quintuply-innervated crustacean muscles

Article by van Harreveld, A.

In collection: Animals

URL: http://doi.wiley.com/10.1002/cne.900700208

Entry: http://read.somethingorotherwhatever.com/entry/VanHarreveld1939

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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