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

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

Swiss cheeses, rational approximation and universal plane curves
Article by Feinstein, JF and Heath, MJ
In collections: Attention-grabbing titles, Food, Geometry
URL: maths.nottingham.ac.uk/persona

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: cms.math.ca/10.4153/CMB-1969-0
PDF: cms.math.ca/openaccess/cmb/v12

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: osapublishing.org/oe/abstract.

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: jstor.org/stable/2319392
PDF: oeis.org/A003018/a003018.pdf

Article by Fisher, GL and Mellor, B.
In collections: Easily explained, Things to make and do
URL: tandfonline.com/doi/abs/10.108

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: doi.wiley.com/10.1002/nme.1620

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

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

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: tac.mta.ca/tac/volumes/31/19/3
PDF: tac.mta.ca/tac/volumes/31/19/3

Gödel's Second Incompleteness Theorem Explained in Words of One Syllable
Article by Boolos, George
In collections: Easily explained, Fun maths facts
URL: mind.oxfordjournals.org/cgi/do

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: emis.de/journals/INTEGERS/pape
PDF: emis.de/journals/INTEGERS/pape

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

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[&ge;]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: rspa.royalsocietypublishing.or

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...

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

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

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: sciencedirect.com/science/arti
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