How Java's floating-point hurts everyone everywhere
Article by Kahan, W and Darcy, JD
In collection: Basically computer science
URL: port70.net/~nsz/articles/float

Division by three
Article by Doyle, Peter G. and Conway, John Horton
In collection: Fun maths facts
We prove without appeal to the Axiom of Choice that for any sets A and B, if there is a one-to-one correspondence between 3 cross A and 3 cross B then there is a one-to-one correspondence between A and B. The first such proof, due to...
URL: arxiv.org/abs/math/0605779v1
PDF: arxiv.org/pdf/math/0605779v1.p

Only problems, not solutions!
Article by Smarandache, Florentin
In collections: Attention-grabbing titles, Puzzles
URL: fs.gallup.unm.edu/opns.pdf

Frustration solitaire
Article by Peter G. Doyle and Charles M. Grinstead and J. Laurie Snell
In collections: Easily explained, Games to play with friends, Probability and statistics, Puzzles
In this expository article, we discuss the rank-derangement problem, which asks for the number of permutations of a deck of cards such that each...
URL: arxiv.org/abs/math/0703900v2
PDF: arxiv.org/pdf/math/0703900v2

The Mathematics of Musical Instruments
Article by Hall, Rachel W. and Josic, Kresimir
In collection: Music
URL: jstor.org/stable/2695241?origi

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

Analysis of Casino Shelf Shuffling Machines
Article by Diaconis, Persi and Fulman, Jason and Holmes, Susan
In collections: Basically physics, Probability and statistics
Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics, and to some...
URL: arxiv.org/abs/1107.2961
PDF: arxiv.org/pdf/1107.2961v2

Topologically Distinct Sets of Non-intersecting Circles in the Plane
Article by Richard J. Mathar
In collections: Easily explained, Geometry
Nested parentheses are forms in an algebra which define orders of evaluations. A class of well-formed sets of associated opening and closing parentheses is well...
URL: arxiv.org/abs/1603.00077v1
PDF: arxiv.org/pdf/1603.00077v1

Counting groups: gnus, moas and other exotica
Article by John H. Conway and Heiko Dietrich and E.A. O’Brien
In collections: Attention-grabbing titles, Animals
The number of groups of a given order is a fascinating function. We report on its known values, discuss some of its properties, and study some related functions.
URL: math.auckland.ac.nz/~obrien/re

Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles
None by Gradwohl, Ronen and Naor, M. and Pinkas, Benny and Rothblum, G.
In collections: Easily explained, Protocols and strategies, About proof

A Hamiltonian circuit for Rubik's Cube
Web page by cuBerBruce
In collections: Easily explained, Puzzles, Fun maths facts
At last, the Hamiltonian circuit problem for Rubik's Cube has a solution! To be a little more mathematically precise, a Hamiltonian circuit of the quarter-turn metric Cayley graph for the Rubik's Cube group has been found.
URL: bruce.cubing.net/ham333/rubikh

Hypercomputation: computing more than the Turing machine
Article by Ord, Toby
In collections: Basically computer science, Unusual computers
Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation...
URL: arxiv.org/abs/math/0209332
PDF: arxiv.org/pdf/math/0209332v1

The role of instrumental and relational understanding in proofs about group isomorphisms
None by Weber, K.
In collections: The act of doing maths, About proof
URL: math.uoc.gr/~ictm2/Proceedings

Renyi's Parking Problem Revisited
Article by Matthew P. Clay and Nandor J. Simanyi
In collection: Easily explained
R\'enyi's parking problem (or $1D$ sequential interval packing problem) dates back to 1958, when R\'enyi studied the following random process: Consider an interval $I$ of length $x$, and sequentially and randomly...
URL: arxiv.org/abs/1406.1781v2
PDF: arxiv.org/pdf/1406.1781v2

New entry!
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 =...
URL: arxiv.org/abs/math/9805045v1
PDF: arxiv.org/pdf/math/9805045v1

Efficient Algorithms for Zeckendorf Arithmetic
Article by Ahlbach, Connor and Usatine, Jeremy and Pippenger, Nicholas
In collections: Easily explained, Fun maths facts, Integerology
We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they...
URL: arxiv.org/abs/1207.4497
PDF: arxiv.org/pdf/1207.4497v1

Asymptotic statistics of the n-sided planar Poisson–Voronoi cell: I. Exact results
Article by Hilhorst, H.J.
In collections: Probability and statistics, Geometry
URL: iopscience.iop.org/1742-5468/2

Fingerprint databases for theorems
Article by Sara C. Billey and Bridget E. Tenner
In collections: Lists and catalogues, The act of doing maths
We discuss the advantages of searchable, collaborative, language-independent databases of mathematical results, indexed by "fingerprints" of small and canonical data. Our motivating example...
URL: arxiv.org/abs/1304.3866v1
PDF: arxiv.org/pdf/1304.3866v1

Division by zero
Article by Emil Jeřábek
As a consequence of the MRDP theorem, the set of Diophantine equations provably unsolvable in any sufficiently strong theory of arithmetic is algorithmically undecidable. In contrast, we show the decidability of Diophantine equations provably unsolvable in Robinson's arithmetic Q. The...
URL: arxiv.org/abs/1604.07309
PDF: arxiv.org/pdf/1604.07309v1
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