Kindergarten Quantum Mechanics
Article by Coecke, Bob
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a...
URL: arxiv.org/abs/quant-ph/0510032

Two short proofs of the Perfect Forest Theorem
Article by Yair Caro and Josef Lauri and Christina Zarb
In collections: About proof, Fun maths facts
A perfect forest is a spanning forest of a connected graph $G$, all of whose components are induced subgraphs of $G$ and such that all vertices have odd degree in the...
URL: arxiv.org/abs/1612.05004v1
PDF: arxiv.org/pdf/1612.05004v1

Rational Polynomials That Take Integer Values at the Fibonacci Numbers
Article by Keith Johnson and Kira Scheibelhut
In collections: Fibonaccinalia, Fun maths facts, Integerology
An integer-valued polynomial on a subset $S$ of $\mathbb{Z}$ is a polynomial $f(x) \in \mathbb{Q}[x]$ with the property...
URL: jstor.org/stable/10.4169/amer.

Algebraic theory of Penrose's non-periodic tilings of the plane
Article by Bruijn, NG De
In collection: Geometry
URL: alexandria.tue.nl/repository/f

A number system with an irrational base
In collections: Unusual arithmetic, Fun maths facts, Integerology
URL: jstor.org/discover/10.2307/302

No, This is not a Circle
Article by Zoltán Kovács
In collections: Attention-grabbing titles, Easily explained, Drama!, Geometry
A curve, also shown in introductory maths textbooks, seems like a circle. But it is actually a different curve. This paper discusses some easy approaches to classify the result, including a GeoGebra applet...
URL: arxiv.org/abs/1704.08483v2
PDF: arxiv.org/pdf/1704.08483v2

Random Triangles and Polygons in the Plane
Article by Jason Cantarella and Tom Needham and Clayton Shonkwiler and Gavin Stewart
In collections: Probability and statistics, Geometry
We consider the problem of finding the probability that a random triangle is obtuse, which was first raised by Lewis Caroll. Our investigation...
URL: arxiv.org/abs/1702.01027v1
PDF: arxiv.org/pdf/1702.01027v1

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

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...
URL: arxiv.org/abs/1806.02282v1
PDF: arxiv.org/pdf/1806.02282v1

An Infinite Set of Heron Triangles with Two Rational Medians
Article by Buchholz, Ralph H and Rathbun, Randall L
In collections: Geometry, Fun maths facts
URL: jstor.org/stable/2974977

Light reflecting off Christmas-tree balls
Web page by Joseph O'Rourke
In collection: Easily explained
'Twas the night before Christmas and under the tree Was a heap of new balls, stacked tight as can be. The balls so gleaming, they reflect all light rays, Which bounce in the stack every which way. When, what to my wondering mind does occur: A...
URL: mathoverflow.net/questions/501

Giuga Numbers and the arithmetic derivative
Article by Grau, José María and Oller-Marcén, Antonio M.
In collections: Unusual arithmetic, Integerology
We characterize Giuga Numbers as solutions to the equation $n'=an+1$, with $a \in \mathbb{N}$ and $n'$ being the arithmetic derivative. Although this fact does not refute Lava's conjecture, it brings...
URL: arxiv.org/abs/1103.2298
PDF: arxiv.org/pdf/1103.2298v1

The Curling Number Conjecture
Article by Benjamin Chaffin and N. J. A. Sloane
In collections: Easily explained, Integerology
Given a finite nonempty sequence of integers S, by grouping adjacent terms it is always possible to write it, possibly in many ways, as S = X Y^k, where X and Y are sequences and Y is nonempty. Choose the version...
URL: arxiv.org/abs/0912.2382v5
PDF: arxiv.org/pdf/0912.2382v5

The Maximum Throughput Rate for Each Hole on a Golf Course
Article by Whitt, Ward
In collections: Games to play with friends, Basically physics, Probability and statistics
URL: columbia.edu/~ww2040/golf_thro

Detection of transposition errors in decimal numbers
Article by Freeman, H
In collection: Basically computer science
URL: ieeexplore.ieee.org/xpls/abs_a

New entry!
Book by John Horton Conway
In collection: Attention-grabbing titles
John Horton Conway's unique approach to quadratic forms was the subject of the Hedrick Lectures that he gave in August of 1991 at the Joint Meetings of the Mathematical Association of America and the American...
URL: bookstore.ams.org/car-26
PDF: maths.ed.ac.uk/~v1ranick/paper

New entry!
A universal differential equation
Article by Lee A. Rubel
In collections: Fun maths facts, Unusual computers
There exists a non trivial fourth-order algebraic differential equation $P(y',y'',y''',y'''') = 0,$ where $P$ is a polynomial in four variables, with integer coefficients, such that for any continuous function $\phi$ on...
URL: projecteuclid.org/euclid.bams/

New entry!
The graphs behind Reuleaux polyhedra
Article by Luis Montejano and Eric Pauli and Miguel Raggi and Edgardo Roldán-Pensado
In collection: Geometry
This work is about graphs arising from Reuleaux polyhedra. Such graphs must necessarily be planar, $3$-connected and strongly self-dual. We study the question of when these...
URL: arxiv.org/abs/1904.12761v1
PDF: arxiv.org/pdf/1904.12761v1

New entry!
Article by Alexander A. Voronov
In collections: Attention-grabbing titles, Food
We introduce a new operad, which we call the Swiss-cheese operad. It mixes naturally the little disks and the little intervals operads. The Swiss-cheese operad is related to the configuration spaces of points on the upper...
URL: arxiv.org/abs/math/9807037v1
PDF: arxiv.org/pdf/math/9807037v1

New entry!
Planar Hypohamiltonian Graphs on 40 Vertices
Article by Mohammadreza Jooyandeh and Brendan D. McKay and Patric R. J. Östergård and Ville H. Pettersson and Carol T. Zamfirescu
In collection: Fun maths facts
A graph is hypohamiltonian if it is not Hamiltonian, but the deletion of any single vertex gives a...
URL: arxiv.org/abs/1302.2698v4
PDF: arxiv.org/pdf/1302.2698v4
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