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: http://arxiv.org/abs/quant-ph/0510032

Entry: http://read.somethingorotherwhatever.com/entry/Coecke2005

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: http://arxiv.org/abs/1612.05004v1

PDF: http://arxiv.org/pdf/1612.05004v1

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

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: http://www.jstor.org/stable/10.4169/amer.math.monthly.123.4.338

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

Algebraic theory of Penrose's non-periodic tilings of the plane

Article by Bruijn, NG De

In collection: Geometry

URL: http://alexandria.tue.nl/repository/freearticles/597566.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Bruijn1981

A number system with an irrational base

In collections: Unusual arithmetic, Fun maths facts, Integerology

URL: http://www.jstor.org/discover/10.2307/3029218?uid=3738032&uid=2&uid=4&sid=21103722830183

Entry: http://read.somethingorotherwhatever.com/entry/item40

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: http://arxiv.org/abs/1704.08483v2

PDF: http://arxiv.org/pdf/1704.08483v2

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

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: http://arxiv.org/abs/1702.01027v1

PDF: http://arxiv.org/pdf/1702.01027v1

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

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: http://arxiv.org/abs/math/0209332

PDF: http://arxiv.org/pdf/math/0209332v1

Entry: http://read.somethingorotherwhatever.com/entry/Ord2002

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

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

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

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: http://www.jstor.org/stable/2974977

Entry: http://read.somethingorotherwhatever.com/entry/Buchholz2013

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: http://mathoverflow.net/questions/50150/light-reflecting-off-christmas-tree-balls

Entry: http://read.somethingorotherwhatever.com/entry/item17

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: http://arxiv.org/abs/1103.2298

PDF: http://arxiv.org/pdf/1103.2298v1

Entry: http://read.somethingorotherwhatever.com/entry/Grau2011

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: http://arxiv.org/abs/0912.2382v5

PDF: http://arxiv.org/pdf/0912.2382v5

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

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: http://www.columbia.edu/~ww2040/golf_throughput_POMS_2015.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Whitt2013

Detection of transposition errors in decimal numbers

Article by Freeman, H

In collection: Basically computer science

URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1447797

Entry: http://read.somethingorotherwhatever.com/entry/Freeman1967

New entry!

The Sensual (quadratic) Form

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: https://bookstore.ams.org/car-26

PDF: https://www.maths.ed.ac.uk/~v1ranick/papers/conwaysens.pdf

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

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: https://projecteuclid.org/euclid.bams/1183548125

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

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: http://arxiv.org/abs/1904.12761v1

PDF: http://arxiv.org/pdf/1904.12761v1

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

New entry!

The Swiss-Cheese Operad

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: http://arxiv.org/abs/math/9807037v1

PDF: http://arxiv.org/pdf/math/9807037v1

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

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: http://arxiv.org/abs/1302.2698v4

PDF: http://arxiv.org/pdf/1302.2698v4

Entry: http://read.somethingorotherwhatever.com/entry/PlanarHypohamiltonianGraphson40Vertices

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

Posts one interesting reference a day.

http://read.somethingorotherwhatever.com

Joined Apr 2017