Article by Andrew Bremner and Allan Macleod

In collection: Puzzles

For a non-zero integer \(N\), we consider the problem of finding \(3\) integers \( (a, b, c) \) such that \[ N = \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}. \] We show that the existence of solutions is related to points of infinite order on a family of elliptic curves. We discuss strictly positive solutions and prove the...

URL: http://ami.ektf.hu/uploads/papers/finalpdf/AMI_43_from29to41.pdf

Entry: https://read.somethingorotherwhatever.com/entry/AnUnusualCubicRepresentationProblem

Article by Glenis, Spyros and Kapovich, M. and Brodskiy, N. and Dydak, J. and Lang, U. and Ballinger, B. and Blekherman, G. and Cohn, H. and Giansiracusa, N. and Kelly, E. and Others

In collection: Geometry

Although the geometric equality of figures has already been studied thoroughly, little work has been done about the comparison of unequal figures. We are used to compare...

URL: https://arxiv.org/abs/math/0611062

PDF: https://arxiv.org/pdf/math/0611062

Entry: https://read.somethingorotherwhatever.com/entry/Glenis2008

Article by Demaine, E.D. and Fekete, S.P. and Lang, R.J.

In collection: Geometry

We show that deciding whether a given set of circles can be packed into a rectangle, an equilateral triangle, or a unit square are NP-hard problems, settling the complexity of these natural packing problems. On the positive side, we show that any set of circles of total area 1 can be...

URL: http://arxiv.org/abs/1008.1224

PDF: http://arxiv.org/pdf/1008.1224v2

Entry: https://read.somethingorotherwhatever.com/entry/Demaine2010

In collection: History

Postprint (author's final draft)

URL: http://upcommons.upc.edu/handle/2117/78617

Entry: https://read.somethingorotherwhatever.com/entry/BlancoAbellan2015

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 question of interest; I hope you concur! From each point outside, I wondered if light Could...

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

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

Article by Hans-J. Boehm

In collections: Basically computer science, Unusual arithmetic

Rounding errors are usually avoidable, and sometimes we can afford to avoid them.

URL: https://dl.acm.org/doi/10.1145/2911981

Entry: https://read.somethingorotherwhatever.com/entry/Smalldatacomputingcorrectcalculatorarithmetic

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 construction.

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

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

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

Article by Glen Miller

URL: http://www.ncbi.nlm.nih.gov/pubmed/19543813

Entry: https://read.somethingorotherwhatever.com/entry/item13

Article by Miquel, Alexandre

In collections: History, The act of doing maths, About proof

URL: https://www.fing.edu.uy/~amiquel/publis/effectiveness.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Miquel2007

Article by Lemoine, Julien and Viennot, Simon

In collections: Unusual arithmetic, Computational complexity of games

Sprouts is a two-player topological game, invented in 1967 in the University of Cambridge by John Conway and Michael Paterson. The game starts with p spots, and ends in at most 3p-1 moves. The first player who cannot play loses. The complexity of...

URL: http://arxiv.org/abs/1008.2320

PDF: http://arxiv.org/pdf/1008.2320v1

Entry: https://read.somethingorotherwhatever.com/entry/Lemoine2010

Article by C. Krattenthaler

In collections: Art, Combinatorics

These notes provide a survey of the theory of plane partitions, seen through the glasses of the work of Richard Stanley and his school.

URL: http://arxiv.org/abs/1503.05934v2

PDF: http://arxiv.org/pdf/1503.05934v2

Entry: https://read.somethingorotherwhatever.com/entry/PlanepartitionsintheworkofRichardStanleyandhisschool

Article by Marshall Bern and Erik D. Demaine and David Eppstein and Eric Kuo and Andrea Mantler and Jack Snoeyink

In collection: Things to make and do

Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper, we study the limits of unfoldability by studying nonconvex polyhedra with the same combinatorial structure as convex polyhedra. In particular,...

URL: http://erikdemaine.org/papers/Ununfoldable/

Entry: https://read.somethingorotherwhatever.com/entry/UnunfoldablePolyhedrawithConvexFaces

Article by Battisti, F and Carli, M and Neri, A and Egiaziarian, K

In collections: Basically computer science, Fibonaccinalia

URL: http://www.comlab.uniroma3.it/Marco/Articoli%20Battisti/A%20Generalized%20Fibonacci%20LSB%20Data%20Hiding%20Technique.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Battisti2006

Article by Alexandre Silva and Francesco Monticone and Giuseppe Castaldi and Vincenzo Galdi and Andrea Alù and Nader Engheta

In collections: Basically physics, Unusual computers

We introduce the concept of metamaterial analog computing, based on suitably designed metamaterial blocks that can perform mathematical operations (such as spatial differentiation, integration, or...

URL: http://science.sciencemag.org/content/343/6167/160

Entry: https://read.somethingorotherwhatever.com/entry/PerformingMathematicalOperationswithMetamaterials

Web page by Mike Sebastian

In collections: Basically computer science, Easily explained, Lists and catalogues

Results from the evaluation of this equation in degrees mode: arcsin (arccos (arctan (tan (cos (sin (9) ) ) ) ) )

URL: http://www.rskey.org/~mwsebastian/miscprj/results.htm

Entry: https://read.somethingorotherwhatever.com/entry/CalculatorForensics

Article by Friedman, Harvey M

Let k be a positive integer. There is a longest finite sequence x1,...,xn in k letters in which no consecutive block xi,...,x2i is a subsequence of any other consecutive block xj,...,x2j. Let n(k) be this longest length. We prove that n(1) = 3, n(2) = 11, and n(3) is incomprehensibly large. We give a lower bound for n(3) in terms of the familiar Ackerman hierarchy. We also give...

URL: http://u.osu.edu/friedman.8/files/2014/01/LongFinSeq98-2f0wmq3.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Friedman1998

Article by Scott Chapman and Christopher O'Neill

In collections: Animals, Attention-grabbing titles, Easily explained, Unusual arithmetic, Food, Integerology

Every day, 34 million Chicken McNuggets are sold worldwide. At most McDonalds locations in the United States today, Chicken McNuggets are sold in packs of 4, 6, 10, 20, 40, and 50 pieces. However, shortly...

URL: http://arxiv.org/abs/1709.01606v1

PDF: http://arxiv.org/pdf/1709.01606v1

Entry: https://read.somethingorotherwhatever.com/entry/FactoringintheChickenMcNuggetmonoid

Article by Rika Akiyama and Nozomi Abe and Hajime Fujita and Yukie Inaba and Mari Hataoka and Shiori Ito and Satomi Seita

In collections: Attention-grabbing titles, Games to play with friends, Things to make and do

We treat the boundary of the union of blocks in the Jenga game as a surface with a polyhedral structure and consider its genus. We generalize the...

URL: http://arxiv.org/abs/1708.01503v1

PDF: http://arxiv.org/pdf/1708.01503v1

Entry: https://read.somethingorotherwhatever.com/entry/MaximumgenusofthegeneralizedJengagame

Article by Golumbic, Martin Charles and Wassermann, Amir

URL: http://link.springer.com/10.1007/s003730050028

Entry: https://read.somethingorotherwhatever.com/entry/Golumbic1998

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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