An unusual cubic representation problem
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...

Comparison of geometric figures
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: arxiv.org/abs/math/0611062
PDF: arxiv.org/pdf/math/0611062

Circle Packing for Origami Design Is Hard
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: arxiv.org/abs/1008.1224
PDF: arxiv.org/pdf/1008.1224v2

On gardeners, dukes and mathematical instruments
In collection: History
Postprint (author's final draft)
URL: upcommons.upc.edu/handle/2117/

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 question of interest; I hope you concur! From each point outside, I wondered if light Could...
URL: mathoverflow.net/questions/501

Small-data computing: correct calculator arithmetic
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: dl.acm.org/doi/10.1145/2911981

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 construction.
URL: arxiv.org/abs/1704.08483v2
PDF: arxiv.org/pdf/1704.08483v2

London Calling Philosophy and Engineering: WPE 2008
Article by Glen Miller
URL: ncbi.nlm.nih.gov/pubmed/195438

The experimental effectiveness of mathematical proof
Article by Miquel, Alexandre
In collections: History, The act of doing maths, About proof
URL: fing.edu.uy/~amiquel/publis/ef

Computer analysis of Sprouts with nimbers
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: arxiv.org/abs/1008.2320
PDF: arxiv.org/pdf/1008.2320v1

Plane partitions in the work of Richard Stanley and his school
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: arxiv.org/abs/1503.05934v2
PDF: arxiv.org/pdf/1503.05934v2

Ununfoldable Polyhedra with Convex Faces
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: erikdemaine.org/papers/Ununfol

A Generalized Fibonacci LSB Data Hiding Technique
Article by Battisti, F and Carli, M and Neri, A and Egiaziarian, K
In collections: Basically computer science, Fibonaccinalia
URL: comlab.uniroma3.it/Marco/Artic

Performing Mathematical Operations with Metamaterials
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: science.sciencemag.org/content

Calculator Forensics
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: rskey.org/~mwsebastian/miscprj

Long finite sequences
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: u.osu.edu/friedman.8/files/201

Factoring in the Chicken McNugget monoid
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: arxiv.org/abs/1709.01606v1
PDF: arxiv.org/pdf/1709.01606v1

Maximum genus of the generalized Jenga game
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: arxiv.org/abs/1708.01503v1
PDF: arxiv.org/pdf/1708.01503v1