Article by Ben Blum-Smith and Japheth Wood

In collections: Easily explained, Fun maths facts, Puzzles

A beautiful result of Thomas Price links the Fibonacci numbers and the Lucas polynomials to the plane geometry of an ellipse. We give a conceptually transparent development of this result that provides a tour of several gems of classical...

URL: http://arxiv.org/abs/1810.00492v3

PDF: http://arxiv.org/pdf/1810.00492v3

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

Article by Vytautas Gruslys and Arès Méroueh

In collections: Animals, Attention-grabbing titles, Combinatorics

In this paper we consider a pursuit-evasion game on a graph. A team of cats, which may choose any vertex of the graph at any turn, tries to catch an invisible mouse, which is constrained to moving along the vertices of the graph. Our main focus shall be on trees. We...

URL: http://arxiv.org/abs/1502.06591v1

PDF: http://arxiv.org/pdf/1502.06591v1

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

Article by William D. Banks

In collections: Fun maths facts, Integerology

It is shown that the set of decimal palindromes is an additive basis for the natural numbers. Specifically, we prove that every natural number can be expressed as the sum of forty-nine (possibly zero) decimal palindromes.

URL: http://arxiv.org/abs/1508.04721v1

PDF: http://arxiv.org/pdf/1508.04721v1

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

Article by John L. Gustafson

In collections: Basically computer science, Unusual arithmetic

URL: http://web.stanford.edu/class/ee380/Abstracts/170201-slides.pdf

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

Article by Anita Buckley and Miles Reid and Shengtian Zhou

In collection: Food

We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold X,D, under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of...

URL: http://arxiv.org/abs/1208.0457v1

PDF: http://arxiv.org/pdf/1208.0457v1

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

Article by Michael Hardy and Catherine Woodgold

In collections: About proof, Integerology

URL: https://link.springer.com/article/10.1007/s00283-009-9064-8

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

Article by Richard Hoshino

In collections: Attention-grabbing titles, Easily explained, Integerology

We say that an ordered pair of positive integers \(a,b\) with \(a \lt b\) is astonishing if the sum of the integers from \(a\) to \(b\), inclusive, is equal to the digits of \(a\) followed by the digits of \(b\). Determine all astonishing ordered pairs.

URL: https://cms.math.ca/publications/crux/issue/?volume=27&issue=1

PDF: https://cms.math.ca/wp-content/uploads/crux-pdfs/CRUXv27n1.pdf

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

Article by Hilhorst, H.J.

In collections: Probability and statistics, Geometry

URL: http://iopscience.iop.org/1742-5468/2005/09/P09005

Entry: https://read.somethingorotherwhatever.com/entry/Hilhorst2005

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 Mary Caswell Stoddard and Ee Hou Yong and Derya Akkaynak and Catherine Sheard and Joseph A. Tobias and L. Mahadevan

In collections: Animals, Food, Geometry, Modelling

Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a global synthesis of how egg-shape differences arise and evolve. Here, we apply...

URL: http://science.sciencemag.org/content/356/6344/1249

PDF: http://science.sciencemag.org/content/356/6344/1249.full.pdf

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

Graphs, friends and acquaintances

Article by C. Dalfó and M. A. Fiol

In collections: Attention-grabbing titles, Easily explained

As is well known, a graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Therefore, it is not surprising that many of the first results concerning graphs made reference to relationships between people...

URL: http://arxiv.org/abs/1611.07462v2

PDF: http://arxiv.org/pdf/1611.07462v2

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

Article by Levien, Raph

In collections: History, Geometry

The beautiful Euler spiral, deﬁned by the linear relationship between curvature and arclength, was ﬁrst proposed as a problem of elasticity by James Bernoulli, then solved accurately by Leonhard Euler. Since then, it has been independently reinvented twice, ﬁrst by Augustin Fresnel to compute diffraction of light through a slit, and...

URL: http://raph.levien.com/phd/euler_hist.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Levien2008

Article by Cui, Weideng

The modified quantized enveloping algebra has a remarkable basis, called the canonical basis, which was introduced by Lusztig. In this paper, all these monomial elements of the canonical basis for type \(A_{2}\) are determined and we also give a conjecture about all polynomial elements of the canonical basis.

URL: http://arxiv.org/abs/1208.5531

PDF: http://arxiv.org/pdf/1208.5531v3

Entry: https://read.somethingorotherwhatever.com/entry/Cui2012

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

Article by Miller, Steven J. and Montague, David

In collections: About proof, Fun maths facts

We generalize Tennenbaum's geometric proof of the irrationality of sqrt(2) to sqrt(n) for n = 3, 5, 6 and 10.

URL: http://arxiv.org/abs/0909.4913

PDF: http://arxiv.org/pdf/0909.4913v2

Entry: https://read.somethingorotherwhatever.com/entry/Miller2009a

Article by Andrew Granville and Greg Martin

In collections: Attention-grabbing titles, Easily explained, Fun maths facts, Integerology

This is a survey article on prime number races. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of the form 4n+3 less than x then there are of the form 4n+1. Similar...

URL: http://arxiv.org/abs/math/0408319v1

PDF: http://arxiv.org/pdf/math/0408319v1

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

In collections: Basically computer science, Basically physics, Unusual computers

URL: http://www.ncbi.nlm.nih.gov/pubmed/19577519

PDF: http://research.microsoft.com/pubs/79271/turing.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Scarle2008

Article by Chris Matthews

In collections: Easily explained, Fun maths facts

Discusses Yolŋu mathematics and the interconnected relationships of Gurruṯu, and shares an activity for teachers and students to explore the connections and patterns in family trees.

URL: https://www.teachermagazine.com.au/articles/indigenous-perspectives-in-maths-understanding-gurruu

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

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

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