On badly approximable numbers and certain games
Article by Schmidt, WM
In collection: Games to play with friends
URL: ams.org/journals/tran/1966-123

Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers
Article by Martin Erik Horn
In collections: Attention-grabbing titles, Fibonaccinalia
The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal...
URL: arxiv.org/abs/0711.4030v1
PDF: arxiv.org/pdf/0711.4030v1

A unique pair of triangles
Article by Yoshinosuke Hirakawa and Hideki Matsumura
In collections: Easily explained, Fun maths facts, Geometry
A rational triangle is a triangle with sides of rational lengths. In this short note, we prove that there exists a unique pair of a rational right triangle and a rational isosceles triangle which have the same perimeter and the same area. In the proof, we determine...
URL: arxiv.org/abs/1809.09936v1
PDF: arxiv.org/pdf/1809.09936v1

New entry!
Gergonne's Card Trick, Positional Notation, and Radix Sort
Article by Ethan D. Bolker
In collections: Easily explained, Fun maths facts
Gergonne's three pile card trick has been a favorite of mathematicians for nearly two centuries. This new exposition uses the radix sorting algorithm well known to computer scientists to explain why the trick works, and to explore generalizations. The...
URL: tandfonline.com/doi/abs/10.416
PDF: maa.org/sites/default/files/Bo

Avian egg shape: Form, function, and evolution
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: science.sciencemag.org/content
PDF: science.sciencemag.org/content

Developing a Mathematical Model for Bobbin Lace
Article by Veronika Irvine and Frank Ruskey
In collections: Art, Geometry, Modelling
Bobbin lace is a fibre art form in which intricate and delicate patterns are created by braiding together many threads. An overview of how bobbin lace is made is presented and illustrated with a simple, traditional bookmark design. Research on the topology of textiles and...
URL: arxiv.org/abs/1406.1532v3
PDF: arxiv.org/pdf/1406.1532v3

Packing circles and spheres on surfaces
In collections: Basically computer science, Geometry
Inspired by freeform designs in architecture which involve circles and spheres, we introduce a new kind of triangle mesh whose faces’ incircles form a packing. As it turns out, such meshes have a rich geometry and allow us to cover surfaces with circle patterns, sphere packings, approximate circle packings,...
URL: dl.acm.org/citation.cfm?id=161
PDF: geometrie.tugraz.at/wallner/pa

The Origin of Chemical Elements
Article by Alpher, R. and Bethe, H. and Gamow, G.
In collection: Basically physics
URL: en.wikipedia.org/wiki/Alpher%E

The Muddy Children : A logic for public announcement
Article by Hughes, Jesse
URL: phiwumbda.org/~jesse/slides/Mu

Mechanisms by Tchebyshev
Web page by
In collections: Basically physics, History, Things to make and do, Geometry
This project gathers all the mechanisms created by a great Russian mathematician Pafnuty Lvovich Tchebyshev (1821—1894). Some of them have been stored in museums: twenty are in the Polytechnical museum (Moscow), five are in the Museum of the History of Saint Petersburg State University, some are in The Musée des Arts...
URL: en.tcheb.ru/

Zaphod Beeblebrox's Brain and the Fifty-ninth Row of Pascal's Triangle
Article by Andrew Granville
In collection: Attention-grabbing titles
URL: dms.umontreal.ca/~andrew/PDF/b

What is the smallest prime?
Article by Chris K. Caldwell and Yeng Xiong
In collections: Easily explained, History, Notation and conventions, Integerology
What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first...
URL: arxiv.org/abs/1209.2007v2
PDF: arxiv.org/pdf/1209.2007v2

Fusible numbers and Peano Arithmetic
Article by Jeff Erickson and Gabriel Nivasch and Junyan Xu
In collection: Unusual arithmetic
Inspired by a mathematical riddle involving fuses, we define the "fusible numbers" as follows: $$0$$ is fusible, and whenever $$x,y$$ are fusible with $$|y-x|<1$$, the number $$(x+y+1)/2$$ is also fusible. We prove that the set of fusible numbers, ordered by the usual order on...
URL: arxiv.org/abs/2003.14342v1
PDF: arxiv.org/pdf/2003.14342v1

On Some two way Classifications of Integers
Article by J. Lambek and L. Moser
In collections: Fun maths facts, Integerology
In this note we use the method of generating functions to show that there is a unique way of splitting the non-negative integers into two classes in such a way that the sums of pairs of distinct integers will be the same (with same multiplicities) for both classes. We prove a...
URL: cambridge.org/core/journals/ca
PDF: cambridge.org/core/services/ao

Fractions without Quotients: Arithmetic of Repeating Decimals
Article by Plagge, Richard
In collections: Notation and conventions, Unusual arithmetic, Easily explained
URL: maa.org/sites/default/files/pd

Denser Egyptian Fractions
Article by Martin, Greg
In collections: Easily explained, Fun maths facts
An Egyptian fraction is a sum of distinct unit fractions (reciprocals of positive integers). We show that every rational number has Egyptian fraction representations where the number of terms is of the same order of magnitude as the largest denominator, improving a result from an earlier paper to...
URL: arxiv.org/abs/math/9811112
PDF: arxiv.org/pdf/math/9811112v1

National Curve Bank
Article by Shirley B. Gray and Stewart Venit and Russ Abbott
In collections: Lists and catalogues, Geometry
The National Curve Bank is a resource for students of mathematics. We strive to provide features - for example, animation and interaction - that a printed page cannot offer. We also include geometrical, algebraic, and historical aspects of curves, the kinds of attributes that make the mathematics special...
URL: web.calstatela.edu/curvebank/h