Article by Sachi Hashimoto and Borys Kadets

In collections: Attention-grabbing titles, Combinatorics, Integerology

A Fano problem is an enumerative problem of counting \(r\)-dimensional linear subspaces on a complete intersection in \(\mathbb{P}^n\) over a field of arbitrary characteristic, whenever the corresponding Fano scheme is finite. A...

URL: http://arxiv.org/abs/2002.04580v1

PDF: http://arxiv.org/pdf/2002.04580v1

Entry: https://read.somethingorotherwhatever.com/entry/38406501359372282063949allthatMonodromyofFanoProblems

Web page by Clark Kimberling

In collections: Easily explained, Fun maths facts, Integerology, Puzzles

Fractal sequences have in common with the more familiar geometric fractals the property of self-containment. An example of a fractal sequence is 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, . . . If you delete the first occurrence of each positive integer,...

URL: https://faculty.evansville.edu/ck6/integer/fractals.html

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

Article by Socolar, Joshua E. S. and Taylor, Joan M.

In collection: Geometry

We show that a single tile can fill space uniformly but not admit a periodic tiling. The space--filling tiling that can be built from copies of the tile has the structure of a union of honeycombs with lattice constants of \(2^n a\), where \(a\) sets the scale of the most dense lattice and \(n\) takes...

URL: http://arxiv.org/abs/1003.4279

PDF: http://arxiv.org/pdf/1003.4279v2

Entry: https://read.somethingorotherwhatever.com/entry/Socolar2010

Article by Ralph C. Merkle and Robert A. Freitas Jr. and Tad Hogg and Thomas E. Moore and Matthew S. Moses and James Ryley

In collections: Basically computer science, Things to make and do, Unusual computers

A new paradigm for mechanical computing is demonstrated that requires only two basic parts, links and rotary joints. These basic parts...

URL: http://arxiv.org/abs/1801.03534v1

PDF: http://arxiv.org/pdf/1801.03534v1

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

Article by Allis, Victor

In collection: Games to play with friends

A Shannon C-type strategy program, VICTOR, is written for Connect-Four, based on nine strategic rules. Each of these rules is proven to be correct, implying that conclusions made by VICTOR are correct. Using VICTOR, strategic rules where found which can be used by Black to at least draw the game, on each 7 × (2n) board,...

URL: http://www.informatik.uni-trier.de/~fernau/DSL0607/Masterthesis-Viergewinnt.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Allis1988

Article by Derek Orr

In collection: Unusual arithmetic

In this paper, we discuss a similar functional to that of a standard integral. The main difference is in its definition: instead of taking a sum, we are taking a product. It turns out this new "star-integral" may be written in terms of the standard integral but it has many different (and similar) interesting properties compared...

URL: http://arxiv.org/abs/1805.01861v1

PDF: http://arxiv.org/pdf/1805.01861v1

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

Article by Chung, Ping Ngai and Fernandez, Miguel and Shah, Niralee and Sordo Vieira, Luis and Wikner, Elena

In collections: Easily explained, Geometry, Things to make and do

We provide examples of perimeter-minimizing tilings of the plane by convex pentagons and examples of perimeter-minimizing tilings of certain small flat tori.

URL: https://msp.org/involve/2014/7-4/p02.xhtml

PDF: http://msp.org/involve/2014/7-4/involve-v7-n4-p02-s.pdf

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

Article by Morris, Sidney

In collections: About proof, Fun maths facts

This article begins with a provocative question: Are there any genuine continuous multivariate real-valued functions? This may seem to be a silly question, but it is in essence what David Hilbert asked as one of the 23 problems he posed at the second...

URL: https://www.ams.org/journals/bull/2021-58-01/S0273-0979-2020-01698-8/

PDF: https://www.ams.org/bull/2021-58-01/S0273-0979-2020-01698-8/S0273-0979-2020-01698-8.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Hilbert13Arethereanygenuinecontinuousmultivariaterealvaluedfunctions

Article by David A. Nash and Sara Randall

In collections: Easily explained, Puzzles

The oval track group, \(OT_{n,k}\), is the subgroup of the symmetric group, \(S_n\), generated by the basic moves available in a generalized oval track puzzle with \(n\) tiles and a turntable of size \(k\). In this paper we completely describe the oval track group for all possible...

URL: http://arxiv.org/abs/1612.04476v3

PDF: http://arxiv.org/pdf/1612.04476v3

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

In collections: About proof, Fun maths facts

Heath-Brown [6] suggested a short proof of the two squares theorem, thereby simplifying ideas of Liouville. Zagier [15] suggested a particularly neat form of this, a "One sentence proof". It consists of two suitable involutions on the finite set of the solutions of p = x 2 +4yz in positive integers. A parity argument...

URL: https://link.springer.com/chapter/10.1007/978-0-387-68361-4_8

Entry: https://read.somethingorotherwhatever.com/entry/Elsholtz2002

Article by Washington, Lawrence and Zagier, Don

In collections: Easily explained, The groups group

URL: http://people.mpim-bonn.mpg.de/zagier/files/exp-math-2/fulltext.pdf

Entry: https://read.somethingorotherwhatever.com/entry/Washington1986

Article by Schumacher, B. and Werner, R. F.

In collection: Basically computer science

We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions this allows us to give an explicit characterization of all local rules...

URL: http://arxiv.org/abs/quant-ph/0405174

Entry: https://read.somethingorotherwhatever.com/entry/Schumacher2004

Article by Akio Hizume

In collections: Puzzles, Easily explained, Fibonaccinalia

URL: http://starcage.org/fibonacci_puzzle/fibonacci_puzzle.html

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

Article by Khovanova, Tanya

In collections: Puzzles, Easily explained

I present and discuss a puzzle about wizards invented by John H. Conway.

URL: http://arxiv.org/abs/1210.5460

PDF: http://arxiv.org/pdf/1210.5460v1

Entry: https://read.somethingorotherwhatever.com/entry/Khovanova2012

Article by Culbertson, Jared and Sturtz, Kirk

In collection: Probability and statistics

Given two measurable spaces \(H\) and \(D\) with countably generated \(\sigma\)-algebras, a prior probability measure \(P_H\) on \(H\) and a sampling distribution \(\mcS:H \rightarrow D\), there is a corresponding inference map \(\mcI:D \rightarrow H\) which is unique...

URL: http://arxiv.org/abs/1205.1488

PDF: http://arxiv.org/pdf/1205.1488v3

Entry: https://read.somethingorotherwhatever.com/entry/Culbertson2012

Article by Jitsuro Nagura

In collections: Fun maths facts, Integerology

URL: https://projecteuclid.org/euclid.pja/1195570997

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

Article by Bartholdi, Laurent and Henriques, André G.

In collections: Attention-grabbing titles, Easily explained, Things to make and do, Food, Geometry, Fun maths facts

There are two standard ways of peeling an orange: either cut the skin along meridians, or cut it along a spiral. We consider here the second method, and study the shape of the spiral strip, when...

URL: http://arxiv.org/abs/1202.3033

PDF: http://arxiv.org/pdf/1202.3033v1

Entry: https://read.somethingorotherwhatever.com/entry/Bartholdi2012

Article by Rachel Wulan Nirmalasari Wijaya and Andrea Semaničová-Feňovčíková and Joe Ryan and Thomas Kalinowski

In collections: Attention-grabbing titles, Basically computer science, Food

A simple graph \(G=(V,E)\) admits an \(H\)-covering if every edge in \(E\) is contained in a subgraph \(H'=(V',E')\) of \(G\) which is isomorphic to...

URL: http://arxiv.org/abs/1607.07911v2

PDF: http://arxiv.org/pdf/1607.07911v2

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

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

Article by Uspensky, V

In collection: Fun maths facts

URL: http://linkinghub.elsevier.com/retrieve/pii/0304397594902224

Entry: https://read.somethingorotherwhatever.com/entry/Uspensky1994

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

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