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Mathematics Magazine - February 2016

I enjoy when mathematics is motivated or inspired from a real-life situation. The first two articles are prime examples. In the first, Jessica Sklar and Tom Edgar were motivated by unusual wiring in a home that leads to analysis of the Lights Out game. The second article by Franklin Mendivil and Jeff Hooper considers permutations related to the transpose of a matrix, motivated from a data storage perspective. 

Elsewhere in the issue, Elizabeth Wilcox channels Lewis Carroll to explore the Chermak-Delgado lattice and Burkard Polster and Marty Ross consider Pythagorean-like visual proofs. Besides an interview with woodcarver Bjarne Jespersen, there are also some proof without words, the Reviews and Problems sections, and the solutions to the 76th Annual Putnam Competition.

Michael A. Jones, Editor

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Vol. 89, No. 1, pp 1 – 79

Articles

A Confused Electrician Uses Smith Normal Form

Tom Edgar and Jessica K. Sklar

In this paper we define “confused electrician games,” which generalize “Lights Out,” a game popular in mathematical literature. In addition to “Lights Out,” many more recent computer game puzzles can be modeled as confused electrician games.We provide examples of this, and explain how to solve such games using the Smith normal form of a matrix. We note that in many cases, this method is very efficient compared to another, more obvious, method.

To purchase from JSTOR: 10.4169/math.mag.89.1.3

Proof Without Words: Perfect Numbers and Sums of Odd Cubes

Roger B. Nelsen

We show wordlessly that every even perfect number greater than six is a sum of consecutive odd cubes.

To purchase from JSTOR: 10.4169/math.mag.89.1.14

Transposition as a Permutation: A Tale of Group Actions and Modular Arithmetic

Jeff Hooper and Franklin Mendivil

Converting a matrix from row-order storage to column-order storage involves permuting the entries of the matrix. How can we determine this permutation given only the size of the matrix? Unexpectedly, the solution to this question involves the use of elementary group theory and number theory. This includes the Chinese remainder theorem, finding multiplicative generators modulo pn for prime p, and using these to find orbit generators for a group action, a subgroup of acting on all of ℤN.

To purchase from JSTOR: 10.4169/math.mag.89.1.16

Proof Without Words: Sum of Triangular Numbers

Ángel Plaza

The triangular numbers are given by the following explicit formulas: Tn = 1 + 2 + ⋯ n =. Here it is proved visually that  .

To purchase from JSTOR: 10.4169/math.mag.89.1.36

Exploring the Chermak-Delgado Lattice

Elizabeth Wilcox

Need a project to satisfy your craving for abstract algebra? Or do you have a student nosing around your office looking for a project? The Chermak–Delgado lattice is a sublattice of the subgroup lattice of a finite group. The details of its definition don′t require advanced group theory, though working with this lattice can send one on a journey through deeper, more advanced techniques. This makes the Chermak–Delgado lattice the perfect starting point for an undergraduate project after an abstract algebra class. This article guides the curious reader through a series of exercises about the Chermak–Delgado lattice to provide preparation and fuel interest, before posing several open-ended questions for investigation.

To purchase from JSTOR: 10.4169/math.mag.89.1.38

Proof Without Words: The Sum  and Its Partial Sums

Óscar Ciaurri

We provide a visual proof of the identity  including its partial sums.

To purchase from JSTOR: 10.4169/math.mag.89.1.45

One-Glance(ish) Proofs of Pythagoras′ Theorem for 60-Degree and 120-Degree Triangles

Burkard Polster and Marty Ross

In this article we present some elementary proofs of the 60-degree and 120-degree counterparts of Pythagoras′ theorem that mimic the two (most) famous one-glance proofs of Pythagoras′ theorem.

To purchase from JSTOR: 10.4169/math.mag.89.1.47

Bjarne Jespersen: The Magic Woodcarver*

Amy L. Reimann and David A. Reimann

To purchase from JSTOR: 10.4169/math.mag.89.1.55

Problems and Solutions

Proposals, 1986-1990

Quickies, 1057-1058

Solutions, 1956-1960

Answers, 1057-1058

To purchase from JSTOR: 10.4169/math.mag.89.1.58

Reviews

Moral hazard; recreational mathematics; Tower of Hanoi; crime in L.A.

To purchase from JSTOR: 10.4169/math.mag.89.1.67

News and Letters

76th Annual William Lowell Putnam Mathematical Competition

To purchase from JSTOR: 10.4169/math.mag.89.1.69

Dummy View - NOT TO BE DELETED