# Math Horizons Contents—November 2016

Can you convince your skeptical friend that 0.999... = 1? What if your friend insists that there's an infinitesimal difference between the two values? In this issue of Math Horizons, Brian Dawson takes a look at whether 0.999... = 1 in the realm of hyperreal numbers.

Here are more highlights:
• In 1996 Math Horizons interviewed a group of students at the Joint Mathematics Meetings; now, 20 years later, one of those students, Darren Glass, interviews another group of students.
• Katharine Merow writes about Maryna Viazovska's recent result on high-dimensional sphere packing.
• Award-winning high school teacher Patrick Honner encourages math students to pursue a teaching career.
• David Clark writes about a trip to Japan, where he took students to see sangaku —mathematical art hung in shrines and temples when the country was closed to the West.
• And on the cover is one of Larry Riddle's symmetric fractals created using group theory.

Enjoy these articles and more in the November issue of Math Horizons. —David Richeson, Editor

Volume 24, Issue 2

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## Articles

### 0.999... = 1: An Infinitesimal Explanation (PDF)

p. 5.
Bryan Dawson
If we allow infinitesimals, does 0.999... still equal 1?

### Seeking Sangaku: Visiting Japan's Homegrown Mathematics

p. 8.
David Clark
Students bring traditional Japanese mathematics back to Virginia.
To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.8

### Life After Calculus: 20 Years Later

p. 12.
Darren Glass
Math Horizons interviewed Darren Glass when he was an undergraduate; 20 years later he interviews nine students.
To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.12

### Topologically Interesting Felt: How to Make a Möbius Bracelet with Wool

p. 16.
Gwen Fisher explains how to make topological surfaces from wool.

To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.16

### Creating Symmetric Fractals

p. 18.
Larry Riddle uses group theory to create symmetric fractals.

To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.18

### Packing Balls in 3, 8, and 24 Dimensions

p. 22.
Katharine Merow
In March, Maryna Viazovska settled two high-dimensional sphere-packing conjectures.
To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.22

### Getting to Know The Man Who Knew Infinity

p. 25.
William Dunham reviews the
biopic about Srinivasa Ramanujan.
To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.25

## THE BOOKSHELF

p. 26.
My Search for Ramanujan: How I Learned to Count by Ken Ono and Amir D. Azcel
Reviewed by Colm Mulcahy
To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.26

The G. H. Hardy Reader edited by Donald J. Albers, Gerald L. Alexanderson, and William Dunham
Reviewed by Adrian Rice
To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.27

### Tame the GRE Math Subject Test

p. 28.
Mohamed Omar gives some study tips for this notoriously challenging exam.

To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.28

## THE PLAYGROUND!

p. 30.
The Math Horizons problem section, edited by Gary Gordon
To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.30

## AFTERMATH

### I Love Teaching Math; Maybe You Will Too

p. 34.
Patrick
Honner encourages math students to consider a career in teaching.
To purchase the article from JSTOR: http://dx.doi.org/10.4169/mathhorizons.24.2.34

To read the article on the MAA blog: http://horizonsaftermath.blogspot.com/2016/10/i-love-teaching-math-maybe-you-will-too.html