
Mathematical Economics for Mathematics and Statistics Awareness Month
http://www.ams.org/publicoutreach/featurecolumn/fc201804
4
2018
Joe Malkevitch
Game Theory and Social Choice

Neural Nets and How They Learn
http://www.ams.org/publicoutreach/featurecolumn/fc201803
3
2018
David Austin
Discrete Math and Combinatorics
Math and Technology

Jakob Bernoulli's Zoo
http://www.ams.org/publicoutreach/featurecolumn/fc201802
2
2018
Bill Casselman
Discrete Math and Combinatorics
History of Mathematics

RegularFaced Polyhedra: Remembering Norman Johnson
http://www.ams.org/publicoutreach/featurecolumn/fc201801
1
2018
Joe Malkevitch
Discrete Math and Combinatorics
Geometry and Topology
History of Mathematics

How to Differentiate with a Computer
http://www.ams.org/publicoutreach/featurecolumn/fc201712
12
2017
David Austin
Calculus and Analysis

Solar Daze
http://www.ams.org/publicoutreach/featurecolumn/fc201711
11
2017
Bill Casselman
Calculus and Analysis
History of Mathematics
Math and the Sciences

The Early History of Calculus Problems, II
http://www.ams.org/publicoutreach/featurecolumn/fc201710
10
2017
Tony Phillips
Calculus and Analysis
History of Mathematics

Ranking, Grading, and Genealogy
http://www.ams.org/publicoutreach/featurecolumn/fc201709
9
2017
Joe Malkevitch
Game Theory and Social Choice
Discrete Math and Combinatorics
History of Mathematics

Untangling Your Square Dance
http://www.ams.org/publicoutreach/featurecolumn/fc201708
8
2017
David Austin
Geometry and Topology
Algebra

The Joy of Barycentric Subdivision
http://www.ams.org/publicoutreach/featurecolumn/fc201706
6
2017
Bill Casselman
Geometry and Topology
Probability and Statistics

Surface Topology in Bach Canons, II: The Torus
http://www.ams.org/publicoutreach/featurecolumn/fc201705
5
2017
Tony Phillips
Geometry and Topology
Math and the Arts

Remembering Bill Thurston (19462012)
http://www.ams.org/publicoutreach/featurecolumn/fc201704
4
2017
Joe Malkevitch
Geometry and Topology
History of Mathematics

Patterns in Permutations
http://www.ams.org/publicoutreach/featurecolumn/fc201703
3
2017
David Austin
Discrete Math and Combinatorics
Math and the Sciences

Assembly Required
http://www.ams.org/publicoutreach/featurecolumn/fc201702
2
2017
Bill Casselman
Discrete Math and Combinatorics
Geometry and Topology

Building Trees for Biologists
http://www.ams.org/publicoutreach/featurecolumn/fc201701
1
2017
Joe Malkevitch
Discrete Math and Combinatorics
Math and the Sciences

Finding Holes in the Data
http://www.ams.org/publicoutreach/featurecolumn/fc201612
12
2016
David Austin
Geometry and Topology
Math and Technology

Circles and Squares ... and Primes
http://www.ams.org/publicoutreach/featurecolumn/fc201611
11
2016
Bill Casselman
Calculus and Analysis
Algebra
History of Mathematics

Surface Topology in Bach Canons, I: The Mobius strip
http://www.ams.org/publicoutreach/featurecolumn/fc201610
10
2016
Tony Phillips
Geometry and Topology
Math and the Arts

Theoretical Mathematics Finds Use in EconomicsA Tribute to Lloyd Shapley
http://www.ams.org/publicoutreach/featurecolumn/fc201609
9
2016
Joe Malkevitch
Discrete Math and Combinatorics
Game Theory and Social Choice

Game. SET. Polynomial.
http://www.ams.org/publicoutreach/featurecolumn/fc201608
8
2016
David Austin
Discrete Math and Combinatorics
Algebra

The Legend of Abraham Wald
http://www.ams.org/publicoutreach/featurecolumn/fc201606
6
2016
Bill Casselman
Probability and Statistics
History of Mathematics

The Early History of Calculus Problems
http://www.ams.org/publicoutreach/featurecolumn/fc201605
5
2016
Tony Phillips
History of Mathematics
Calculus and Analysis

Mathematics and Crystal Balls
http://www.ams.org/publicoutreach/featurecolumn/fc201604
4
2016
Joe Malkevitch
History of Mathematics
Probability and Statistics

Knot Quandaries Quelled by Quandles
http://www.ams.org/publicoutreach/featurecolumn/fc201603
3
2016
David Austin
Algebra
Geometry and Topology

It Just Keeps Piling Up!
http://www.ams.org/publicoutreach/featurecolumn/fc201602
2
2016
Bill Casselman
Probability and Statistics
Discrete Math and Combinatorics

Are Precise Definitions a Good Idea?
http://www.ams.org/publicoutreach/featurecolumn/fc201601
1
2016
Joe Malkevitch
History of Mathematics
Geometry and Topology

Petals, Flowers and Circle Packings
http://www.ams.org/publicoutreach/featurecolumn/fc201512
12
2015
David Austin
Calculus and Analysis
Geometry and Topology

Circles and Squares
http://www.ams.org/publicoutreach/featurecolumn/fc201511
11
2015
Bill Casselman
History of Mathematics
Geometry and Topology
Algebra
Later on, mathematicians took up the much more difficult question, can we find a formula for rk(n), the number of ways to express n as a sum of k integral squares? This last question led to some of the most sophisticated mathematics of the 20th century, as did a common generalization of all these questions...

Hidden Symmetries of Labyrinths from Antiquity and the Middle Ages
http://www.ams.org/publicoutreach/featurecolumn/fc201510
10
2015
Tony Phillips
History of Mathematics
Geometry and Topology
The purpose of this column is to point out that the great majority of labyrinth designs share a topological symmetry which, while not obvious, cannot be accidental...

Mathematics and Ecology
http://www.ams.org/publicoutreach/featurecolumn/fc201509
9
2015
Joe Malkevitch
Math and Nature
Math and the Sciences
Rather than try to show the huge range of ways that mathematics is assisting biologists in understanding the vast landscape of modern biology, I will take a look at a rather small domain, which offers ways to look at some traditional topics from a novel point of view...

Game. SET. Line.
http://www.ams.org/publicoutreach/featurecolumn/fc201508
8
2015
David Austin
Discrete Math and Combinatorics
Geometry and Topology
Linear Algebra
After playing the game for a while, two natural questions appear, which we will explore: "How many cards need to be turned face up to guarantee the presence of a set?" and "What is the probability that the initial twelve cards do not contain a set?"...

Sums and Integrals: The Swiss analysis knife
http://www.ams.org/publicoutreach/featurecolumn/fc201506
6
2015
Bill Casselman
Calculus and Analysis
History of Mathematics
The charm of the formula discovered by him [Euler] and MacLaurin is that it applies to a remarkable assortment of mathematical questions...

Math and the Sewing Machine
http://www.ams.org/publicoutreach/featurecolumn/fc201505
5
2015
Tony Phillips
Miscellaneous
Math and Technology
In this column I will explore mathematical aspects of the action of the sewing machine and of the often associated bobbin winder...

Mathematical Careers
http://www.ams.org/publicoutreach/featurecolumn/fc201504
4
2015
Joe Malkevitch
Game Theory and Social Choice
Math and the Sciences
You don't have to be a 'genius' to enjoy mathematics and have a career in it...

The Stable Marriage Problem and School Choice
http://www.ams.org/publicoutreach/featurecolumn/fc201503
3
2015
David Austin
Game Theory and Social Choice
Discrete Math and Combinatorics
This column will present the gametheoretic results contained in the original GaleShapley paper along with Roth's subsequent analysis. Pathak calls the deferred acceptance algorithm "one of the great ideas in economics," and Roth and Shapley were awarded the 2012 Nobel Prize in economics for this work...

The Mathematics of the Rainbow, Part II
http://www.ams.org/publicoutreach/featurecolumn/fc201502
2
2015
Bill Casselman
Math and Nature
History of Mathematics
I'll first recall in some detail the steps leading to Airy's formula for the intensity of light in a rainbow, and then say something about how Airy made it possible to compare his theory to experiment...

Mathematics and Psychology
http://www.ams.org/publicoutreach/featurecolumn/fc201501
1
2015
Joe Malkevitch
Game Theory and Social Choice
Math and the Sciences
We will see that mathematics in its own terms and psychology in its own terms have benefited from their interaction with each other...

How to Grow and Prune a Classification Tree
http://www.ams.org/publicoutreach/featurecolumn/fc201412
12
2014
David Austin
Discrete Math and Combinatorics
Math and the Sciences
In what follows, we will describe the work of Breiman and his colleagues as set out in their seminal book "Classification and Regression Trees." Theirs is a very rich story, and we will concentrate on only the essential ideas...

Why Do We Expect Lots of Twin Primes?
http://www.ams.org/publicoutreach/featurecolumn/fc201411
11
2014
Bill Casselman
History of Mathematics
Calculus and Analysis
One important question is, how are prime numbers distributed among the integers? The answer is, in a very few words, rather randomly, given certain basic statistics...

The Topology of Impossible Spaces
http://www.ams.org/publicoutreach/featurecolumn/fc201410
10
2014
Tony Phillips
Geometry and Topology
Math and the Arts
The purpose of this month's article is to bring once more to the public consciousness some work of Sir Roger Penrose...

Mathematics and Chemistry: Partners in Understanding Our World
http://www.ams.org/publicoutreach/featurecolumn/fc201409
9
2014
Joe Malkevitch
Math and the Sciences
Discrete Math and Combinatorics
Here I will give a sketch of some of the issues arising from using mathematics in fields outside of mathematics, but for this column I will use examples from the area of chemistry...

Congressional Redistricting and Gerrymandering
http://www.ams.org/publicoutreach/featurecolumn/fc201408
8
2014
David Austin
Game Theory and Social Choice
Geometry and Topology
Discrete Math and Combinatorics
We'll look at some measures that have been created to constrain gerrymandering...

Feeling Your Way Around in High Dimensions
http://www.ams.org/publicoutreach/featurecolumn/fc201406
6
2014
Bill Casselman
Linear Algebra
Geometry and Topology
The simplest objects of interest in any dimension, which are also the basis for approximating arbitrary objects, are the convex polytopes. and in this column I'll explain how to begin to probe them...

The Knots in the Quipu, and in the Friar's Belt
http://www.ams.org/publicoutreach/featurecolumn/fc201405
5
2014
Tony Phillips
History of Mathematics
Math and the Arts
Geometry and Topology
In a canonical numerical quipu, each pendent (or subsidiary) displays a number: a positive integer, expressed in decimal notation...

Magical Mathematics  A Tribute to Martin Gardner
http://www.ams.org/publicoutreach/featurecolumn/fc201404
4
2014
Joe Malkevitch
History of Mathematics
Perhaps no one has done more to make the world aware of mathematics than Martin Gardner...

How to Make a 3D Print
http://www.ams.org/publicoutreach/featurecolumn/fc201403
3
2014
David Austin
Geometry and Topology
Math and Technology
Mathematically speaking, the 3D print is constructed from a 1dimensional path. This article will describe how to find that path...

Stereographic Projection
http://www.ams.org/publicoutreach/featurecolumn/fc201402
2
2014
Bill Casselman
Geometry and Topology
History of Mathematics
In effect, stereographic projection wraps the plane around the sphere, missing only that one point...

Periods
http://www.ams.org/publicoutreach/featurecolumn/fc201401
1
2014
Joe Malkevitch
Discrete Math and Combinatorics
After a brief introduction to the combinatorics on words, which builds on some of the same ground that was discussed in a prior note, I will look at a remarkable theorem due to the mathematicians Herbert Wilf and Nathan Jacob Fine...

The Polish Attack on Enigma II: Zygalski sheets
http://www.ams.org/publicoutreach/featurecolumn/fc201312
12
2013
Bill Casselman
History of Mathematics
I'll say a little bit about how the mathematics was applied to reading German messages, up until a drastic change in procedure by the Germans, and I'll say more about how the Poles recovered after this change...

Fedorov's Five Parallelohedra
http://www.ams.org/publicoutreach/featurecolumn/fc201311
11
2013
David Austin
Geometry and Topology
We will see how some elegant ideas of Conway and Sloane, introduced in the 1990s, lead to Fedorov's determination of the five parallelohedra....

Spherical Dodecahedral Space
http://www.ams.org/publicoutreach/featurecolumn/fc201310
10
2013
Tony Phillips
Geometry and Topology
In this column I propose to work through this construction and to start by analyzing spherical dodecahedral space as an object in polyhedral geometry. ....

Words and More Words
http://www.ams.org/publicoutreach/featurecolumn/fc201309
9
2013
Joe Malkevitch
Discrete Math and Combinatorics
Here I will take a brief look at some of the ways mathematics has looked at words in the hope of exploiting the resulting ideas....

The Frobenius Problem: How I bought Chicken McNuggets with exact change
http://www.ams.org/publicoutreach/featurecolumn/fc201308
8
2013
David Austin
Calculus and Analysis
Discrete Math and Combinatorics
Though the problem seems like one from discrete mathematics, we will see an unexpected interplay between the continuous and discrete worlds as we use somewhat elementary techniques from calculus to arrive at a solution...

More ENIGMA
http://www.ams.org/publicoutreach/featurecolumn/fc201306
6
2013
Bill Casselman
History of Mathematics
What I want to discuss in this feature is one part of Enigma operation that has been much written about elsewhere, but which still causes some confusion. This is the way in which key presses lead to rotor motion....

Galileo's Arithmetic
http://www.ams.org/publicoutreach/featurecolumn/fc201305
5
2013
Tony Phillips
History of Mathematics
The manuscripts allow us very unusual, if not unique, access to the private calculations of a great scientist; it is as if we could look over his shoulder and watch him at work...

Sustainability
http://www.ams.org/publicoutreach/featurecolumn/fc201304
4
2013
Joe Malkevitch
Game Theory and Social Choice
Math and Nature
Can mathematics help us understand issues of sustainability and make it possible to realize enjoyable lives for all the people who share this planet, now and far into the future?...

Using Projective Geometry to Correct a Camera
http://www.ams.org/publicoutreach/featurecolumn/fc201303
3
2013
David Austin
Linear Algebra
Geometry and Topology
There's nothing particularly deep in this problem or the solution, but I hope that it demonstrates some of the pleasure to be found in using one's mathematical intuition...

How to Read QR Symbols Without Your Mobile Telephone
http://www.ams.org/publicoutreach/featurecolumn/fc201302
2
2013
Bill Casselman
Linear Algebra
Math and Technology
How does your phone read the information in a QR code symbol? How is information stored on it?...

Hurricane Sandy Meets Mathematics
http://www.ams.org/publicoutreach/featurecolumn/fc201301
1
2013
Joe Malkevitch
Math and Nature
A sensitivity to mathematics and its powerful analytical tools helps give insight into Sandy's devastation and how to minimize the consequences of future powerful storms...

Who's Number 1? Hodge Theory Will Tell Us
http://www.ams.org/publicoutreach/featurecolumn/fc201212
12
2012
David Austin
Discrete Math and Combinatorics
Linear Algebra
This article describes a method, proposed by Jiang, Lim, Yao, and Ye, that uses Hodge theory to rank a large number of alternatives...

Can You Do Better?
http://www.ams.org/publicoutreach/featurecolumn/fc201211
11
2012
Bill Casselman
Geometry and Topology
History of Mathematics
Recently, there has been a great deal of activity concerning the case of packing regular tetrahedra in space, which is what motivated me to put together this column.

William Thurston
http://www.ams.org/publicoutreach/featurecolumn/fc201210
10
2012
Tony Phillips
Geometry and Topology
What I'd like to do in this column is give an impression of what it was like to interact with him as a fellow mathematician or as a student.

Mathematical Modeling
http://www.ams.org/publicoutreach/featurecolumn/fc201209
9
2012
Joe Malkevitch
Miscellaneous
Math and Technology
My purpose here is to try to clarify what it means to "model with mathematics," and more broadly to deal with related phrases.

It's a Small World After All
http://www.ams.org/publicoutreach/featurecolumn/fc201208
8
2012
David Austin
Discrete Math and Combinatorics
Math and Technology
In this article, we will look at this phenomenon from a mathematical perspective and learn how human networks are organized, perhaps unwittingly, to create this phenomenon.

What Does a Circle Look Like?
http://www.ams.org/publicoutreach/featurecolumn/fc201206
6
2012
Bill Casselman
History of Mathematics
Geometry and Topology
It is in the very beginning of Apollonius' treatise the "Conics" that he deals with the question we are concerned with, and I'll try to explain, roughly, what he does.

Old Babylonian Multiplication and Reciprocal Tables
http://www.ams.org/publicoutreach/featurecolumn/fc201205
5
2012
Tony Phillips
History of Mathematics
These "table texts" are the first known examples of a tradition of mathematical tablemaking that is still alive and useful today.

More Precious than Gold?
http://www.ams.org/publicoutreach/featurecolumn/fc201204
4
2012
Joe Malkevitch
History of Mathematics
Probability and Statistics
My goal here is to briefly discuss what is meant by the phrase data mining and what mathematical tools and ideas have been brought to bear in trying to make progress in this field.

A (Very Short) Detour for the Traveling Salesman
http://www.ams.org/publicoutreach/featurecolumn/fc201203
3
2012
David Austin
Discrete Math and Combinatorics
In this article, we'll explore why the Traveling Salesman Problem is an interesting problem and describe a recent result concerning it.

Archimedes on the Circumference and Area of a Circle
http://www.ams.org/publicoutreach/featurecolumn/fc201202
2
2012
Bill Casselman
Geometry and Topology
History of Mathematics
The area of any circle is equal to a rightangled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle.

Weird Rulers
http://www.ams.org/publicoutreach/featurecolumn/fc201201
1
2012
Joe Malkevitch
Discrete Math and Combinatorics
Hopefully this tour of ideas on the periphery of studying Golomb rulers will give you a flavor of the fun and excitement of what mathematics is about.

Arrangements and Duality or How I Learned to Slice a Ham and Cheese Sandwich
http://www.ams.org/publicoutreach/featurecolumn/fc201112
12
2011
David Austin
Geometry and Topology
Math and Technology
The aim of this article is to describe what the discrepancy of a set of points is and how to compute it efficiently.

Fragments of Greek Mathematics
http://www.ams.org/publicoutreach/featurecolumn/fc201111
11
2011
Bill Casselman
History of Mathematics
It might be very surprising that some of the oldest remnants of Greek mathematics have been found on Elephantine Island, at the southern boundary of Egypt.

Xray Crystallography and the Fourier Transform
http://www.ams.org/publicoutreach/featurecolumn/fc201110
10
2011
Tony Phillips
Math and the Sciences
History of Mathematics
When a monochomatic Xray diffracts off a crystal it performs part of a mathematical operation: the Fourier transform.

Going, Going, ..., Gone!
http://www.ams.org/publicoutreach/featurecolumn/fc201109
09
2011
Joe Malkevitch
Geometry and Topology
It may surprise you to learn how much insight into auctions mathematics has been able to provide in recent years.

The Shadow Knows: How to measure time with a sundial
http://www.ams.org/publicoutreach/featurecolumn/fc201108
08
2011
David Austin
Math and Nature
Math and the Sciences
In this article, we'll consider some mathematical issues involved in constructing a sundial.

What's Normal?
http://www.ams.org/publicoutreach/featurecolumn/fcarcnormalintegral
06
2011
Bill Casselman
Calculus and Analysis
Probability and Statistics
Any method of numerical integration, such as Simpson's rule, works rapidly and accurately in any range of practical significance. But if we take the problem as a somewhat theoretical one, there are many interesting questions that arise.

How Not to Square the Circle
http://www.ams.org/publicoutreach/featurecolumn/fcarccusa
05
2011
Tony Phillips
History of Mathematics
Geometry and Topology
Nicholas of Cusa was attacking a problem dating back to the ancient Greeks. The solution would have made him famous forever.

Complexity
http://www.ams.org/publicoutreach/featurecolumn/fcarccomplexity
04
2011
Joe Malkevitch
Math and Technology
History of Mathematics
In honor of Mathematics Awareness Month I will take an idiosyncratic look at mathematical aspects of complexity, in particular some history of mathematical approaches and insights into this subject.

Aligning Sequence Reads to Assemble the Genome Puzzle
http://www.ams.org/publicoutreach/featurecolumn/fcarcdnapuzzle
03
2011
David Austin
Math and Technology
Math and the Sciences
In this column, I will describe current technology that is used in genome sequencing and see how mathematics plays a crucial role in processing the data.

Why Only Five?
http://www.ams.org/publicoutreach/featurecolumn/fcarcfivepolyhedra
02
2011
Bill Casselman
History of Mathematics
Geometry and Topology
In this column I want to give some idea of how subtle Euclid can be by tracing the reasoning involved in proving the last major assertion of the Elements, that there are no more than five regular polyhedra.

The Price of Anarchy
http://www.ams.org/publicoutreach/featurecolumn/fcarcanarchy
01
2011
Joe Malkevitch
Game Theory and Social Choice
What Prisoner's Dilemma and Braess's Paradox point out is that there are situations where, if individuals are left to make their own decisions, the result might be that as a group or as individuals they are worse off.

How Many Times Do I Have to Shuffle This Deck?
http://www.ams.org/publicoutreach/featurecolumn/fcarcshuffle
12
2010
David Austin
Probability and Statistics

Geometry and the Discrete Fourier Transform
http://www.ams.org/publicoutreach/featurecolumn/fcarcgeodft
11
2010
Bill Casselman
Geometry and Topology

Farey Numbers and the Magnetic Cactus
http://www.ams.org/publicoutreach/featurecolumn/fcarcphyllotaxis
10
2010
Tony Phillips
Math and Nature
Math and the Sciences

Who Won!
http://www.ams.org/publicoutreach/featurecolumn/fcarcscores
09
2010
Joe Malkevitch
Game Theory and Social Choice

Multiplication is Easier When It's Complex
http://www.ams.org/publicoutreach/featurecolumn/fcarcmultiplication
08
2010
David Austin
Math and Technology
Discrete Math and Combinatorics

How Did Escher Do It?
http://www.ams.org/publicoutreach/featurecolumn/fcarccirclelimit
06
2010
Bill Casselman
Math and the Arts

From Pascal's Triangle to the Bellshaped Curve
http://www.ams.org/publicoutreach/featurecolumn/fcarcnormal
05
2010
Tony Phillips
Probability and Statistics

Mathematics and Sports
http://www.ams.org/publicoutreach/featurecolumn/fcarcsports
04
2010
Joe Malkevitch
Discrete Math and Combinatorics

Moving Remy in Harmony: Pixar's Use of Harmonic Functions
http://www.ams.org/publicoutreach/featurecolumn/fcarcharmonic
03
2010
David Austin
Math and Technology
Math and the Arts
Differential Equations

Crypto Graphics
http://www.ams.org/publicoutreach/featurecolumn/fcarcdatamatrix
02
2010
Bill Casselman
Math and Technology
Linear Algebra

Keep on Trucking
http://www.ams.org/publicoutreach/featurecolumn/fcarctrucking
01
2010
Joe Malkevitch
Discrete Math and Combinatorics

Puzzling Over Exact Cover Problems
http://www.ams.org/publicoutreach/featurecolumn/fcarckanoodle
12
2009
David Austin
Discrete Math and Combinatorics

Marian Rejewski and the First Break into Enigma
http://www.ams.org/publicoutreach/featurecolumn/fcarcenigma
11
2009
Bill Casselman
History of Mathematics

A NonCommutative Marriage System in the South Pacific
http://www.ams.org/publicoutreach/featurecolumn/fcarcvanuatu
10
2009
Tony Phillips
Algebra
Game Theory and Social Choice

School Choice
http://www.ams.org/publicoutreach/featurecolumn/fcarcschoolchoice
09
2009
Joe Malkevitch
Game Theory and Social Choice

We Recommend a Singular Value Decomposition
http://www.ams.org/publicoutreach/featurecolumn/fcarcsvd
08
2009
David Austin
Linear Algebra

How Much Longer Can This Go On?
http://www.ams.org/publicoutreach/featurecolumn/fcarclongestsubsequence
06
2009
Bill Casselman
Algebra
Discrete Math and Combinatorics

Simon Newcomb and "Natural Numbers" (Benford's Law)
http://www.ams.org/publicoutreach/featurecolumn/fcarcnewcomb
05
2009
Tony Phillips
Probability and Statistics
History of Mathematics

Mathematics and Climate
http://www.ams.org/publicoutreach/featurecolumn/fcarcclimate
04
2009
Joe Malkevitch
Math and the Sciences

No Static at All: Frequency modulation and music synthesis
http://www.ams.org/publicoutreach/featurecolumn/fcarcsynthesizer
03
2009
David Austin
Math and the Arts
Math and Technology
Calculus and Analysis

The Mathematics of Rainbows
http://www.ams.org/publicoutreach/featurecolumn/fcarcrainbows
02
2009
Bill Casselman
Math and Nature

People Making a Difference
http://www.ams.org/publicoutreach/featurecolumn/fcarcklee
01
2009
Joe Malkevitch
Geometry and Topology

"Trees, Teeth, and Time: The mathematics of clock making
http://www.ams.org/publicoutreach/featurecolumn/fcarcsternbrocot
12
2008
David Austin
Algebra
Discrete Math and Combinatorics

<![CDATA[From Bézier to Bernstein]]>
http://www.ams.org/publicoutreach/featurecolumn/fcarcbezier
11
2008
Bill Casselman
Calculus and Analysis

Insideout Frieze Symmetries in Ancient Peruvian Weavings
http://www.ams.org/publicoutreach/featurecolumn/fcarcweaving
10
2008
Tony Phillips
History of Mathematics
Math and the Arts

Gray Codes
http://www.ams.org/publicoutreach/featurecolumn/fcarcgray
09
2008
Joe Malkevitch
Discrete Math and Combinatorics

Percolation: Slipping through the Cracks
http://www.ams.org/publicoutreach/featurecolumn/fcarcpercolation
08
2008
David Austin
Probability and Statistics

The Mathematics of Surveying: Part II. The Planimeter
http://www.ams.org/publicoutreach/featurecolumn/fcarcsurveyingtwo
06
2008
Bill Casselman
John Eggers
Calculus and Analysis
Math and the Sciences
History of Mathematics

The Mathematics of Surveying: Part I
http://www.ams.org/publicoutreach/featurecolumn/fcarcsurveyingone
05
2008
Tony Phillips
Geometry and Topology
History of Mathematics

The Process of Electing a President
http://www.ams.org/publicoutreach/featurecolumn/fcarcelections
04
2008
Joe Malkevitch
Game Theory and Social Choice

Random Numbers: Nothing Left to Chance
http://www.ams.org/publicoutreach/featurecolumn/fcarcrandom
03
2008
David Austin
Probability and Statistics
Algebra

What is the Length of a Year on Planet Sitnikov?
http://www.ams.org/publicoutreach/featurecolumn/fcarcsitnikov
02
2008
Bill Casselman
Calculus and Analysis
Math and the Sciences

Urban Geometry
http://www.ams.org/publicoutreach/featurecolumn/fcarcurbangeom
01
2008
Joe Malkevitch
Discrete Math and Combinatorics
Geometry and Topology

Pulling Digits out of Pi
http://www.ams.org/publicoutreach/featurecolumn/fcarcpi
12
2007
David Austin
Geometry and Topology
Calculus and Analysis

Strange Associations
http://www.ams.org/publicoutreach/featurecolumn/fcarcassociahedra
11
2007
Bill Casselman
Geometry and Topology
Discrete Math and Combinatorics

Taxi!
http://www.ams.org/publicoutreach/featurecolumn/fcarctaxi
10
2007
Joe Malkevitch
Geometry and Topology

Image Compression: Seeing What's Not There
http://www.ams.org/publicoutreach/featurecolumn/fcarcimagecompression
09
2007
David Austin
Math and Technology
Linear Algebra

Time and the Hour Running Through Rough Days
http://www.ams.org/publicoutreach/featurecolumn/fcarctime
08
2007
Bill Casselman
History of Mathematics
Geometry and Topology

The Mathematics Behind Quantum Computing: Part II
http://www.ams.org/publicoutreach/featurecolumn/fcarcquantumtwo
06
2007
Tony Phillips
Math and Technology
Algebra

The Mathematics Behind Quantum Computing: Part I
http://www.ams.org/publicoutreach/featurecolumn/fcarcquantumone
05
2007
Tony Phillips
Math and Technology
Algebra

Mathematics and the Brain
http://www.ams.org/publicoutreach/featurecolumn/fcarcbrain
04
2007
Joe Malkevitch
Math and the Sciences
Math and Technology

That Knotty DNA
http://www.ams.org/publicoutreach/featurecolumn/fcarcknotsdna
03
2007
David Austin
Math and the Sciences
Geometry and Topology

All for Nought
http://www.ams.org/publicoutreach/featurecolumn/fcarcindiazero
02
2007
Bill Casselman
History of Mathematics

Rationality and Game Theory
http://www.ams.org/publicoutreach/featurecolumn/fcarcrationality
01
2007
Joe Malkevitch
Game Theory and Social Choice

How Google Finds Your Needle in the Web's Haystack
http://www.ams.org/publicoutreach/featurecolumn/fcarcpagerank
12
2006
David Austin
Math and Technology
Discrete Math and Combinatorics
Linear Algebra

Lorenz and Modular Flows: A Visual Introduction
http://www.ams.org/publicoutreach/featurecolumn/fcarclorenz
11
2006
Jos Leys
Math and the Sciences
Linear Algebra

The Princess of Polytopia: Alicia Boole Stott and the 120cell
http://www.ams.org/publicoutreach/featurecolumn/fcarcboole
10
2006
Tony Phillips
History of Mathematics
Geometry and Topology

Finite Geometries?
http://www.ams.org/publicoutreach/featurecolumn/fcarcfinitegeometries
09
2006
Joe Malkevitch
History of Mathematics
Geometry and Topology

Voronoi Diagrams and a Day at the Beach
http://www.ams.org/publicoutreach/featurecolumn/fcarcvoronoi
08
2006
David Austin
Geometry and Topology

<![CDATA[Simple Chaos  The Hénon map]]>
http://www.ams.org/publicoutreach/featurecolumn/fcarchenon
06
2006
Bill Casselman
Calculus and Analysis

The Octosphericon and the Cretan Maze
http://www.ams.org/publicoutreach/featurecolumn/fcarcoctocretan
05
2006
Tony Phillips
Geometry and Topology
Math and the Arts

Mathematics and Internet Security
http://www.ams.org/publicoutreach/featurecolumn/fcarcinternet
04
2006
Joe Malkevitch
Math and Technology
History of Mathematics

When Kissing Involves Trigonometry
http://www.ams.org/publicoutreach/featurecolumn/fcarckissing
03
2006
David Austin
Geometry and Topology
History of Mathematics

Variations on Graph Minor
http://www.ams.org/publicoutreach/featurecolumn/fcarcgminor
02
2006
Bill Casselman
Geometry and Topology
Discrete Math and Combinatorics

Trees: A Mathematical Tool for All Seasons
http://www.ams.org/publicoutreach/featurecolumn/fcarctrees
01
2006
Joe Malkevitch
Discrete Math and Combinatorics

Penrose Tilings Tied up in Ribbons
http://www.ams.org/publicoutreach/featurecolumn/fcarcribbons
12
2005
David Austin
Geometry and Topology

The Mathematical Uncertainty Principle
http://www.ams.org/publicoutreach/featurecolumn/fcarcuncertainty
11
2005
Tony Phillips
Calculus and Analysis
Math and the Sciences

Mental Calculation
http://www.ams.org/publicoutreach/featurecolumn/fcarctomography
10
2005
Bill Casselman
Math and Technology
Calculus and Analysis

Sales and Chips
http://www.ams.org/publicoutreach/featurecolumn/fcarctsp
09
2005
Joe Malkevitch
Discrete Math and Combinatorics

Penrose Tiles Talk Across Miles
http://www.ams.org/publicoutreach/featurecolumn/fcarcpenrose
08
2005
David Austin
Geometry and Topology

Topology of Venn Diagrams
http://www.ams.org/publicoutreach/featurecolumn/fcarcvenn
06
2005
Tony Phillips
Geometry and Topology
Discrete Math and Combinatorics

Slingshots and Space Shots
http://www.ams.org/publicoutreach/featurecolumn/fcarcslingshot
05
2005
Bill Casselman
Calculus and Analysis
Math and the Sciences

Mathematics and Cosmology
http://www.ams.org/publicoutreach/featurecolumn/fcarccosmology
04
2005
Joe Malkevitch
History of Mathematics

Resolving Bankruptcy Claims
http://www.ams.org/publicoutreach/featurecolumn/fcarcbankruptcy
03
2005
Joe Malkevitch
Game Theory and Social Choice

The Center of Population of the United States
http://www.ams.org/publicoutreach/featurecolumn/fcarcpopulationcenter
02
2005
David Austin
Geometry and Topology

Euler's Polyhedral Formula: Part II
http://www.ams.org/publicoutreach/featurecolumn/fcarceulersformulaii
01
2005
Joe Malkevitch
Geometry and Topology
History of Mathematics

Euler's Polyhedral Formula
http://www.ams.org/publicoutreach/featurecolumn/fcarceulersformula
12
2004
Joe Malkevitch
Geometry and Topology
History of Mathematics

Mathematical Marriages
http://www.ams.org/publicoutreach/featurecolumn/fcarcmarriage
11
2004
Joe Malkevitch
Discrete Math and Combinatorics
Game Theory and Social Choice

Voting Games: Part II
http://www.ams.org/publicoutreach/featurecolumn/fcarcvoting.games.two
10
2004
Joe Malkevitch
Game Theory and Social Choice

Voting Games: Part I
http://www.ams.org/publicoutreach/featurecolumn/fcarcweighted1
09
2004
Joe Malkevitch
Game Theory and Social Choice

Machine Scheduling
http://www.ams.org/publicoutreach/featurecolumn/fcarcmachines1
08
2004
Joe Malkevitch
Discrete Math and Combinatorics

Bin Packing and Machine Scheduling
http://www.ams.org/publicoutreach/featurecolumn/fcarcpackings1
06
2004
Joe Malkevitch
Discrete Math and Combinatorics

Bin Packing
http://www.ams.org/publicoutreach/featurecolumn/fcarcbins1
05
2004
Joe Malkevitch
Discrete Math and Combinatorics

Networks
http://www.ams.org/publicoutreach/featurecolumn/fcarcnetworks1
04
2004
Joe Malkevitch
Discrete Math and Combinatorics

Diagonals: Part II
http://www.ams.org/publicoutreach/featurecolumn/fcarcgallery1
03
2004
Joe Malkevitch
Geometry and Topology

Diagonals: Part I
http://www.ams.org/publicoutreach/featurecolumn/fcarcdiagonals1
02
2004
Joe Malkevitch
Geometry and Topology

Cubes
http://www.ams.org/publicoutreach/featurecolumn/fcarccubes1
01
2004
Joe Malkevitch
Geometry and Topology
Algebra

Colorful Mathematics: Part IV
http://www.ams.org/publicoutreach/featurecolumn/fcarccolorapp1
12
2003
Joe Malkevitch
Geometry and Topology
Math and Technology

Colorful Mathematics: Part III
http://www.ams.org/publicoutreach/featurecolumn/fcarccolour1
11
2003
Joe Malkevitch
Geometry and Topology

Colorful Mathematics: Part II
http://www.ams.org/publicoutreach/featurecolumn/fcarccolor1
10
2003
Joe Malkevitch
Geometry and Topology

Colorful Mathematics: Part I
http://www.ams.org/publicoutreach/featurecolumn/fcarccoloring1
09
2003
Joe Malkevitch
Geometry and Topology
History of Mathematics

A Discrete Geometrical Gem
http://www.ams.org/publicoutreach/featurecolumn/fcarcsylvester1
08
2003
Joe Malkevitch
Geometry and Topology
Discrete Math and Combinatorics

Primes
http://www.ams.org/publicoutreach/featurecolumn/fcarcprimes1
06
2003
Joe Malkevitch
Algebra

Oriented Matroids: The Power of Unification
http://www.ams.org/publicoutreach/featurecolumn/fcarcoriented1
05
2003
Joe Malkevitch
Geometry and Topology
Discrete Math and Combinatorics

Mathematics and Art
http://www.ams.org/publicoutreach/featurecolumn/fcarcart1
04
2003
Joe Malkevitch
Math and the Arts

Combinatorial Games (Part II) Different Moves for Left and Right
http://www.ams.org/publicoutreach/featurecolumn/fcarcpartizan1
03
2003
Joe Malkevitch
Geometry and Topology
Discrete Math and Combinatorics

Digital Revolution (III)  Error Correction Codes
http://www.ams.org/publicoutreach/featurecolumn/fcarcerrors1
02
2003
Joe Malkevitch
Math and Technology

Matroids: The Value of Abstraction
http://www.ams.org/publicoutreach/featurecolumn/fcarcmatroids1
01
2003
Joe Malkevitch
Linear Algebra
Discrete Math and Combinatorics

Combinatorial Games (Part I): The World of Piles of Stones
http://www.ams.org/publicoutreach/featurecolumn/fcarcgames1
12
2002
Joe Malkevitch
Game Theory and Social Choice
Discrete Math and Combinatorics

Linkages (Part II)  Old Wine in New Bottles
http://www.ams.org/publicoutreach/featurecolumn/fcarclinks1
11
2002
Joe Malkevitch
Geometry and Topology
Discrete Math and Combinatorics

October: Digital Revolution (II)  Compression Codes and Technologies
http://www.ams.org/publicoutreach/featurecolumn/fcarccompression1
10
2002
Joe Malkevitch
Math and Technology

September: Linkages: From Fingers to Robot Arms (I) Introduction
http://www.ams.org/publicoutreach/featurecolumn/fcarclinkages1
09
2002
Joe Malkevitch
Geometry and Topology
Discrete Math and Combinatorics
History of Mathematics

July/August: The Digital Revolution (I)  Barcodes: Introduction
http://www.ams.org/publicoutreach/featurecolumn/fcarcbarcodes1
08
2002
Joe Malkevitch
Algebra
Discrete Math and Combinatorics
Math and Technology

Apportionment II
http://www.ams.org/publicoutreach/featurecolumn/fcarcapportionii1
06
2002
Joe Malkevitch
Game Theory and Social Choice

Apportionment I
http://www.ams.org/publicoutreach/featurecolumn/fcarcapportion1
05
2002
Joe Malkevitch
Game Theory and Social Choice

Mathematics and the Genome
http://www.ams.org/publicoutreach/featurecolumn/fcarcgenome1
04
2002
Joe Malkevitch
History of Mathematics
Discrete Math and Combinatorics

Voting and Elections
http://www.ams.org/publicoutreach/featurecolumn/fcarcvotingintroduction
03
2002
Joe Malkevitch
History of Mathematics
Game Theory and Social Choice

Nets: A Tool for Representing Polyhedra in Two Dimensions
http://www.ams.org/publicoutreach/featurecolumn/fcarcnets
02
2002
Joe Malkevitch
Geometry and Topology

Alberti's Perspective Construction
http://www.ams.org/publicoutreach/featurecolumn/fcarcalberti1
01
2002
Tony Phillips
Geometry and Topology
Math and the Arts

Topology and Verb Classes
http://www.ams.org/publicoutreach/featurecolumn/fcarcsyntax1
12
2001
Tony Phillips
Geometry and Topology
Calculus and Analysis
Math and the Arts

Finitedimensional Feynman Diagrams
http://www.ams.org/publicoutreach/featurecolumn/fcarcfeynman1
11
2001
Tony Phillips
Math and the Sciences
Calculus and Analysis

The Romance of DoubleEntry Bookkeeping
http://www.ams.org/publicoutreach/featurecolumn/fcarcbook1
10
2001
Tony Phillips
Miscellaneous
Algebra

Latin Squares in Practice and in Theory II
http://www.ams.org/publicoutreach/featurecolumn/fcarclatinii1
09
2001
Tony Phillips
Algebra
History of Mathematics
Probability and Statistics

Latin Squares in Practice and in Theory I
http://www.ams.org/publicoutreach/featurecolumn/fcarclatini1
08
2001
Tony Phillips
Algebra
History of Mathematics
Probability and Statistics

Fourier Analysis of Ocean Tides III
http://www.ams.org/publicoutreach/featurecolumn/fcarctidesiii1
06
2001
Tony Phillips
History of Mathematics
Calculus and Analysis
Math and the Sciences

Fourier Analysis of Ocean Tides II
http://www.ams.org/publicoutreach/featurecolumn/fcarctidesii1
05
2001
Tony Phillips
History of Mathematics
Calculus and Analysis
Math and the Sciences

Fourier Analysis of Ocean Tides I
http://www.ams.org/publicoutreach/featurecolumn/fcarctidesi1
04
2001
Tony Phillips
History of Mathematics
Calculus and Analysis
Math and the Sciences

A New Solution to the Three Body Problem  And More
http://www.ams.org/publicoutreach/featurecolumn/fcarcorbits1
03
2001
Bill Casselman
Calculus and Analysis
Math and the Sciences

The Mathematical Study of Mollusk Shells
http://www.ams.org/publicoutreach/featurecolumn/fcarcshell1
02
2001
Tony Phillips
Math and Nature
Calculus and Analysis

Celestial Mechanics on a Graphing Calculator
http://www.ams.org/publicoutreach/featurecolumn/fcarckepler1
01
2001
Tony Phillips
Calculus and Analysis
Math and Technology

Packing Pennies in the Plane
http://www.ams.org/publicoutreach/featurecolumn/fcarccass1
12
2000
Bill Casselman
Geometry and Topology

The Mathematics of Communication
http://www.ams.org/publicoutreach/featurecolumn/fcarcinfo1
11
2000
Tony Phillips
Math and Technology
Probability and Statistics

Mathematical Card Tricks
http://www.ams.org/publicoutreach/featurecolumn/fcarcmulcahy1
10
2000
Colm Mulcahy
Algebra
Miscellaneous

The Mathematics of Piano Tuning
http://www.ams.org/publicoutreach/featurecolumn/fcarcpiano1
09
2000
Tony Phillips
Calculus and Analysis
Math and the Arts

Navigational Mathematics
http://www.ams.org/publicoutreach/featurecolumn/fcarcnavigation1
08
2000
Tony Phillips
Geometry and Topology

The Catastrophe Machine
http://www.ams.org/publicoutreach/featurecolumn/fcarccusp1
06
2000
Tony Phillips
Calculus and Analysis
Math and the Sciences

The Antikythera Mechanism II
http://www.ams.org/publicoutreach/featurecolumn/fcarcdiff1
05
2000
Tony Phillips
History of Mathematics
Math and the Sciences

The Antikythera Mechanism I
http://www.ams.org/publicoutreach/featurecolumn/fcarckyth1
04
2000
Tony Phillips
History of Mathematics
Math and the Sciences

Visual Explanations in Mathematics
http://www.ams.org/publicoutreach/featurecolumn/fcarcvisual1
03
2000
Tony Phillips
Geometry and Topology

The ABC of DNA Computing
http://www.ams.org/publicoutreach/featurecolumn/fcarcdnaabc1
02
2000
Tony Phillips
Math and the Sciences
Math and Technology
Discrete Math and Combinatorics

The Method of Archimedes
http://www.ams.org/publicoutreach/featurecolumn/fcarcarchimedes1
01
2000
Tony Phillips
History of Mathematics
Geometry and Topology
Calculus and Analysis

The Mathematical CAT scan
http://www.ams.org/publicoutreach/featurecolumn/fcarccatscan1
12
1999
Tony Phillips
Math and the Sciences
Calculus and Analysis

Metonymy and Metaphor in Mathematics
http://www.ams.org/publicoutreach/featurecolumn/fcarcmetonymy1
11
1999
Tony Phillips
Math and the Arts
Algebra
Calculus and Analysis

The Differential Geometry of the Sphericon
http://www.ams.org/publicoutreach/featurecolumn/fcarcsphericon1
10
1999
Tony Phillips
Geometry and Topology

Descartes' Lost Theorem
http://www.ams.org/publicoutreach/featurecolumn/fcarcdescartes1
09
1999
Tony Phillips
Geometry and Topology
History of Mathematics

The Most Irrational Number
http://www.ams.org/publicoutreach/featurecolumn/fcarcirrational1
08
1999
Tony Phillips
Geometry and Topology
Algebra
Math and Nature

Multiple Mathematical Intelligences
http://www.ams.org/publicoutreach/featurecolumn/fcarcmi1
06
1999
Tony Phillips
Miscellaneous

From Euclid and Euler to Publickey Codes
http://www.ams.org/publicoutreach/featurecolumn/fcarccodes1
05
1999
Tony Phillips
Algebra
Math and Technology

Knots and their Polynomials
http://www.ams.org/publicoutreach/featurecolumn/fcarcknots1
04
1999
Tony Phillips
Geometry and Topology
Algebra

<![CDATA[Math and the Musical Offering]]>
http://www.ams.org/publicoutreach/featurecolumn/fcarccanons
03
1999
Tony Phillips
Math and the Arts
Calculus and Analysis

Gravitational Lensing and Geometric Lensing
http://www.ams.org/publicoutreach/featurecolumn/fcarcgrav_lens
02
1999
Tony Phillips
Math and the Sciences
Geometry and Topology

A Prime Case of Chaos
http://www.ams.org/publicoutreach/featurecolumn/fcarcprimechaos
01
1999
Steve Weintraub
Miscellaneous

Calculating Pi using Elementary Calculus
http://www.ams.org/publicoutreach/featurecolumn/fcarcpicalc
12
1998
Steve Weintraub
Calculus and Analysis

FactorizationUnique and Otherwise
http://www.ams.org/publicoutreach/featurecolumn/fcarcfactorization
11
1998
Steve Weintraub
Algebra

<![CDATA[André Weil, May 6, 1906August 6, 1998]]>
http://www.ams.org/publicoutreach/featurecolumn/fcarcweil
10
1998
Steve Weintraub
History of Mathematics

Prize Winners at the 1998 International Congress of Mathematicians
http://www.ams.org/publicoutreach/featurecolumn/fcarcicm1998prizes
09
1998
Steve Weintraub
Miscellaneous

Polyhedra
http://www.ams.org/publicoutreach/featurecolumn/fcarcpolyhedra
08
1998
Steve Weintraub
Geometry and Topology

Turing Machines
http://www.ams.org/publicoutreach/featurecolumn/fcarcturing
07
1998
Steve Weintraub
Math and Technology
History of Mathematics

"The Trigonometry of Escher's Woodcut "Circle Limit III"
http://www.ams.org/publicoutreach/featurecolumn/fcarccircle_limit_iii
06
1998
Steve Weintraub
Geometry and Topology
Math and the Arts

Newton Basins
http://www.ams.org/publicoutreach/featurecolumn/fcarc199805
05
1998
Steve Weintraub
Calculus and Analysis

Quadric Surfaces
http://www.ams.org/publicoutreach/featurecolumn/fcarc199804
04
1998
Steve Weintraub
Linear Algebra

1998 Mathematics Awareness Week
http://www.ams.org/publicoutreach/featurecolumn/fcarc199803
03
1998
Steve Weintraub
Math and Technology

<![CDATA[Tiling the Poincaré Disk]]>
http://www.ams.org/publicoutreach/featurecolumn/fcarc199802
02
1998
Steve Weintraub
Geometry and Topology

The Mathematics Behind the Nobel Prize in Economics
http://www.ams.org/publicoutreach/featurecolumn/fcarcblackscholesito
01
1998
Steve Weintraub
Math and the Sciences

G. H. Hardy (18771947)
http://www.ams.org/publicoutreach/featurecolumn/fcarc199712
12
1997
Steve Weintraub
History of Mathematics

Fourier Approximation
http://www.ams.org/publicoutreach/featurecolumn/fcarc199711
11
1997
Steve Weintraub
Calculus and Analysis

J. J. Sylvester (18141897)
http://www.ams.org/publicoutreach/featurecolumn/fcarc199710
10
1997
Steve Weintraub
History of Mathematics

An Aperiodic Tiling
http://www.ams.org/publicoutreach/featurecolumn/fcarc199709
09
1997
Steve Weintraub
Geometry and Topology

Pathfinder pictures from Mars
http://www.ams.org/publicoutreach/featurecolumn/fcarc199708
08
1997
Steve Weintraub
Math and the Sciences
Math and Technology

Mathematical Insights for Medical Imaging
http://www.ams.org/publicoutreach/featurecolumn/fcarc199707
07
1997
Steve Weintraub
Math and Technology
Calculus and Analysis

You Can't Always Hear the Shape of a Drum
http://www.ams.org/publicoutreach/featurecolumn/fcarc199706
06
1997
Steve Weintraub
Geometry and Topology
Calculus and Analysis

A Wallpaper Pattern
http://www.ams.org/publicoutreach/featurecolumn/fcarc199705
05
1997
Steve Weintraub
Algebra
Geometry and Topology

Hyperbolic Space Tiled by Dodecahedra, 1
http://www.ams.org/publicoutreach/featurecolumn/fcarc199704
04
1997
Steve Weintraub
Geometry and Topology

Mathematics Awareness Week 1997
http://www.ams.org/publicoutreach/featurecolumn/fcarc199703
03
1997
Steve Weintraub
Math and Technology

The Unknotting Number of a Knot
http://www.ams.org/publicoutreach/featurecolumn/fcarc199702
02
1997
Steve Weintraub
Geometry and Topology