## Of frolics and tangos

Shecky over at Math Frolic has been getting antsy. One blog isn't enough for him. Now there's Math Tango!

From the welcome post:

WELCOME Math-Frolickers!… MathTango is intended (and it'll be a bit of an experiment) to be the new residence for longer, more original entries that were occasionally posted at Math-Frolic (including book reviews, interviews, and just lengthier posts in general). Math-Frolic will continue to be a linkblog for quick links to mathematical content that I find interesting and wish to pass along, as well as a portal to many other sites/pages, and will continue posting several entries per WEEK. MathTango, on-the-other-hand, is intended to have only a few postings per MONTH.

Tomorrow, the first post appears (a book review).

I look forward to following Shecky's new baby blog.

## Have you heard of Math Munch?

I just discovered the Math Munch blog. It promotes itself as "A Weekly Digest of the Mathematical Internet." Their blog further explains:

Here you will find links to lots of cool mathy things on the internet. We'll post some new items each week for you to enjoy. We hope you are as inspired and excited by these creations as we are!

This is a really terrific blog that's been publishing for just a bit over a year. It's chock full of images, graphics, and videos. Justin, Paul, and Anna, the "Math Munch Team" are doing a terrific job so I want to give them a plug.

## Glen Van Brummelen – Inspired by Math #18

Today I got to interview another great author of a Princeton University Press title. "Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry" is a delightful exploration of the techniques that ancient and medieval people from different cultures used to navigate and map the stars and the seas along with modern methods. There's a strong focus on the historical setting for these explorations. This setting brings the mathematics to life. I was very impressed to learn how very smart ancient astronomers and mathematicians were. Our twentyfirst century perception that we are smarter than our predecessors is simply not true. I was also delighted to learn an elegant variation of the familiar Pythagorean Theorem when applied to a sphere.

I thoroughly enjoyed getting exposed to this very elegant branch of mathematics and hope you too will catch some of Professor Van Brummelen's enthusiasm.

Chapter 1 of the book is available as a free PDF download.

## About Glen Van Brummelen

From the Quest University Website:

Glen Van Brummelen, mathematics tutor, is a historian of mathematics, especially trigonometry and astronomy in ancient Greece and medieval Islam. He is past president of the Canadian Society for History and Philosophy of Mathematics, and senior fellow at the Dibner Institute for History of Science at MIT. In addition to authoring 30 scholarly and 10 encyclopedia articles, he is co-editor of "Mathematics and the Historian's Craft" (Springer) and recently published the first history of trigonometry in over a century with Princeton University Press called "The Mathematics of the Heavens and the Earth: The Early History of Trigonometry".

Glen has taught mathematics at small liberal arts colleges his entire career. He has taught over 30 different courses, including most traditional topics in math but also mathematics and music, mathematics and democracy, mathematics and computer graphics, spherical trigonometry (using a 19th-century textbook), and how to be an ancient astronomer. Several of his students have published their undergraduate research with him in recent years. In the summer he teaches the history of math regularly at MathPath, a math camp for bright 7th- and 8th-graders.

As if this wasn't enough, he keeps busy with his three very active kids of his own: Ariel (13), Matthew (9) and Andrew (5), all of whom will be mathematicians some day, and wife Heide (age unspecified). He is an avid soccer player, and played goal on the college team at his two previous colleges. He is undefeated at chess in the past 20 years, with a record of 2-0. Glen notes that "the key is to choose one's opponents carefully".

## About "Heavenly Mathematics"

From the Princeton University Press Website:

Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.

Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.

## Keith Devlin – Inspired by Math #17

Dr. Keith Devlin joins me for a second podcast interview. Keith Devlin and I first spoke last February. Last night Keith Devlin shared in great detail his experience teaching "Introduction to Mathematical Thinking" MOOC (Massive Open Online Course). If you're considering enrolling in the MOOC when it's next offered in March, or if you might someday want to teach a MOOC, assist in a MOOC, or if you just want to understand the important role of MOOCs in the future of education, you won't want to miss this podcast.

Oh, and there's a teaser at the end about Dr. Devlin's next big "thing," being announced in just a few weeks.

More about Keith Devlin:

Dr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 31 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio.

## More information

- Introduction to Mathematical Thinking, information and registration for March 4, 2013 MOOC.
- Optional Text for the course.
- Keith Devlin's MOOCtalk blog.
- "Devlin's Angle" column at the Mathematical Association of America Blog
- Professor Devlin's Blog

## Steven Strogatz – Inspired by Math #16

Shecky over at the Math Frolic Blog has been a great supporter of this podcast series and recently made this observation:

I've been pleasantly surprised by the degree to which 'math people,' including such prominent and busy ones as [Ian] Stewart, Keith Devlin, Steven Strogatz and others, are willing to share themselves with the learning community, through such online outlets. It is really wonderful, and I think a reflection of the desire on the part of mathematicians to transform their subject from one that is too-often feared to one for eager engagement.

Having had the opportunity to have a very pleasant and very informal conversation with Dr. Steven Strogatz this afternoon really brought home Shecky's point. Dr. Strogatz and others are making a difference by giving generously of their time to bloggers who aren't likely to reach as many people as their books will reach.

At the bottom of this post I feature two of Dr. Strogatz' books, "The Joy of x," published by Houghton Mifflin Harcourt, and the lesser known but equally important book, "The Calculus of Friendship," published by the Princeton University Press. We discuss both in the podcast.

## About Steven Strogatz

From Dr. Strogatz' web-site:

Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. He holds a joint appointment in the College of Arts and Sciences (Mathematics) and the College of Engineering (Mechanical and Aerospace Engineering).

After graduating summa cum laude in mathematics from Princeton in 1980, Strogatz studied at Trinity College, Cambridge, where he was a Marshall Scholar. He did his doctoral work in applied mathematics at Harvard, followed by a National Science Foundation postdoctoral fellowship at Harvard and Boston University. From 1989 to 1994, Strogatz taught in the Department of Mathematics at MIT. He joined the Cornell faculty in 1994.

He has received numerous awards for his research, teaching, and public service, including: a Presidential Young Investigator Award from the National Science Foundation (1990); MIT's highest teaching prize, the E. M. Baker Award for Excellence in Undergraduate Teaching (1991); the J.P. and Mary Barger '50 Teaching Award (1997), the Robert '55 and Vanne '57 Cowie Teaching Award (2001), the Tau Beta Pi Teaching Award (2006), and the Swanson Teaching Award (2009), all from Cornell's College of Engineering; and the Communications Award from the Joint Policy Board for Mathematics (2007), a lifetime achievement award for the communication of mathematics to the general public. In 2009 he was elected a Fellow of the Society for Industrial and Applied Mathematics for his “investigations of small-world networks and coupled oscillators and for outstanding science communication.” In 2012 he was elected a Fellow of the American Academy of Arts and Sciences.

Strogatz is passionate about public outreach and loves sharing the beauty of math and science with a wide audience. He has spoken at TED and is a frequent guest on RadioLab. In the spring of 2010 he wrote a weekly blog about mathematics for the New York Times; the Harvard Business Review described these columns as "must reads for entrepreneurs and executives" and "a model for how mathematics needs to be popularized." His second New York Times series, Me, Myself and Math, appeared in the fall of 2012. Strogatz has also filmed a series of 24 lectures on Chaos for the Teaching Company’s Great Courses series. He is the author of Nonlinear Dynamics and Chaos (1994), Sync (2003), and The Calculus of Friendship (2009). His most recent book, The Joy of x, was published in October 2012.

## About "The Joy of x"

From Amazon.com:

A world-class mathematician and regular contributor to the New York Times hosts a delightful tour of the greatest ideas of math, revealing how it connects to literature, philosophy, law, medicine, art, business, even pop culture in ways we never imagined

Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.

Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.

Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

## About "The Calculus of Friendship"

From the publisher's website:

The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough.

Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters.

For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

## An elegant puzzle at the New York Times

Joshua Zucker shared this great Numberplay puzzle at the New York Times Wordplay Blog:

Start with a first row with two number ones separated by a space:

Row 1: 1 1

For each subsequent row, insert the sum between each two adjacent numbers, so you get:

Row 2: 1 2 1

Row 3: 1 3 2 3 1

Row 4: 1 4 3 5 2 5 3 4 1

How many 2013s are in row 2013?

## Mircea Pitici – Inspired by Math #15

Mircea Pitici has taken on a huge task, to present the best articles in Mathematics for the year. For three years running he's edited a book for Princeton University Press with his picks. Since identifying great communicators is a big interest of mine I'm delighted to get to pick his brain for an hour.

*[ Note: The audio is a little bit choppy in places, especially the first few seconds. The phone connection was not the best so we did the best we could do. Call quality aside, this is an important interview for anyone interested in math communication. ]*

## About Mircea Pitici

From Mircea's Cornell web-site:

Mircea has taught mathematics courses and writing seminars at Cornell University, Ithaca College, and Wells College. He received a teaching award from the Cornell Department of Mathematics in 2011 and the Buttrick-Crippen Scholarship awarded by the Knight Institute of Writing in the Disciplines in 2008.

Deeply interested in mathematical communication to professional audiences and to the general public, Mircea edits the annual series The Best Writing on Mathematics (Princeton University Press). He holds a bachelor’s degree in mathematics from the University of Bucharest, Romania, and a master’s degree from Cornell, and he is working toward a doctorate in mathematics education at Cornell.

## About "The Best Writing on Mathematics 2012"

From the Princeton University Press web-site:

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

## Ian Stewart – Inspired by Math #14

I was very honored to have Dr. Ian Stewart give me an hour of his time this morning to interview him about his enthusiasm for communicating Math to the public. Dr. Stewart is the author of a couple of dozen very popular Math books. You can see a list at Amazon.com. Dr. Stewart and I got to talk about one of his most recent books, "The Mathematics of Life," (published by Perseus Books Group) and about a number of other topics.

## About Dr. Stewart

From Wikipedia:

Ian Nicholas Stewart FRS (born 24 September 1945) is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. He is the first recipient of the Christopher Zeeman Medal, awarded jointly by the LMS and the IMA for his work on promoting mathematics.

Stewart was born in 1945 in England. While in the sixth form at school, Stewart came to the attention of the mathematics teacher. The teacher had Stewart sit mock A-level examinations without any preparation along with the upper-sixth students; Stewart placed first in the examination. This teacher arranged for Stewart to be admitted to Cambridge on a scholarship to Churchill College, where he obtained a BA in Mathematics. Stewart then went to the University of Warwick for his doctorate, on completion of which in 1969 he was offered an academic position at Warwick. He is now Professor of Mathematics at the University of Warwick. He is well known for his popular expositions of mathematics and his contributions to catastrophe theory.

While at Warwick he edited the mathematical magazine Manifold. He also wrote a column called "Mathematical Recreations" for Scientific American magazine for several years.

Stewart has held visiting academic positions in Germany (1974), New Zealand (1976), and the U.S. (University of Connecticut 1977–78, University of Houston 1983–84).

## About The Mathematics of Life

From the publisher's site: (Perseus Books Group)

Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world--and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world--and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.

## A new approach to mental math

I received an email from Anton Prosolov, a programmer from Norway. His site, King of Mnemonics, sells software that Anton developed, and a novel he wrote.

I have invented a brand new approach to mental math that focuses on something people are good at (which is memory) rather than something they're bad at (which is arithmetics).

For the first time in history, ANY person can now learn how to perform truly amazing calculations in his/her head - things like weekdays, cubic roots and square roots...

Anton asked for me to plug his work. I like what he's doing (although I've not used his software or read his novel.) So, I offered him a plug but I made him work for it. I emailed him some questions about what he's up to. Below are Anton's responses. Enjoy!

**You have a fascination with Pythagoras. Why is that? And, who were the Pythagoreans?**

The Pythagoreans were a mathematical / religious cult in ancient Greece. This combination of mathematics and the supernatural is a perfect fit for me, since I needed a reason WHY people would want to learn my Algorithms. The reason is of course to gain immense power and knowledge in a different dimension called the Other Side (that's what my novel is about).

**So, there was a dark side to the Pythagoreans?**

Yes. My novel depicts several true historic occurrences, and one of them is the murder of their fellow Pythagorean Hippasus due to his discovery of irrational numbers. Like I said, they were sort of a cult. Of course, since this is a fictional novel, I made them even MORE sinister than they actually were.

**What was Pythagoras famous for, other than for the Pythagorean Theorem?**

He was one of the earliest famous cult leaders, with lots of capricious rules and prohibitions.

**What is your novel about?**

My novel is about the struggles of the (evil) Pythagoreans to gain access to an other dimension called the Other Side (with the help of my 5 magic Algorithms). Fortunately, their efforts are being sabotaged by mysterious self-fulfilling Prophecies.

**Your software helps people to learn and practice several techniques that use mnemonics, right?**

That's correct!

**What is a mnemonic and how do mnemonics help with things like difficult multiplications and date calculations?**

Well, Wikipedia defines a mnemonic as a "learning technique that aids information retention". I do have some genuine mnemonics, such as this poem that is actually the multiplication table (it's used in the Absolute Power Algorithm):

fact dense fogs warm suns defy

ares ably reign fierce aides rely

roger swam duct rescue nora

lug's bergs saved beside aura

wergem oiner bown webnew

beldi wolm nelect wifew

fewgwe siwo lesta biol

However, for the most part, you have to memorize several tables in order to do my Algorithms (12 tables in total). This is (technically speaking) NOT a mnemonic. Nevertheless, it's something that involves memory (rather than arithmetics), which is why "King of Mnemonics" is still a fitting name for my software. By the way, utilizing long-term memory (which people are good at) rather than arithmetics (which people are bad at) is precisely the reason why ANYONE can do my Algorithms. This is a brand new approach (invented by me) and the only one that works for ordinary people (I know, because my wife and friends can now calculate weekdays, square and cubic roots in their head because of King of Mnemonics).

**What does the "Absolute Power Algorithm" calculate?**

You can calculate things like 794 * 586 in your head (two 3-digit numbers where all digits are different). However, this is the most difficult Algorithm of the 5 and I do NOT claim that anyone can do it (in fact, my novel is called "Are you the reincarnation of Pythagoras ?", and he or she is the only person in the world (besides the evil Pythagorean Grand Master) who can do the Absolute Power Algorithm quickly enough (under 1 minute). That person is the world's only hope, because it's the most important Algorithm on the Other Side.

**Is there a next project for you?**

I have some ideas for other Algorithms (not necessarily mathematical), but you won't see them for a while, since I have to do them in my spare time, and it took me 10 years to finish my currect project. It would speed things up a lot if I could do this full-time, which is my dream.

## The Enigma of the Spiral Waves is now available

I'm excited to announce that Volume Two of Matthew Watkins' "Secrets of Creation" trilogy, "The Enigma of the Spiral Waves," is now available.

From the author's web site:

The Enigma of the Spiral Waves takes its readers further into into the workings of the number system. Continuing to make use of Watkins and Tweed's innovative visual approach to communicating advanced mathematical ideas without any need for formulas, equations, x's or y's, the reader is introduced to the mystifying "Riemann zeros" and the notorious Riemann Hypothesis. It's eventually explained how the weird set of frequencies met at the end of Volume 1 have all of the mathematical "fingerprints" necessary to strongly suggest that they correspond to the vibrations of some kind of (unknown) "system". As Oxford mathematics professor Marcus du Sautoy has said, "We have all this evidence that the Riemann zeros are vibrations, but we don't know what's doing the vibrating."

I loved Volume One, "The Mystery of the Prime Numbers," and I reviewed it here.

Shecky at the Math-Frolic Blog has a great interview with Dr. Watkins here.

I will be doing a podcast interview with Dr. Watkins so stand by for that.

More information about the trilogy is available on the author's site.