## James Tanton – Inspired by Math #11

The MAA recently published a book, Mathematics Galore!, of creative classroom activities by James Tanton. These activities are great explorations for high school and motivated middle school students to work through alone, or for group work in Math Circles. I got a review copy of the book and instantly fell in love with it. I've been a fan of James' for some time, and I've plugged his work a number of times.

When "Mathematics Galore" was published I used the event as an opportunity to congratulate James and as an excuse to interview James for my "Inspired by Math" podcast series.

If you've been as enthralled as I've been by James' Youtube videos, or as impressed as I've been with his textbooks, you'll enjoy listening to this interview and getting to know James a little bit more personally.

## About James Tanton

Believing that mathematics really is accessible to all, James Tanton (PhD, Mathematics, Princeton 1994) is committed to sharing the delight and the beauty of the subject. In 2004 James founded the St. Mark’s Institute of Mathematics, an outreach program promoting joyful and effective mathematics education. He worked as a full-time high school teacher at St. Mark’s School in Southborough MA,(2004-2012) and he conducted, and continues to conduct, mathematics graduate courses for teachers through Northeastern University and American University. He also gives professional development workshops across the nation and Canada.

James recently relocated to Washington D.C. and is currently a visiting scholar of the Mathematical Association of America. He also conducts the professional development program for Math For America program in D.C.

James is the author of SOLVE THIS: MATH ACTIVITIES FOR STUDENTS AND CLUBS (MAA, 2001), THE ENCYCLOPEDIA OF MATHEMATICS (Facts on File, 2005), MATHEMATICS GALORE! (MAA, 2012) and twelve self-published texts. He is the 2005 recipient of the Beckenbach Book Prize, the 2006 recipient of the Kidder Faculty Prize at St. Mark’s School, and a 2010 recipient of a Raytheon Math Hero Award for excellence in school teaching.

He also publishes research and expository articles, and through his extracurricular research classes for students has helped high school students pursue research projects and also publish their results.

## James Tanton's Coordinates

Web-site: jamestanton.com

Youtube channel: http://www.youtube.com/user/drjamestanton

Facebook page: http://www.facebook.com/tanton.math

Twitter feed: https://twitter.com/jamestanton

## About "Mathematics Galore"

Mathematics Galore! showcases some of the best activities and student outcomes of the St. Mark's Institute of Mathematics and invites you to engage in the mathematics yourself! Revel in the delight of deep intellectual play and marvel at the heights to which young scholars can rise. See some great mathematics explained and proved via natural and accessible means.

Based on 26 essays ("newsletters") and eight additional pieces, Mathematics Galore! offers a large sample of mathematical tidbits and treasures, each immediately enticing, and each a gateway to layers of surprising depth and conundrum. Pick and read essays in no particular order and enjoy the mathematical stories that unfold. Be inspired for your courses, your math clubs and your math circles, or simply enjoy for yourself the bounty of research questions and intriguing puzzlers that lie within.

## Another clever exploration by James Tanton

I really enjoy James Tanton's Math explorations because they tend to be easy to describe and rich in exploration value. Here's such an exploration:

The problem statement is very simple. Is there a way in which we can say that there are more triangular numbers than square numbers? If so, how do we compare the sizes of the two sets? Can we compute the ratio of triangular to square numbers where both T(n) and S(n) are less than an arbitrary constant? Can we generalize what we find for other polygonal numbers?

This is a great exploration!

## Two new videos by James Tanton

After a hiatus of several months Dr. Tanton is making videos again. Here are two new ones.

Lulu has two children. You are told that at least one of her children is a boy who was born on a Tuesday. What is the probability that her other child is also a boy?

The answer will surprise you!

Here is a cute geometry puzzle: Imagine you are an archeologist and have come across just a small section of a rim of an ancient wheel. What size wheel did it come from?

This is a great puzzle to give to geometry students too. Hand out a picture of an arc of a circle and ask if is possible to find the measure of that arc using only basic tools - and them have students actually do it.

## Tanton tantalizes with an Euler gem

James Tanton has produced another great video, this one on a very intriguing partitioning problem with a very clever solution.

There are four ways to break the number 6 down into a sum of distinct numbers: 6 = 5+1 = 4+2 = 3+2+1. There are four ways to break the number of 6 down into odd numbers: 5+1 = 3+3 = 3+1+1=1 = 1+1+1+1+1+1. It is no coincidence that the count of ways are the same. In 1740 Euler proved it will always be so! His proof is ingenious and here it is! I've also added a challenge at the end to discover other bizarre results like this one. (I bet you can do it!)

I thoroughly enjoy Tanton's ability to find interesting problems and make them accessible to those of us who aren't professional mathematicians. In fact, all of Tanton's videos are accessible to motivated high school students.

I was delighted to see Mr. Tanton included in Math Pickle's page of inspired people.

A MathPickle guy to the core - James Tanton is a fully fledged mathematician with a fantastic web site that offers videos for school teachers and first year university lecturers. Visit his web site here.

## New James Tanton video on sums of cubes

Have you ever wondered why the sum of the cubes of consecutive positive integers is always a square? The key to one visual proof lies in the humble multiplication table and in an array of square dots.

Here's a new video from James Tanton that shows in a remarkably elegant way that 1^3 + 2^3 + 3^3 + ... + n^3 = (1+2+3+...+n)^2.

And, you don't need to have very much of a background in Math to follow the proof. Absolutely amazing!

[youtube]http://www.youtube.com/watch?v=fKrN2-urUkE[/youtube]

## 13 surprising Fibonacci appearances

One of my great Math heroes, James Tanton, has written a great essay that provides thirteen examples of the Fibonacci sequence appearing in strange and unexpected places.

"I have YouTube videos presenting some surprising appearances of the Fibonacci numbers and I’ve been tweeting little puzzlers about the Fibonacci numbers for some time. Here, at long last, is my list of Fibonacci results, and a clever way to prove them all. Some of these puzzlers are classic, some are new to the world."

## Wild About Math blogs 5/27/11

Welcome to Wild About Math blogs!

This is the last edition. If you'd like to put on your own personal Math blog carnival I recommend you follow the large list of blogs at Mathblogging.org and let us all know about the articles you like. I thought I had a pretty big list of Math blogs in my RSS reader; their list is much bigger. You can subscribe to parts or to all of their list via RSS and you can even follow the twitter feeds of a bunch of Math bloggers.

I discovered some really wonderful BBC Math radio shows. See here.

Math Teachers at Play Carnival #38 is up at Mathematics and Multimedia.

I've been spending time at the Math Pickle site, greatly enjoying the simple yet deep and difficult to solve Math puzzles and games there. The "inspired people" page is particularly noteworthy. There are some familiar faces on the page, Martin Gardner, Vi Hart, and James Tanton to name a few. And, there are a bunch of people I don't know much about who I'll have to read up on. Here's one inspired person from the list:

Leo Moser seems to have been the first person who advocated unsolved problems being used in K-12 education. He asked many tough problems with child-like zeal: “What’s the area of the smallest house that a unit worm can live comfortably?” meaning what shape can cover a worm no matter how he curls up?

And, also from the Math Pickle site, is a video of a fun division game with some deep stuff going on beneath the surface.

## Wild About Math blogs 5/13/11

Welcome to the post-Mother's Day edition of Wild About Math Blogs!

Carnival of Mathematics #77 has been posted at Jost a Mon.

Scientific American just republished a wonderful article they originally published in 1961: The Mathematician as an Explorer. Hat tip to Shecky.

Murray at squareCircleZ has a very thought provoking article: Is there a place for invention in math?

Each time one prematurely teaches a child something he could have discovered for himself, that child is kept from inventing it and consequently from understanding it completely.

Statistics lovers might enjoy this little gem from xkcd:

## Wild About Math blogs 4/22/11

Welcome to another edition of Wild About Math blogs!

I'm about to start a new blog about the intersection of Math+kids+exploration+programming+Mathematica.

I’m about to start a blog about programming with Mathematica as a way for kids (and adults) to get engaged with Math. I’m pretty new to Mathematica and I find myself getting stuck with some of the basics (which will make the new blog all the more valuable.)

If you have experience with Mathematica and can help me with writing some simple animations I would be incredibly grateful and, of course, I will acknowledge you in the blog and (if you like) I’ll link to your site.

In the new blog I’ll be writing how-to articles where I dissect some simple Mathematica code and show readers how to do neat explorations.

If you can help please drop me an email at

## Wild About Math bloggers 3/4/11

Welcome to Spring, at least here in Santa Fe, where it's 60 degrees! Just a few weeks ago it dipped to -10 degrees here. Onto Math ...

James Tanton has a really great, very accessible, four part introduction to the Partition Numbers and to the hunt for structure in these numbers. Here's the first video:

[youtube]http://www.youtube.com/watch?v=9k9xL9w7-3w[/youtube]

Patrick at Math jokes 4 mathy folks has a great puzzle:

Append the digit 1 to the end of every triangular number. For instance, from 3 you’d get 31, and from 666 you’d get 6,661. Now take a look at all of the divisors of the numbers you’ve created. What are the units digits of the divisors for every number created in this way? Can you prove that this result always holds?

Hat tip to Brent.