# Marjorie Rice, Inspired by Math, and Subways

Welcome to this week’s Math Munch!

A few weeks ago, I learned about an amazing woman named Marjorie Rice.  Marjorie is a mathematician – but with a very unusual background.

Marjorie had no mathematical education beyond high school.  But, Marjorie was always interested in math.  When her children were all in school, Marjorie began to read about and work on math problems for fun.  Her son had a subscription to Scientific American, and Marjorie enjoyed reading articles by Martin Gardner (of hexaflexagon fame).  One day in 1975, she read an article that Martin Gardner wrote about a new discovery about pentagon tessellations.  Before several years earlier, mathematicians had believed that there were only five different types of pentagons that could tessellate – or cover the entire plane without leaving any gaps.   But, in 1968, three more were discovered, and, in 1975, a fourth was found – which Martin Gardner reported on in his article.

When she read about this, Marjorie became curious about whether she could find her own new type of pentagon that could tile the plane.  So, she got to work.  She came up with her own notation for the relationships between the angles in her pentagons.  Her new notation helped her to see things in ways that professional mathematicians had overlooked.  And, eventually… she found one!  Marjorie wrote to Martin Gardner to tell him about her discovery.  By 1977, Marjorie had discovered three more types of pentagons that tile the plane and her new friend, the mathematician Doris Schattschneider, had published an article about Marjorie’s work  in Mathematics Magazine.

There are now fourteen different types of pentagons known to tile the plane… but are there more?  No one knows for sure.  Whether or not there are more types of pentagons that tile the plane is what mathematicians call an open problem.  Maybe you can find a new one – or prove that one can’t be found!

Marjorie has a website called Intriguing Tessellations on which she’s written about her work and posted some of her tessellation artwork.  Here is one of her pentagon tilings transformed into a tessellation of fish.

By the way, it was Marjorie’s birthday a few weeks ago.  She just turned 90 years old.  Happy Birthday, Marjorie!

Next up, I just ran across a great blog called Wild About Math!  This blog is written by Sol Lederman, who used to work with computers and LOVES math.  My favorite part about this blog is a series of interviews that Sol calls, “Inspired by Math.”  Sol has interviewed about 23 different mathematicians, including Steven Strogatz (who has written two series of columns for the New York Times about mathematics) and Seth Kaplan and Deno Johnson, the producer and writer/director of the Flatland movies.  You can listen to Sol’s podcasts of these interviews by visiting his blog or iTunes.  They’re free – and very interesting!

Finally, what New York City resident or visitor isn’t fascinated by the subway system? And what New York City resident or visitor doesn’t spend a good amount of time thinking about the fastest way to get from point A to point B?  Do you stay on the same train for as long as possible and walk a bit?  Or do you transfer, and hope that you don’t miss your train?

Chris and Matt, on the subway.

Well, in 2009, two mathematicians from New York – Chris Solarz and Matt Ferrisi – used a type of mathematics called graph theory to plan out the fastest route to travel the entire New York City subway system, stopping at every station.  They did the whole trip in less than 24 hours, setting a world record!  Graph theory is the branch of mathematics that studies the connections between points or places.  In their planning, Chris and Matt used graph theory to find a route that had the most continuous travel, minimizing transfers, distance, and back-tracking.  You can listen to their fascinating story in an interview with Chris and Matt done by the American Mathematical Society here.

If you’re interested in how graph theory can be used to improve the efficiency of a subway system, check out this article about the Berlin subway system (the U-bahn).  Students and professors from the Technical University Berlin used graph theory to create a schedule that minimized transfer time between trains.  If only someone would do this in New York…

Bon appetit!

# Domino Computer, Knitting, and Election MArTH

Welcome to this week’s Math Munch!

First up this week is one of the coolest things I’ve seen in a long time: the world’s largest computer made out of dominoes.  A computer made out of dominoes?! you say.  How??

The Domputer, as it’s been called, was the great idea of mathematician, teacher, and entertainer Matt Parker (see a previous post about Matt here), and he and many volunteers built it at the Manchester Science Festival at the end of October.

Matt and some of his teammates testing domino circuits.

So, what is a domino computer, and how does it work?  As Matt is quoted saying in a podcast that featured the project, “A domino computer is exactly that: a computer made out of chains of dominoes.  Flicking over one domino sends a signal racing along the chain, just like current flows down a wire.  And then interacting lines of dominoes can manipulate the signal exactly the way circuit components do.”

At its very, very basic level, a computer is a machine that does calculations in binary.  You input some sequence of 0s and 1s by flipping signals on and off, and your input starts a chain of electrical communications that results in an output of 0s and 1s.  Most computers do this with electrical circuits.  But it can also be done with dominoes – sending an “on” signal means flipping a domino over, and sending an “off” signal means not flipping a domino, or having a chain of falling dominoes that becomes blocked and stops falling.

Making the domputer.

There are lots of different kinds of commands that you can send by flipping switches on and off and making those signals interact.  For example, suppose you want something to happen only if two switches are on – if the first switch is on AND the second switch is on.  For this you would need to make something called an “AND gate” – an interaction in chains of current that will continue the chain if both switches are on and will stop the chain if either (or both) is off.  How would you do that with dominoes?  In this video, Matt demonstrates how to make an AND gate out of dominoes: Domino AND gate.  Check out this video for OR (the chain continues if one or the other or both are on) and XOR (“exclusive or,” the chain continues if one or the other, but not both, are on) gates:

Matt’s Domputer does something very simple: it adds numbers in binary.  But, as you might imagine, it was extremely complicated to build!  According to the Manchester Science Festival Twitter feed, the Domputer used about 10,000 dominoes and would take about 13,600 years to do what a normal processor could do in a second.  Wow!

Here it is in action.  It messed up on this calculation (9+3), but succeeded in later attempts – and is fascinating to watch nonetheless!

Awesome!

Next up, we’ve written about mathematical knitting before (remember Wooly Thoughts and the prime factorization sweater?), but here’s a great site I recently found made by mathematician, knitter, and dancer Sarah-Marie Belcastro.

This site is full of articles and about and patterns for all kinds of cool mathematical objects – like Klein bottles (which make great hats, by the way)!  In her post about knitted Klein bottles (and all of the other objects she makes), Sarah-Marie not only describes how to knit the objects but a lot of mathematics about them.  I don’t know about you, but I always find mathematical ideas easier to understand when I can make models of them, or at least read about models being made.  Sarah-Marie does a great job of blending mathematical descriptions with how-to-make-it recipes.

Some other patterns that I love are Sarah-Marie’s 8-colored two-hole torus pants and this knitted trefoil knot.

Finally, are you wondering what to do with all those campaign posters you have left over from the election?  Here’s George Hart’s take on what to do with them:

Bon appetit!

# Stand-Up, Relatively Prime, and Aliens?

Welcome to this week’s Math Munch!

As you may have noticed, we here at Math Munch are all about good math videos.  Well, with Matt Parker’s math stand-up comedy YouTube channel, we feel like we’ve hit the jackpot!

Yes, you read it right – Matt is a math stand-up comedian.  Matt does stand-up comedy routines about mathematics at schools and math conferences in the United Kingdom.  In fact, he and several other mathematicians and teachers have started an organization called Think Maths that sends funny and entertaining mathematicians to schools to get kids more excited about math.  He also does podcasts  and is writing a book!  Cool!

Here are two of my favorite videos from Matt’s channel.  The first is a problem involving a sleeping princess and a sneaky prince.  I haven’t solved the problem yet – so, if you do, don’t give away the answer!

In the second, Matt shows you how to look like you know how to solve a Rubik’s cube and impress your friends.  And it teaches you some interesting facts about Rubik’s cubes at the same time.

We’ve dug deep into the world of cool, mathy videos – but how about cool, mathy radio?  Personally, I love radio.  And I love math – so what could be better than a radio podcast about math?

Check out this new series of podcasts about mathematics by Samuel Hansen.  It’s called Relatively Prime.  The first episode has just been released!  It’s about the fascinating (and a little scary) topic of the three mathematical tools that you’ll need to survive, in Samuel’s words, “the coming apocalypse.”  And what are these tools?  Game theory, the mathematics of risk, and geometric reasoning.  How will these mathematical ideas help you?  Well, listen to the podcast and find out!  The podcast features interviews with many mathematicians, including Edmund Harris (who we wrote about in April) and Matt Parker.

I especially like this podcast because it gives some good answers to the question, “What can mathematics be used for?”  Even though I love doing math just for fun, I sometimes wonder how math can be used in other subjects and problems I might face in my life outside of math.  If you wonder this sometimes, too, you might like listening to this podcast.

We had the opportunity to interview Samuel about mathematics and the making of Relatively Prime.  Check out the interview on the Q&A page.

Finally, talking about the apocalypse (and the uses of math) makes me think about alien encounters.  What are the chances that there’s an intelligent alien civilization out there?  There are a lot of factors that go into answering this question – such as, what are the chances that a planet will develop life?  The evaluation of these chances is largely a matter of science, as is actually contacting aliens.  But math can be used to come up with a formula that tells us how likely it is that we’ll encounter aliens, given the other chances and how they relate to each other.

The equation that models this is called the Drake Equation.  It was developed in 1961 by a scientist named Dr. Frank Drake and has been used by scientists ever since to calculate the chances that there are intelligent aliens for us to talk to.  The equation is particularly interesting because small changes in, say, the number of stars that have planets, can drastically change the chance that we’ll encounter aliens.

Want to play with this equation?  Check out this awesome infographic about the Drake Equation from the BBC.  You can decide for yourself the chances that a planet will develop life and the number of years we’ll be sending messages to aliens or use numbers that scientists think might be accurate.

Bon appetit!  And watch out for aliens.  If my calculations are correct, there are a lot of them out there.