Tag Archives: geometry

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!

[youtube http://www.youtube.com/watch?v=nv0Onj3wXCE&feature=plcp]

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.

[youtube http://www.youtube.com/watch?v=aPD_OkjnCqU&feature=plcp]

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.

Posted by Anna Weltman. Categories: Math Munch. Tags: equations, game theory, geometry, infographic, interview, podcast, puzzles, video. 11 Comments

Sep. ’12

Demonstrations, a Number Tree, and Brainfilling Curves

Welcome to this week’s Math Munch!

Maybe you’re headed back to school this week. (We are!) Or maybe you’ve been back for a few weeks now. Or maybe you’ve been out of school for years. No matter which one it is, we hope that this new school year will bring many new mathematical delights your way!

A website that’s worth returning to again and again is the Wolfram Demonstrations Project (WDP). Since it was founded in 2007, users of the software package Mathematica have been uploading “demonstrations” to this website—amazing illuminations of some of the gems of mathematics and the sciences.

Each demonstration is an interactive applet. Some are very simple, like one that will factor any number up to 10000 for you. Others are complex, like this one that “plots orbits of the Hopalong map.”

Some demonstrations are great for visualizing facts about math, like these:

Any Quadrilateral Can Tile

A Proof of Euler’s Formula

Cube Net or Not?

There’s also a whole category of demonstrations that can be used as MArTH—mathematical art—tools, including these:

Rotate and Fold Back

Polygons Arranged in a Circle

$turtlefractals$

Turtle Fractals

With over 8000 demonstrations to explore and new ones being added all the time, you can see why the Wolfram Demonstrations Project is worth returning to again and again!

Jeffrey Ventrella’s Number Tree

Next up, check out this number tree. It was created by Jeffrey Ventrella, an innovator, artist, and computer programmer who lives in San Francisco. His number tree arranges the numbers from 1 to 100 according to their largest proper factors. For instance, the factors of 18 are 18, 9, 6, 3, 2, and 1. Once we toss out 18 itself as being “improper”—a.k.a. “uninteresting”—the largest factor of 18 is 9. This in turn has as its largest factor 3, and 3 goes down to 1. Chains of factors like this one make up Jeffrey’s tree. It has a wonderful accumulative feeling to it—it’s great to watch how patterns and complexity build up over time.

(On this theme, WDP also has a demonstrations about trees and about prime factorization graphs.)

Cloctal: “a fractal design that visualizes the passage of time”

There’s lots more math to explore on Jeffrey’s website. His piece Cloctal—a fractal clock—is one of my favorites. What I’d like to feature here, though, is the diverse and intricate work Jeffrey has done with plane-filling and space-filling curves. You can find many examples at fractalcurves.com, Jeffrey’s website that’s chock full of great links.

Jeffrey recently completed a book called Brainfilling Curves. It’s “a visual math expedition, lead by a lifelong fractal explorer.” According to the description, the book picks up where Mandelbrot left off and develops an intuitive scheme for understanding an “infinite universe of fractal beauty.”

An example of a “brainfilling curve” from Jeffrey’s “root8” family

The title comes from the idea that nature uses space-filling curves quite often, to pack intestines into your gut or lots and lots of tissue into the brain you’re using to read this right now! Hopefully you’re finding all of this math quite brainfilling as well.

(And just one more example of why WDP is worth revisiting: here’s a demonstration that depicts the space-filling Hilbert and Moore curves. So much good stuff!)

Finally, here’s a video that Jeffrey made about brainfilling curves. You can find more on his YouTube channel.

Bon appetit!

Posted by Justin Lanier. Categories: Math Munch. Tags: applet, art, curves, demonstrations, Euler's formula, fractals, geometry, nets, numbers, prime factorization, primes, tessellation, video, wolfram. 3 Comments

Aug. ’12

Newroz, a Math Factory, and Flexagons

Welcome to this week’s Math Munch!

You’ve probably seen Venn diagrams before. They’re a great way of picturing the relationships among different sets of objects.

But I bet you’ve never seen a Venn diagram like this one!

Frank Ruskey

That’s because its discovery was announced only a few weeks ago by Frank Ruskey and Khalegh Mamakani of the University of Victoria in Canada. The Venn diagrams at the top of the post are each made of two circles that carve out three regions—four if you include the outside. Frank and Khalegh’s new diagram is made of eleven curves, all identical and symmetrically arranged. In addition—and this is the new wrinkle—the curves only cross in pairs, not three or more at a time. All together their diagram contains 2047 individual regions—or 2048 (that’s 2^11) if you count the outside.

Frank and Khalegh named this Venn diagram “Newroz”, from the Kurdish word for “new day” or “new sun”. Khalegh was born in Iran and taught at the University of Kurdistan before moving to Canada to pursue his Ph.D. under Frank’s direction.

Khalegh Mamakani

“Newroz” to those who speak English sounds like “new rose”, and the diagram does have a nice floral look, don’t you think?

When I asked Frank what it was like to discover Newroz, he said, “It was quite exciting when Khalegh told me that he had found Newroz. Other researchers, some of my grad students and I had previously looked for it, and I had even spent some time trying to prove that it didn’t exist!”

Khalegh concurred. “It was quite exciting. When I first ran the program and got the first result in less than a second I didn’t believe it. I checked it many times to make sure that there was no mistake.”

You can click these links to read more of my interviews with Frank and Khalegh.

I enjoyed reading about the discovery of Newroz in these articles at New Scientist and Physics Central. And check out this gallery of images that build up to Newroz’s discovery. Finally, Frank and Khalegh’s original paper—with its wonderful diagrams and descriptions—can be found here.

A single closed curve—or “petal”— of Newroz. Eleven of these make up the complete diagram.

A Venn diagram made of four identical ellipses. It was discovered by John Venn himself!

For even more wonderful images and facts about Venn diagrams, a whole world awaits you at Frank’s Survey of Venn Diagrams.

On Frank’s website you can also find his Amazing Mathematical Object Factory! Frank has created applets that will build combinatorial objects to your specifications. “Combinatorial” here means that there are some discrete pieces that are combined in interesting ways. Want an example of a 5×5 magic square? Done! Want to pose your own pentomino puzzle and see a solution to it? No problem! Check out the rubber ducky it helped me to make!

A pentomino rubber ducky!

Finally, Frank mentioned that one of his early mathematical experiences was building hexaflexagons with his father. This led me to browse around for information about these fun objects, and to re-discover the work of Linda van Breemen. Here’s a flexagon video that she made.

And here’s Linda’s page with instructions for how to make one. Online, Linda calls herself dutchpapergirl and has both a website and a YouTube channel. Both are chock-full of intricate and fabulous creations made of paper. Some are origami, while others use scissors and glue.