# FIVE, Axiomatic, and Mathekniticians

Welcome to this week’s Math Munch!

It’s time once again for a recap of this month’s post on facebook, and we have some good ones for you. How about a celebration of five and a look at several mathematical artists.

This month marked the five-year anniversary for Math Munch!  Thank you so much to our readers for sticking with us. In honor of the occasion, check out these awesome Numberphile videos, each related to the number 5. There’s the 5 Platonic solids, of course, or Euclid’s 5th postulate, or a fifth-root trick, or even 5 and Penrose tilings. Click on the links to view, or scroll to the bottom of this post.

Up next, meet Timea Tihanyi and Jayadev Athreya. They are a visual artist and mathematics professor, respectively, and the two of them are coming together for a math-art collaboration called Axiomatic.  Geek Wire wrote a nice article about them here. Give it a read. Sadly, there aren’t many images yet, but we hope to see more from this team soon.

Alright, a quick break.  How about taking on this little challenge posted by The Dice Lab.  It features their awesome 120-sided isohedral dice, but the question is this, in their words:

“Rack ’em up! How many d120’s are in this tetrahedral pyramid?”

Finally, We’ve seen our fair share of mathematical fiber arts here on MM. See these previous posts for some mathematical knitting and crochet. Well I had to share a recent writeup by The Guardian on two mathekniticians, a married couple featured here before: Pat Ashforth and Steve Plummer. Read the article. It’s chock full of great images like the one to the left.

Well that’s it for this week’s Math Munch. See you next time, and bon appetit!

# Gödel, Other Crazy Paradoxes, and Math Factor

Welcome to this week’s Math Munch!

Math can be confusing. Everyone knows that. And, actually, that’s what lots of people love about it. Some things in math are more confusing than others. One such thing, in my opinion, is a theorem developed by this kinda creepy-looking guy:

His name is Kurt Gödel, and he’s responsible for a theorem that basically says: You know how you thought we had rules for arithmetic that work, don’t contradict each other, and can answer all kinds of questions with numbers? Well, there are problems with numbers (really strange problems, granted) that our arithmetic cannot answer. And if you try to fix your system so that it can answer those problems, you’ll have issues with other problems. There’s no way to repair your system so that it stays complete and answers all problems.

If this sounds disturbing to you (math doesn’t work?!?!), you’re not alone. Lots of mathematicians were upset by this. They thought, as lots of us do, that math is supposed to be logical. It’s supposed to give us the answers we need. We’re supposed to be able to rely on it. Gödel arrived at this theorem by playing with paradoxes, or statements that self-contradict. (Such as, “Today is opposite day.”) The statement that he came up with really rocked the world of math.

If you’d like to learn more about Gödel and his disturbing theorem, listen to this podcast episode from Radiolab. It talks about Gödel’s life and what his theorem meant for math, with an appearance by everyone’s favorite mathematician, Steve Strogatz!

Gödel’s confusing theorem is only one in a long string of crazy, confusing math paradoxes. Another of my favorites is the Barber Paradox, which mathematician Bertrand Russell came up with. Here it is, in dry-humor video form:

If you like that paradox, you’ll probably also like the Pinocchio Paradox— which was developed by 11-year-old Veronique Eldridge-Smith:

This video comes from the YouTube channel, SpikedMathGames. I suggest you check it out!

Finally, I thought it would be nice to close off this loopy Math Munch post with a loop back to podcasts– and a link to a very large archive of math podcasts called Math Factor. Math Factor is a podcast produced out of the University of Arkansas about all kinds of interesting math. They even have an episode about the topic of this week’s Math Munch! Give it a listen.

Have a terrible opposite day, and bon appetit!

# roTopo, de Gua, and Bibi-binary

Welcome to this week’s Math Munch!

Today we’re going to look at a few examples of going “up a dimension”. Our first example is what got me thinking about this theme. It’s a game called roTopo. (If you have trouble getting it to load, try using a different browser.)

Maybe you have played the game B-Cubed. RoTopo is similar—trace through a sequence of squares as they get eliminated one by one. I like B-Cubed because it combines spatial thinking with strategic thinking—planning ahead. Rotopo, with its twists and turns in 3D, stretches a player’s spatial thinking even further. I hope you enjoy giving it a try! Maybe you could design a roTopo level of your own with a drawing or with some blocks.

What else can we find when we look “up a dimension”? Maybe the most famous theorem in all of mathematics is the Pythagorean theorem. There are several ways we might try to take a^2+b^2=c^2 up a dimension. If we start to increase the numbers in the exponents, like a^3+b^3=c^3, we head in the direction of Fermat’s Last Theorem. If we add more terms, like a^2+b^2+c^2=d^2, we can find distances in 3D instead of 2D.

A right tetrahedron—the kind needed for de Gua’s Theorem.

And if those aren’t enough to make you go “wow”, then you need to hear about De Gua’s Theorem. The Pythagorean Theorem relates the sides of a right triangle. De Gua’s Theorem relates the faces of a right tetrahedron. The sum of the squares of the areas of the the three “leg” faces is equal to the square of the area of the “hypotenuse” face. So wild! You can read a proof de Gua’s Theorem here. The theorem is named for the 18th-century French mathematician who presented it to the Paris Academy of Sciences in 1783 (although it was known to others before him). De Gua’s Theorem in turn is a special case of a still more general theorem. Once mathematicians start upping dimensions, the sky is the limit!

Last up: Bibi-binary. No, that’s not the way that Justin Timberlake counts—although that funny thought is why I Googled “bibibinary” in the first place. But when I did, this totally silly number system popped up!

How to count in Bibi-binary.

Well, I guess it’s not the number system that’s silly so much, since it’s actually just hexadecimal. Hexadecimal is like binary, but up a couple of dimensions. The system uses sixteen symbols to represent numbers, just as the decimal system uses ten symbols and binary uses two. What makes Bibi-binary silly, then, is not its logical structure but how it sounds.

There are sixteen syllables in Bibi-binary, which are made from combinations of four consonants and four vowels. Three is “hi” and eight is “ko”. If you want to have three 16’s and eight more—56—that would be “hiko”. As another example, 66319344 is “hidihidihidiho”. Bibi-binary was invented in 1971 by a French singer and actor named Boby Lapointe.

I think it would be fun to learn to count in Bibi-binary. Can you believe that I could find zero (“ho”) videos online of people counting in Bibi-binary? I wonder if any of our readers might enjoy making one…

Hexadecimal is not just fun and games. It’s also used for making codes to stand for colors, especially in making webpages. Most of Math Munch is either 683D29 or 6AB690, would you believe. You can explore using hexadecimal to name colors in this applet.

You can learn lots more about Bibi-binary on the great website dCode, and you’ll also find an applet there that can convert between decimal and Bibi-binary. DCode has lots of tools related to cryptography (get it?) and other math topics, too.

Do you have any favorite examples of math that goes “up a dimension”? We’d love to hear about them in the comments.

Bibi-bi for now! Bon appetit!

# Rectangles, Explosions, and Surreals

Hi everyone! We’ll be back with a new post next week. Until then, enjoy this “explosive” post from October 2012.

Welcome to this week’s Math Munch!

What is 3 x 4?   3 x 4 is 12.

Well, yes. That’s true. But something that’s wonderful about mathematics is that seemingly simple objects and problems can contain immense and surprising wonders.

How many squares can you find in this diagram?

As I’ve mentioned before, the part of mathematics that works on counting problems is called combinatorics. Here are a few examples for you to chew on: How many ways can you scramble up the letters of SILENT? (LISTEN?) How many ways can you place two rooks on a chessboard so that they don’t attack each other? And how many squares can you count in a 3×4 grid?

Here’s one combinatorics problem that I ran across a while ago that results in some wonderful images. Instead of asking about squares in a 3×4 grid, a team at the Dubberly Design…

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