# 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!

# The Dice Lab, Sum of Cubes, and Double Polyhedra

Welcome to this week’s Math Munch!

It’s the final Thursday of September, so it’s time again for a recap of the month’s best from our Facebook page. This month we have a new sort of dice, a beautiful illustration of a numerical fact, and some wonderful new sculpture work from Rinus Roelofs. Let’s dig in.

First, check out this wonderful image. Meditate on it, and see if you can figure out what’s going on, even if you can’t understand the notation.

It’s showing us a simple way to compute a sum of cubes. They can be broken down and reconstructed as a square! Consider the sum of the first 3 cube numbers, for example: 1+8+27=36, and 36 is the square of 6. One step further, 6 is the sum of the first 3 numbers.

So in the picture above, the sum of the first 5 cubes is equal to the square whose side length is the sum of 1 through 5.  AMAZING, and a beautiful illustration. Can you see why it always works, not just for 1 through 5? That’s key! And now test your understanding: What is the sum of the first 100 cube numbers?

Up next, we’ve met Henry Segerman plenty of times on Math Munch, including a look at the project he shares with Robert Fathauer, called The Dice Lab. They make mathematically interesting dice that have, in most cases, never been produced before. There newest creation (also last? see the video to see what I mean) is a 48-sided dice. Very cool. Can you think of a use for a 48-sided die?  It sure looks cool. Reminds me of a rhombic dodecahedron. Do you see the connection?

Finally, another familiar face – the incredible mathematical artist, Rinus Roelofs – has been making incredible things. We met Roelofs in July, but his facebook page has been full of activity since then. His recent work has focused on double-covered polyhedra.  You’ll have to click over and browse to see what I mean. Recently he posted a project I might want to take on. These are fold-up models for his creations. Check out the gallery below.

I’m not 100% sure how that cube one works, but I think I can figure it out, and I bet some of you can too. Of course, I’m sure we’ll make mistakes, but if we keep on learning, I bet we can get this figured out. If anyone ends up making a template of their own, email it to us and we’ll share it on the site.

Until next time, bon appetit!

# Maria Chudnovsky, Puzzlebomb, and Some Futility

Welcome to this week’s Math Munch!

This week we meet an incredible mathematician, take on a tough number puzzle, check out a wonderful mathematical card trick, and much more.

A while ago we shared an interview with mathematician Fan Chung Graham.  The interview was posted by Anthony Bonato, The Intrepid Mathematician. Well, this week we share another of his interviews, this time with Maria Chudnovsky, graph theorist and star of not one, but two television commercials. (A rare feat for a mathematician.) Maria is also a winner of the extraordinary MacArthur “Genius” Grant. You can check out the video below or click here for the full interview.

Up next, our friends over at The Aperiodical do a lot of great things for the math world. One contribution is the monthly Puzzlebomb put on by Katie Steckles.

This month’s puzzle is MODOKU, a sort of sudoku style puzzle where columns and rows span the possible remainders mod 7 and mod 5. Check it out! Thanks to Katie for such a lovely puzzle! You can click below for an interactive version with complete instructions.

Finally this week, it’s time again to look at a Futility Closet, a phenomenal blog containing the odd mathematical tidbit. We’ll take a look at three of them.

Here’s a weird arithmetic fact I found there. Do you see what’s going on there? I have absolutely no idea how often this kind of thing is true, if ever again, but it gets me thinking.

Here’s another incredible one. We’ve posted about Pascal’s (Yang-Hui’s) Triangle lots of times (1 2), and I’ve come across a lot of fascinating stuff about it, but this is new to me. Apparently, “the product of the six numbers surrounding any interior number in Pascal’s triangle is a perfect square.” Can you prove it?

Now on to the biggie…  This is such a cool card trick! Here’s the trick as explained by Futility Closet:

“I hand you an ordinary deck of 52 cards. You inspect and shuffle it, then choose five cards from the deck and hand them to my assistant. She looks at them and passes four of them to me. I name the fifth card.”         !!!!!!!!!!

The key to the magic is this chart:

{low, middle, high} = 1
{low, high, middle} = 2
{middle, low, high} = 3
{middle, high, low} = 4
{high, low, middle} = 5
{high, middle, low} = 6

Can you figure out how it works from the chart alone? You’ll need a good assistant to get on board, and it wouldn’t hurt to practice a bit. Then get ready to impress. Oh, and if you can’t figure out the trick from the chart alone, then just head over to Futility Closet and read the full explanation.

Well that’s it for this week. Hope you found something delicious. Bon appetit!