Math Hombre

 May I March from April?

I was supposed to post the March/April Playful Math Carnival, but it's May! May the 4th even, happy Star Wars Day to them that celebrate it.

180 is a pretty amazing math number. 18 divisors, more than any smaller number. 18 divisors also makes it refactorable, divisible by the Very abundant, as you might guess. Harshad (or Niven) also, divisible by the sum of its digits. The sum of two squares (both squares of divisors!) For Euler's totient function, 

Of course, 180 is probably most famous in math for being the sum of the angles in a triangle, or have the degrees of a full turn. How would you prove the triangle relation? (I tell my math history students that is one of the few theorems every math major should be able to prove.)

Welcome to the 145th edition of the Playful Math Carnival. Once known as the Math Teachers at Play Carnival, this edition follows the Denise Gaskins' (founder of this here carnival) blowout 144th Anniversary Edition, as night doth follow gentle day, and by that we were blown away.  

Sadly, there's nothing interesting about the pentagonal semiprime 145. Well, besides 145=1!+4!+5!. There are only four numbers for which that's true.  And it's the fourth number that's a sum of squares in two different ways. And it's a Leyland number, because 3^4+4^3=145. (I wonder what the next Leyland numbers before and after are?) And the 145th prime number is 829 and 145829 is prime and the largest prime factor of 145 is 1+4+5+8+2+9 and that 145 is congruent to 1 in mod 8, mod 2, and mod 9. But besides that...  there's practically nothing. (All these are from Pat Bellew's fun number site.) And 145 shows up in Matt Parker's melancoil. 145 degrees (F) makes something medium rare...  maybe that should be the goal for this edition?

Volvo 145. Ove approved.

Hop in the 145 and let's go! 

Books & Essays

Just before this month started I got to participate in a nifty mathzine fest from Becky Warren, Chris Nho and Ayliean. Technically February, it was after Denise's edition so I'm counting it. Several of the results are on the Public Math website, which has more besides. Also see the mathszine hashtag on Twitter.

That was my introduction to Ayliean, who had some thoughts on STEMinism.

Some of those zines inspired Sophia Wood for her first Fractal Kitty zine, on the Cantor Set.

Jim Propp was musing on division by zero. History, what ifs, new possible numbers...

Edmund Harriss has a new children's book out, HELLO NUMBERS! What Can You Do? and has been out supporting the release. Read more at Chalkdust's Math Book of the Year series. Also super curious about Eugenia Cheng's Molly and the Mathematical Mystery.

One of the many fun parts about teaching our capstone course, the Nature of Modern Mathematics, is the reading. Instead of me mandating a book (most instructors choose the excellent Journey Through Genius, by William Dunham), the learners can choose a book. Comes a day, we then have a book club class where people get to discuss with others reading their book, then share with the class what they thought. I try to keep notes, demonstrating poor steno skills.

The possibles this year are on this Google doc, which gets revised year to year.

To celebrate the release of the newest great and greatest new children's math book... by which I mean Which One Doesn't Belong? by the #MTBoS' own Christopher Danielson, of course... I thought I'd recap some of my favorite math picture books. This list also has MTBoS support, as I solicited suggestions from the MTBoS for a colleague.


The request was for a parent with a mathematically curious child (really, could be anyone then, am I right?) of 4 or 5 years.

Top:

• Moebius Noodles, Maria Droujkova's great book about big math ideas to explore. There were articles about calculus in kindergarten when it first came out.
• Great new book: Which One Doesn¹t Belong. OK, I'll say more. I love this book because it's clever and pretty, but also because it can teach you how to read mathematically rich literature.
• Math Curse, Lane and Scieska: just the best math book ever written. Nearly anything can be a problem, you know.

• Anno's Mysterious Multiplying Jar, or anything by Mitsumasa Anno. Just charming books, and lovely besides.
• Spaghetti and Meatballs For All, Marilyn Burns: my favorite of the explicitly mathematical genre. Tang and Murphy have their place but Burns is the queen of the genre. (Greedy Triangle, Smarty Pants, $1 Word...) 
• Princess of the genre, Elinor Pinczes: One Hundred Hungry Ants, A Remainder of One, ...
• Infinity and Me by Kate Hosford
• Tessallation!  by Emily Grosvenor
• Grandfather Tang’s Story, by Ann Tompert
• The Dot and the Line, by Norton Juster

Biography:

• Paul Erdos, The Boy Who Loved Math by Deborah Helligman
• Fibonacci, Blockhead by Joseph D'Agnese
• Eratosthanes, The Librarian Who Measured the Earth by Katherine Lasky
• Einstein usually gets lumped in here. Not a mathematician, technically, but if you're being that technical, loosen up! Try Odd Boy Out or On a Beam of Light

What to do:

• Chris Hunter has a bunch of recommendations plus how to use them.
• Another post with a lot of suggestions at Algebra's Friend
• Suzanne Alejandre suggested the old (aka classic) NCTM guide, Welchman-Tischler's book, might provide ideas? (She found a digital copy; use the NEXT button)
• Marilyn Burns (herself) just suggested this starting point from PBS

Possibly for older, but like Madeline L'Engle, I think people underestimate kids:

• The Phantom Tollbooth, by Norman Juster
• The Man Who Counted, by Malba Tahan
• Flatland, by Edwin Abbott 
• The Number Devil, by Hans Magnus Enzensberger
• The Adventures of Penrose the Mathematical Cat, by Theoni Pappas
• The Cat in Numberland, by Ivar Ekeland and John O'Brien
• A Wrinkle in Time, Madeline L'Engle (First I heard of a tesseract.) There's an audiobook where L'Engle reads it herself. Highly recommended.

Special opportunity today, to meet and greet the author of a fun new math book.

Emily Grosvenor (twitter, website) is a "reporter, travel writer and essayist" who has gotten all the way to Mathland with her illustrated children's book Tessalation!. After a successful Kickstarter, the book is available for pre-order or as an e-book at Amazon (free for Kindle Unlimited) and direct order from Waldorf Books. I am between having received my electronic and my physical copy, and find the book just charming.

Emily was willing to answer a few questions, so here we go!

Q. Do you remember when you first noticed tessellations?

No. I first learned about them in 4th grade -- every part of my creativity seems to have it seeds in the 4th grade, it must be a seminal year for development. We did an activity in gifted class where we made tessellations. I made an uninspired tessellation of a seal jumping out of the ocean. But it was fun. And clearly it stuck, since I was still thinking about it almost three decades later. 

Q. Do you have a tessellation from someone else that you like especially? (Maybe a favorite Escher tessellation?)

I'm a big fan of Horseman But honestly, I think my favorite is just the simple hexagon tessellation. We just got bees at our home in McMinnville. I have great hopes I'll see one there, soon!  

Q. What makes tessellations worth thinking about and exploring for you?

I find patterns soothing to look at. Honestly, visual culture bothers me a lot. Usually there is so much going on, and I get distracted easily. But with tessellation you can take in the chaos and then let the eye, and the mind, settle on an individual part. Also, I am very compelled by the idea of seeing myself as a part of a greater whole. Not just with my family, but with my community. One of themes behind Tessalation! is that the world is not as chaotic as it seems, that there is an inherent beauty and order to it, and we can be a part of it. 

Q. What was your experience on the first World Tessellation Day?

It was a crazy day! My best friend was in town with her kids and husband and we threw a party at the McMinnville Public Library. We had a tessellation station, we screened the book on the wall, we had hexagon cookies, tiling turtles tessellated games, and coloring pages from the book. It was a BLAST! I was so tired. I probably should have been tweeting out tessellations all day, but there were a couple hundred people around the world who were posting images. In all, I was happy with the outcome. When I got a chance I checked in and retweeted, liked or posted what I could. People who like tessellations really love them. Also, it's a visual meme, which makes it easy to get behind.  

Emily created World Tessellation Day, and used it to launch the book. She has a fun post about the book launch here. The twitter stream for #WorldTessellationDay had a ton of fun participation from genuinely around the world.

Q. Why should it be an annual event?

Why should anything? It's fun. Fun to post, fun to make, fun to see all of the creativity happening around the world. I was most impressed by the posts coming in from Spain showing all of the tessellated mosaics available in plain view in public spaces. There are a lot of silly holidays. We share World Tessellation Day with National Flip Flop Day, for example. Who cares about flip flops? Well, someone does. If anyone cares about something there should be a day for it.

Didn't realize it was also flip flop day - despite Danica McKellar's tweet. Doh.

Q. What’s challenging for you when you are developing a tessellation?

I actually don't do a lot of designing tessellations. Notice I did not make the illustrations in the book, for example. But I did try to create the feeling of tessellating in the rhyme scheme and overall meter of the book. I wanted there to be a strong connection between how the text feels when read out loud and what you are looking at. Can words tessellate? I think I tried to do that. 

Q. Do you have a general process you follow?

The best part of this project has been how it has opened this entire world to me of math play, tessellation and visual culture. I launched this project thinking that tessellations are awesome but not really having any idea of the scope of talent out there or of the artists who are working in tessellation. I've been touched by people who have reached out from around the world to share in the excitement. But my favorite moments are when my 3-year-old, Griffin, finds them in plain sight. Just yesterday he got a new pair of Timberline sandals and said: Mama -- there's a tessellation on my foot! 

Fascinating!


Thanks, Emily, for the book, and holiday and interview.

Oh! I should have asked how she got connected with her talented illustrator, Maima Widya Adiputri (Tumblr, FairyFrame).

Find out much more about this book from other stops on the booktour.

Find out more about tessellations from the resources on my page.

Or start immediately making your own! One of my most recent ones to play with on GeoGebra is a funky hexagon one, with a glide reflection similar to what the Horseman has.

PS>
#TessellationNation, now #tessnat, is coming at TwitterMathCamp16. Christopher Danielson was thinking it should be based on people's questions, so hop on Twitter to chip in, or share them here.

So far:
Christopher ‏@Trianglemancsd
We proposed this session as one revolving around our questions. Maybe you could share of those here before TMC?
I would like to learn more about how to categorize tessellations.
I wonder about the relationship between "tiling" and "tessellation".
I am super curious about the tilings in mosques. Are they tessellations? Why do they so rarely appear in the math analyses of tessellations I've encountered?
#tessnat There's a start on where my mind is for #TMC16. What about you, Tessellation Nation?

Malke Rosenfeld ‏@mathinyourfeet
1. Hi #tessnat. My goals: try & try again. I would like to play with diff kinds of tiles to help me ask new questions.
2. After I play I'd like to talk abt my notices/Qs and then design a tile that is simple but creates an interesting result/design #tessnat
3. I would also like to observe someone designing/creating an anthropomorphic tiling if that ends up happening. #tessnat

Megan Schmidt ‏@Veganmathbeagle
@Trianglemancsd OH!
I want to draw the things, whatever that means. #tessnat
Ok. My needs are "be in the #tessnat morning session." :)

Planning my fall pre-service elementary math course, I was thinking about books. In the distant past we've read Deb Schifter's What's Happening in Math Class? (strong teacher narratives), and more recently Jo Boaler's What's Math Got to Do It. (Here's a recount of one of our book discussions about it.) But in my other classes, it's been very good to offer choice to students. (Here's a post about that.) I'm a big believer that teacher-to-teacher reflective conversation is the best PD, and book discussions make good context for those discussions. (A pdf of some research on this by Burbank, Kurchauk and Bates in The New Educator.)

I was finalizing my list for them to choose among, and thought to ask on Twitter. As usual, unexpected generosity in people thinking and answering. (I don't know why it's still unexpected.) Here's the responses:





 

Today's the day! The crowdfunding for Sue Van Hattum's book Playing with Math opens up. I'm excited about the book, proud to be part of it in a little way and so happy for her.

If there's one phrase that captures my approach to mathematics learning and teaching, it's 'playing with math.'  So I'm really cheesed that Sue has stolen this title for memoirs... wait. That's not where I was going with this. Besides, the full title is Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers

I didn't meet Sue until after she had moved away from here (West Michigan), but got to know her via what is now the Math-Twitter-Blogosphere, and then in real life on one of her return visits. In this book she has gathered together many of my favorite aspects of the math community and culture, plus more that I have yet to know.  I got to be a realatively early reader of the manuscript (found a v1 file on my computer!), and have seen it start good and get better from there. This is going to be an amazing resource. Her philosophy in building the book was very much about building a community, sharing the people and math of which she is so fond with you. I think you'll find it intriguing, entertaining and helpful. Bloggers, math circles, living math forum... Sue is great at connecting people.

I'm a great believer that teachers get better through conversation, and every piece in this comes across as powerful teacher or learner sharing. It's a rare anthology where you feel like you wouldn't cut a thing, but this is one of those. The pieces I have returned to more than once already include Bob and Ellen Kaplan's reflection on a prison math circle, Maria Droujkova's rejoicing in confusion, Malke Rosenfeld's mapping the territory, and Allisson Cuttler's putting herself in her students' shoes. And... it could easily become the table of contents. In editing, Sue worked hard to preserve the author's voice, make the book very inclusive of student and teacher diversity, and to represent each of her three communities.

And each teacher story finishes with a puzzle or game. Tanton, Halabi, Gaskins, Salomon... Van Hattum. In addition to editing, Sue is a great and reflective teacher, and her own writing and games are an important part of the book. It is very much like a teacher weaving a lesson together from student work and responses, the way she tells her vision of mathematics learning from such a wide variety of different authors.

Nix the Tricks and Moebius Noodles are both great examples of books that are from and for the math community, and this is a great next step. Please consider supporting it; I think you'll be glad you did.

Some other resources, reviews and comments:

• IncitEd crowdfunding site - support the book and get a pdf or paper copy
• Playing with Math website
• Sue Van Hattum
• Fawn Nguyen
• Denise Gaskins
• Shireen Dadmehr
• and, I'm sure, more to come.

A family favorite to which we were introduced by Sue. Our semi-annual gaming get togethers are now pretty highly anticipated!