Math Hombre

Interesting time to be hosting this carnival! I feel like there's a small resurgence with blogging, and I want to be part of it. I've really missed writing informally professionally. I've been a part-time host since Math Teachers at Play 22, 14 years ago!, and a big part of the original purpose of the blog was to collect, curate and share things that delighted and supported me. If you're interested in hosting, contact Denise Gaskins, the founder of this here carnival. The January carnival will be at her blog, but I think February is open!

177 is semiprime, for which two primes? 

177 is the ninth Leyland number, of the form x^y+y^x. What are x & y for 177? They're both prime, which should be a special kind of Leyland I think.

177 is the first "non-trivial" 60-gonal number. (1 and 60 are too easy.) What is the next 60-gonal number? (Pictured) What does the sequence of the first non-trivial n-gonal numbers look like? (6, 9, ...)

177 is a Leonardo number, so named by Edsgard Dijkstra for their relation to the Fibonacci numbers. The first five are 1, 1, 3, 5, 9... can you determine the pattern?

But the coolest thing to me is that it's the magic constant of the smallest magic square of distinct primes! I'll get you started...

Welcome one and all! Come on in and have a ball. 159 is semiprime and that's just fine.

Lucky that I'm hosting this, or is it just that 159 is lucky. How do you get lucky? Start with the counting numbers. Delete every 2nd number, leaving 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45... odd.  The 2nd number remaining is 3, so delete every 3rd number, leaving 1 3 7 9 13 15 19 21 25 27 31 33 37 39 43 45... now that's interesting in and of itself. Next delete every 7th number, leaving 1 3 7 9 13 15 21 25 27 31 33 37 43 45 ...; now delete every 9th number; etc.  How far do we have to go before we know 159 is lucky? Does knowing 151 is the previous lucky number help? Interesting to look at the gaps in each step, and the cutlist for each step.

Is it rarer to be a semiprime or a number with only odd digits? Odd increasing digits? Linear pattern in its digits?  Alyssa would like it as is.

Pat Bellew's 159 facts are that 159 is the sum of 3 consecutive prime numbers (which?) and can be written as the difference of two squares in two different ways (don't you want to find them?).

He also has that __ __ •159 = __ __ __ __ using all 9 nonzero digits. Of course, you can brute force it, but can you deduce this digitally complete product?

What #playfulmath have you seen this month? Here's some of what I have noticed.

September started with Math on a Stick in full swing. Doesn't get more playful than that!

Katie Steckles and Jimi went over the math in the Spider-Man No Way Home end credits. I lost my mind when watching it in the theatre, and am so glad someone's sharing it. SO MANY MC Escher references.

And as if the visuals weren't sufficient, the song is De La Soul's great cover of the Schoolhouse Rock classic, Three is a Magic Number.

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.

Welcome to the 133rd installment of the Playful Math Carnival.

133 is the 6th octagonal number. How many carnivals until the 7th octagonal? What kind of pattern do the 6th polygonal numbers make? (Play with some figural number GeoGebra.)

133 is also semiprime - the product of two prime factors. (Which two?) What is the next semiprime number? 133 is also a Harshad (aka Niven) number, a number divisible by the sum of its digits. It's an unusual stretch where 3 of four consecutive integers are Harshad - which are the other two? There's also a new to me fact: 133 is the number of partitions of 55 into distinct odd parts, which seems equivalent to the number of symmetric Ferrers graphs with 55 nodes. I haven't made sense of this yet, though! 133 is happy in base 10, so a good number for this holiday edition.






Last fact and shout out to Megan Schmidt: 133 is a square spiral corner number! Is that connected to any of the patterns discussed above?
 Literal math playing...

• Dave Coffey gave a presentation on Math Play with a Purpose at Global Math. He talks about redeeming Bingo, among other things.
• Speaking of Bingo, two of the groups at this semester's Family Math Nights made actual math games out of a Bingo premise. Meg and Madison made Food Bingo, which makes it about attributes of food. Erica and Claire had Star Bingo which used better number cards and some choice to enhance the game.
• There was one game that I liked more than the PSTs who ran it! Give Hamburger a try.
• Probably the breakout and most original game of FMN was You Must Cross the River. Eddie and Climie brought this D&D style game.
• One of my HS preservice teachers tried to gamify Which One Doesn't Belong... I think Danielle is on to something.
• Denise Gaskins, the founder of this here blog carnival, shares one of her many Hundred Chart Games.
• Marilyn Burns shares her two dice sum game, which is a classic for a reason. She shares using it in 2nd and 7th grade!
• Kent Haines assembled a Holiday Gift Guide for math games that might be too late for shopping this holiday from this post, but you'll want to keep this list.

Some playful interactives...

• NRICH shared a puzzle that is part about area, but made challenging through Cuisenaire Rods. Great lesson.
• Kevin Forster shared Factris which is a multiplication/factoring version of Tetris. 
• Scott Farrar made a cool GeoGebra activity implementing Always/Sometimes/Never with quadrilaterals. 

Math stories...

• Fawn Nguyen made it to 2 complete school years of Visual Patterns. She wrote a great post about just how many ways there are to see these.
• Desmos has started a series of math stories, starting with Alison Hamburger. Can't wait to read more of these.
• Edmund Harriss was interviewed on My Favorite Theorem where he shares the connection between Curvahedra and Gauss-Bonet.
• Dylan Kane is Explaining Less which is probably strongly correlated with Playing More.
• Pat Bellew is back at On This Day in Math, delighting every day with great math stories.
• A comedian former math teacher shares the untold story of the Pythagorean Theorem.
• Since there's one video, what about Kurt Vonnegut with the shape of stories?

Math art to round us out...

• Isohedral rounded up some of my favorite animated math artists in this post.
• Very excited that Clarissa Grandi has a math art activity book coming out.  Look at her website and you'll see why I'm excited.
• Nathaniel Highstein did an Islamic Geometry project with his students. Scroll down this thread to see their work and how he tiled them!
• Paula Beardell Krieg has been killing it, but if I was picking one recent post it's this one about the gyrobifastigium. You heard me.
• Simon Gregg tweeted some mathart that turned into WODB and latin squares and more, as only Simon can do. But what better captures the spirit of Playful Math?

Math art from the Public Domain Review.

The previous Playful Math was at Arithmophobia No More and the next is at Math Misery?. Would you like to host? Contact Denise Gaskins, or see the Playful Math homepage. People don't submit a ton of posts anymore, but I enjoy looking back at what I've found helpful from the math ed community and sharing it all together. So many resources and so much fun to be had.

Happy Holidays, or New Decade Blessings, or Sweet Playful Math!

4th annual World Tessellation Day. Begun in 2016 by Emily Grosvenor for M. C. Escher's birthday. (More of that story and Emily's book.) Don't think I'll get a chance to make a new tessellation for today, but here are some of my favorites from the past year. (Mine followed by the real treats from others.)

Mine:

In Isometric

GeoGebra applet

GeoGebra applet

GeoGebra applet

GeoGebra applet

Others':

• David Petro's double translation tessellation in Desmos
• Regolo double rotation elephants.
• Marcelo Henrique Tatuador's cool graphic 2 tile.