- 108 beads on a Tibetan Buddhist Mala.
- 108 pressure points in the human body.
- 108 suitors courting Odysseus' wife Penelope.
- An official Major League Baseball baseball has 108 stitches. In 2016 the Chicago Cubs won the World Series for the first time in 108 years, ending the longest championship drought in North American professional sports. The Cubs' win came in the 10th inning with 8 runs. From what perspective would you see the maximum fraction of stitches?
- Police departments in India are warning iPhone users to ignore this Siri prank: users say "108" to Siri, then close their eyes. When a user says "108" to Siri, it automatically dials local emergency services. (The prank ask users to close their eyes because there is a five-second window where a user can press cancel, in case a call was placed accidentally.)
- Wikipedia notes: "The well known bas-relief carving at the famous Angkor Wat temple in Cambodia relates the Hindu story of a serpent being pulled back and forth by 108 gods and asuras (demons), 54 gods pulling one way, and 54 asuras pulling the other, to churn the ocean of milk in order to produce the elixir of immortality." Also, in karate, "The ultimate Gōjū-ryū kata, Suparinpei, literally translates to 108. Suparinpei is the Chinese pronunciation of the number 108, while gojūshi of Gojūshiho is the Japanese pronunciation of the number 54. The other Gōjū-ryū kata, Sanseru (meaning "36") and Seipai ("18") are factors of the number 108."

- 108 is an Italian street artist. The first painting I saw of theirs is Rational/Irrational.
- 108 eyes was a graphic found on Tumblr from playful_geometer. I liked it enough to make this pattern in GeoGebra. (Or maybe just the kite spiral and no eyes.)

More mathily:

- So why can we add 100 and 8 and get a number divisible by 9? That's weird, right?
- It can be factored as 1x2x2x3x3x3. (Next up, 27648.) This means 108 is
*hyperfactorial*. - 108 degree angles in a regular pentagon, which makes it Golden ratio adjacent. Also 36 and 72 degrees are the angles in the golden triangle, which Euclid directs as the isosceles triangle with base angles double the other angle. 36, 72, 108...
- I got wondering if many other numbers are multiples of the same number with (non-ending) zeroes removed.
- New to me was the idea of a refactorable number: a number divisible by the count of its divisors, also called the tau numbers. 108 is the 18th tau number. Can you find all 17 prior?

I discovered many of these things when (accidentally?) hosting Carnival of Maths 108.

There weren't many submissions this month, so many of these are blogposts I've noticed in the past month. I encourage you to think about submitting - either your own or others - and hosting. Denise Gaskins is the originator of this carnival, and has a submission form. Last carnival at Give Me a Sine; next carnival at Math Mama Writes. (Hi, Sue!)

Long preamble! Let's Play Math, shall we?

**Just, Wow!**

Fawn Nguyen has many excellent posts, sites and presentations, but still occasionally has one that makes you say just wow. Her post on doing the Euclidean Algorithm with her middle school students was like that for me. Mike Lawler did an excellent follow up on the material with his family mathematicians.

Lana Pavlova explored what it means to be good at mathematics in this mindset-rich post.

Megan Schmidt blew me away with her rigorous honesty in her Ignite presentation on We Are Powerless. Link goes to the playlist, and you will enjoy every one you listen to. Only time for two more? José Luis Vilson, My Kids Can Do That Math, Too, and Robyn Drew, The Mystery of the Circle are where I'd start.

Mike Lawler also got his boys exploring convex pentagon tilings via Evelyn Lamb's post on Math Under Her Feet. These are amazing geometric patterns.

Nice post about teacher's Math Circles by Katrina Schwartz at KQED/Mindshift. tl;dr: Doing math helps us empathize with students and teach better.

Chase Orton shared numberless data problems, extending Brian Bushart's numberless story problem idea.

Denise Gaskins has a quick note about how even a workbook can be a moment for play.

Rupesh Gesota does an in-depth interview with a student on different division methods.

**Creationism**

Vincent Pantaloni tweeted some awesome phasing GeoGebra tessellations.

Sasha (AO) Fradkin has a Kickstarter on for the book Funville Adventures, a math-inspired fantasy. (Her post to introduce it.)

Edmund Harris has some math-art shirts for sale. I ... can't decide.

Simon Gregg shared his students' responses to MANY Which-One-Doesn't-Belong situations.

Several of us enjoyed playing with the Girih Designer that Anugrah Andisetiawan shared. (Islamic/PatternBlock tessellations and patterns.)

by coronaking |

Paula Beardell Krieg completed an amazing book making and money math project with 2nd graders.

**Watch Out**

Kyle Pearce shared his presentation Beauty and Complexity of Elementary Mathematics.

Kristin Gray has a whole sequence of number routines at the Teaching Channel.

Somehow I had missed the amazing Infinite Series YouTube channel from PBS, with Kelsey Houston-Edwards illuminating mind-blowing topics.

3 Blue 1 Brown released a terrific introduction to calculus in 10 essential YouTube videos.

Benjamin Leis wrote a response to Peter Liljedahl's Global Math presentation, and then tried out VNPS with one of my favorite mathgames, Sprouts. (This was a new-to-me blog I've subscribed to now.)

**Advanced Topics**

Mike Lawler also also got exploring complex roots & juggling with 3-D printing, sparked by a John Carlos Baez post. Beautiful, etherial structures.

Sam Shah did an intriguing exploration of Graham's Number. He's also looking

I've invited the #MTBoS to follow along with my summer online calculus course. There are some cool teachers dropping knowledge on my students - awesome!

One of the posts I'll share with those students is Simon Gregg's circle and square optimization post, with bonus generalization & striking images.

A couple of the images for this post were made with a GeoGebra factoring applet. How would you picture 108?

I'm getting to do a little (too little) in David Coffey's Math Recovery/Design Thinking course this summer. Here's his intro to SAFARI design.

Dan Meyer bids adieu to Malcolm Swan. Dr. Swan moved the whole field forward and he'll be missed.