I was frankly a bit surprised at how interesting 138 is. 138 is a sphenic number(the product of three distinct primes from the Greek for "wedge shaped"), but is special among the sphenics for being the smallest product of 3 primes, such that in base 10, the third prime is a concatenation of the other two: (2)(3)(23). What is the next such special sphenic? (Some of the pictures here were made with some Brent Yorgey inspired GeoGebra or David Mrugala inspired GeoGebra.

138 is the sum of four consecutive primes (29 + 31 + 37 + 41); which is the previous and the next? 138 the sum of 2 successive primes; which? And not only is 138 the average of twin primes, it is a number such that 6 times 138, is the center of twin primes, 827 and 829. Is there another number like that?

I had never heard of Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms in exactly one way. 138 is an Ulam number... what are the two terms which make it? Which is the first counting number not an Ulam number?

Obviously, this month's edition is in the time of social distancing. So it has produced some stand out creative home mathematics. Nikky Case made an interactive explanation how the epidemiological models work. Eva Thanheiser wrote a post about numeracy in the pandemic time. Here's an applet if you're trying to model a gathering... or a classroom?

Denise Gaskins, the initiator of this here carnival here, has a post for those new to it on how to homeschool math and Peter Rowlett at the Aperiodical wrote about playful math at home.

Whilst there you might check out the 2020 Lockdown Math-Off, with some really accessible entries this year. And you can submit until they run out of entries or they're allowed outside.

Lily Cole |

**Math Art**

Evelyn Lamb collected some of my favoritest math away from school resources. Cited there, Annie Perkins' #mathartchallenge (Twitter) is maybe my favorite thing ever. Here's the home (blog) for it. Brings together so many amazing projects from so many amazing artists and mathers. Like, Paula Krieg's origami firework on Day 53. Several have compulsed me to try to make things, like the Hitomezahi stitching from Day 14. Annie's going until she hits the magical 100!

Clarissa Grandi's #Maydala challenge has filled Twitter with lovely images.

Clarissa herself |

Janet Annetts |

Japleen Kaur |

Miss Bowkett |

Paula Krieg |

**More mathy math**

Henri Picciotto put together two amazing posts looking at wallpaper symmetries, and a catalog of pattern block Wallpaper symmetries; part I and part II. (Challenging, I think, because the blocks themselves are so symmetric.)

Luca Moroni pointed out Raffaella Mulas' self-illustrated article on Wild Mathematics. Quick mind bending read or just ponder the pictures.

Paula Krieg also pointed out this classic puzzle that Dr Olsen points out can be made from origami.

Karen Campe covers a wide variety of puzzles, from the jigsaw to the Catriona Shearer.

Simon Gregg started this thread about duck tiles, which continue to delight. He also published a sweet book on pattern blocks. If you just want the pdf, let them know and they'll donate the book to a local school.

Pat Bellew (of On This Day in Math) chases a white rabbit, running around My avorite Theorem and the arithmetic triangle. (I'm hoping that catches on over Pascal's someday.)

**Justin Time**

Not sure how to categorize this, ironically, but Justin Aion's post on alignment charts and teaching is amazing.

**Games**

Denise Gaskins, the initiator of this here carnival here, has a War meta-post with variations from preK through HS. I use several of these in a variety of classes.

Sam Shah collected many activities and games you can do over videochat with a class. Nia (@ihartnia) put together a Google doc of quarantine games: tinyurl.com/quarantinegamez

Dan Finkel updated his Horseshoe Math game with a theme song!

Ben Orlin shared 6 intriguing pen and paper strategy games.

Kent Haines' kids are chips off the ol' block, having invented Math Ball.

My retired colleague Char Beckmann developed many math games with our students and they've all been collected here. Materials, instructions, and video demonstrations.

This past semester I got to supervise three preservice elementary teacher/math majors in their senior projects to make math games. Char Beckmann's project! Our emphasis was to make instructional games that you could play with materials on hand or with minimal printing. Sam Bosma made a fun Guess Who variant for multiplication and division, Multiply Who. Maggie Eisenga developed Choose Your Path, a hit the target game with playing cards with some very cool discrete elements. Grace Gay increased the math content in Quixx, a dice game with some subtle strategy, to make Rolie Polie Operation Olie. All are upper elementary-middle school, and have how-to-play videos.

**In Memoriam**

Playful math lost two giants recently and I wanted to close with some remembrances.

John Conway was an all time great mathematician. Siobhan Roberts, his biographer, wrote two pieces for the New York Times, a memorial and a personal memoir. (Her book is excellent.) Sunil Singh said if you watch just one bit of Conway talking, watch this. James Propp is an unabashed groupie. Ivars Petersen shared a couple recollections. Pat Bellew remembered his impossible knot and Quanta covered its solution. Matt Baker remembered some of his lesser known results. I can't pick a favorite, but some of the most fun I've had with students is the rational tangle.

Don Steward was an amazingly creative and generous middle school maths teacher in England. Brilliant problem poser and visualizer and entirely low tech. Colleen Young wrote about some of her favorites. Jo Morgan wrote about her collaborations. Steven Cavadino shares an irrational triangle. Many people shared their favorite Don Steward task on Twitter. He did a sweet analysis of a Keith Richardson-Jones drawing that inspired some GeoGebra from me. Don's local paper wrote up a note on his importance to the community, and of course you should check the blog of the man himself, which he made arrangements to keep available and free.

On that somber note, we close the carnival. Be safe, be kind!

But on your way out... maybe check last month's Playful Math at Life Through a Mathematician’s Eyes or their recent post, 10 math movie recommendations, and look for next month's at Math Mama Writes, or check her post about Pythagorean Triples for an online math circle. The carnival's homepage is at the site of Denise Gaskins, the initiator of this here carnival here. Contact her for your chance to host!