Ah, so here we are, the 103rd Math Teacher’s At Play organized by Denise Gaskins (@letsplaymath). As per tradition, what’s so cool about 103?

Well, 103 is a prime number! That’s pretty cool. It’s cooler still in that it is a twin prime! Its twin is 101. So which would we consider to be older? 101 or 103? 101 comes first, but it’s a smaller number. I’m willing to go with 101 is the older twin and 103 is the younger twin.

If we write 103 in a handful of bases less than ten, then \(103_{b}\) is prime for bases \(b = 4, 8\). In base 4, \(103_{4} = 19\) and in base 8, we have \(103_{8} = 67\).

Now, twin primes are interesting in that they are part of an open question in mathematics. We have The Twin Prime Conjecture. Are there are an infinite number of primes so that if \(p\) is a prime then \(p + 2\) is also prime. Here, \(p\) and \(p+2\) would be called twin primes. Wolfram Alpha has a good write up on this from which you can merrily go down the rabbit hole.

And that was our first link! See how sneaky that was?

Now for some submissions and whimsy.

Riemann Puns

First we start with this punny blog from Give Me A Sine about undoing the chain rule by Caitlyn Gironda (@Caitlyn_Gironda). Of course, this blog post led to this wonderful punversation.

@caitlyn_gironda everything has a limit …

— Manan Shah (@shahlock) December 19, 2016

Self Reference

Staying on the linguistic side of things, we have this detailed write up from the Mathematical Enchantments blog about logic and self-referential sentences. The article was submitted by Joshua Greene (@JoshuaGreene19). The article does have a references section, though I have to admit that I was a little disappointed that one of the references wasn’t the article itself.

Points of View

If we can stop referring to ourselves, then perhaps this video article from Mike Lawler’s blog (submission also by Joshua Greene) would suit your fancy. The author argues that there is a lot of value in having kids see how other kids think about math problems. I tend to agree with this. It’s good to see how other people approach different problems, mathematical or otherwise. Mathematics is often viewed as a solitary discipline. I have found it to be quite the opposite. Mathematics is conducive to socialization!

Show Your Thinking

Nothing says socialization quite like a math game! And we have this math game from the Show Your Thinking blog. It’s a good way to sneak in the much-needed arithmetic practice that kids need. This was submitted by Megan Schmidt (@veganmathbeagle).

Triangles!

If you had a chance to check out the Mike Lawler’s blog from above, then you saw that there was a somewhat tricky problem to solve. In the same vein, we have an article about Pythagorean Triples that’s worth reading, submitted by the author, Benjamin Leis (@benjamin_leis).

Jealous Husbands

Puzzles tend to be tricky. But some puzzles tend to be tricky to deliver. Peter Rowlett (@peterrowlett) attempts to rephrase The Jealous Husbands problem into something more inline with modern sensibilities. He presents a host of crowd-sourced solutions.

Christmaths

Also from Peter, and inline with the holidays, we have this submission from The Aperiodical about a Mathematical Advent Calendar.

Denise Gaskins has put together a 24-page pdf booklet on Geometric Coloring Designs just in time for the snowflakes! The booklet is free!

Finally, also from Denise, we have Christmas With Alexandria Jones. In Denise’s own words:

A series of fictional math adventures for the holiday season, along with related crafts and activities.

No one has yet signed up to host Carnival #104. Maybe you want to? If so, check out the Math Teacher’s At Play page and speak with Denise!

Enjoy the holidays and Merry Christmas!