About once a year, I sign up to host this longrunning blog carnival. Ever since Google Reader was snatched away, blogs seem to have fewer readers and less activity. Mine certainly has straggled along in recent years. (I guess I needed a very long rest after finishing my big book.) Today, I'm looking forward to exploring the new ideas I'll find online and gather here.
We start with cool facts about 157, and a puzzle...
Cool Little Facts
 157 is the 37th prime number. (37 is prime too.)
 157 is the largest known prime p for which ${\frac {p^{p}+1}{p+1}}$ is also prime (see OEIS: A056826).
157 is a palindromic number in bases 7 (313_{7}) and 12 (111_{12}).  157 is the largest odd integer that cannot be expressed as the sum of four distinct nonzero squares with greatest common divisor 1.

157 is the smallest threedigit prime that produces five other primes by
changing only its first digit: 257, 457, 557, 757, and 857. [Opao]
 157 is the largest rating on the SaffirSimpson Hurricane Wind Scale occurs at sustained winds of 157 mph or higher.
 If we use the English alphabet code a = 1, b = 2, c = 3, … , z = 26, then número primo = 157.
Puzzle
How many 3digit numbers can we find where the last digit equals 2 times the first digit plus 1 times the second digit? 157 is one answer. How would you find the others without tediously checking each 3digit number? (I use a spreadsheet when I want enough data to see patterns, but I worked hard to get the digits apart. Once you find the first few answers by hand, you might see the pattern...)
[Solution at bottom.]
Not Just Blogs...
I'm working on another book, much smaller this time. Althea and the Mystery of the Imaginary Numbers should be ready sometime next year. Since I'm working on a book, I've been thinking a lot about what makes a fun mathy book. It needs a good storyline. It needs interesting math. And if it's for young kids, it needs lovely illustration.
There's a prize for good mathy books, called the Mathical Book Prize. It started in 2015 and doesn't seem to include small publishers like Natural Math (my publisher), so some of my favorites are missing. I think my favorite book on their list might be the picture book Which One Doesn't Belong, by math blogger Christopher Danielson.
Here are a few of my favorites that aren't on their list:
Quack and Count, by Keith Baker (for ages 2 to 7), a board book good for the youngest child who will sit and
listen to a story. And it stays good because it's so luscious. Great
illustrations, fun rhythm and rhyme, cute story, and good mathematics. 7
ducklings are enjoying themselves in every combination. “Slipping, sliding,
having fun, 7 ducklings, 6 plus 1.” (And then 5 plus 2, 4 plus 3, 3 plus 4, and
so on.) It would be great to have a book like this for each number, showing all
the number pairs that make it.
How Hungry Are You? by Donna Jo Napoli and Richard Tchen (for ages 3 to 12), on equal sharing. The picnic starts with just two friends, rabbit is bringing 12
sandwiches and frog is bringing the bug juice. Monkey wants to come, "My
mom just made cookies. I could take a dozen." They figure out how much of
each goody each friend will get. In the end, there are 13 of them, and the
sharing becomes more complicated. One of the delights of this book is the
little icons showing who’s talking. It would make a good impromptu play. [There are lots of good books on equal sharing. Another lovely one is The Doorbell Rang, by Pat Hutchins.]
The Cat in Numberland, by Ivar Ekeland (for ages 5 to adult), starts when Zero knocks on the door of the Hotel Infinity. He’d like
a room, but they’re all full (with the number One in Room One, and so on).
Turns out that’s no problem. The cat who lives in the lobby gets confused  if
the hotel is full, how can the numbers make room for zero just by all moving up
one room? Things get worse when the fractions come to visit. This story is
charming enough to entertain young children, and deep enough to intrigue
anyone. Are you ready to learn about infinity with your 5 yearold?
The Man Who Counted, by Malba Tahan
(for ages 6 to adult), was written in Brazil, and set in the Middle East. We
follow the adventures of Beremiz, an accomplished mathematical problemsolver.
He uses math to settle disputes, solve riddles and mysteries, and entertain his
hosts. The series of 34 adventures, each with a math puzzle, is reminiscent of
the Arabian Nights. If you read one chapter a night, your audience will be
begging for more – and isn’t that the way it should be?
Carry On, Mr. Bowditch, by Jean Lee Latham (for ages 7 to adult), is a
slightly fictionalized account of the life of Nathaniel Bowditch, who loved
math, but had to leave school when his family needed his help. He was
indentured to a ship chandlery for 9 years. Although that dashed his
hopes of someday going to Harvard to study math, it was the right place
to learn the mathematics behind navigation. When he finally went to
sea, he invented a new way to ‘do a lunar’, and spent endless hours
correcting errors in the tables used for navigation. Bowditch’s book,
the American Practical Navigator, first published in 1902, is still
regularly updated, and is carried on U.S. naval vessels to this day.
And coming very soon ... Denise Gaskins' 2nd edition of Word Problems from Literature. (She'll be using kickstarter to raise some funds to get this out the door. Crowdfunding is how tiny publishers make it work!)
...And Now the Blogs (mostly geometry)
Sam Shah on 3D Printing, in which Sam shares lots of cool 3D printing projects but decides they aren't really helping his students learn math. Do you have any 3D printing projects that help your students learn math?
I adore Catriona Schearer's geometry puzzles, which she posts on twitter and elsewhere. Here's a video of her talking about them. (I recommend starting at about 8:30. They wait for participants and talk about Mathigon first.) Here's a lovely puzzle of hers. The big triangle that holds all the others is also isosceles. Find it on her twitter feed, and you'll see lots and lots of thoughts about it.
Puzzle solution: There are 8 of these starting with 1: 113, 124, ..., 179, then 6 starting with 2, up to 2 starting with 4, for a total of 20.