# Nautilus, The Riddler, and Brain Pickings

Welcome to this week’s Math Munch!

Sometimes math pops up in places when you aren’t even looking for it. This week I’d like to share three websites that I enjoy. What they have in common is that they all cover a wide range of subjects—astronomy, politics, pop culture—but also host some great math if you know where to look for it.

First up is a site called Nautilus. In their own words, “We are here to tell you about science and its endless connections to our lives.” Each month they publish articles around a theme. This month’s theme is “Heroes.” Included in Nautilus’s mission is discussing mathematics, and you can find their math articles on this page. Here are a few articles to get you started. Read about how Penrose tiles have made the leap from nonrepeating abstraction to the real world—including to kitchen items. Learn about one of math’s beautiful monsters and how it shook the foundations of calculus. Or you might be interested in learning about how a mathematician is using computers to change the way we write proofs.

Next, you might think that, since the presidential election is now over, you won’t be heading to Nate Silver’s FiveThirtyEight quite as often. But do you know about the site’s column called The Riddler? Each week Oliver Roeder shares two puzzles, the newer Riddler Express and the Riddler Classic. Readers can send in their solutions, and some get featured on the website—that could be you! Here are a couple of puzzles to get you started, and you can also check out the full archive. The Puzzle of the Lonesome King asks about the chances that someone will win a prince-or-princess-for-a-day competition. Can You Win This Hot New Game Show? asks you to come up with a winning strategy for a round of Highest Number Wins. And Solve The Puzzle, Stop The Alien Invasion is just what is says on the tin.

The third site I’d like to point you to is Brain Pickings. It’s a wide-ranging buffet of short articles on all kinds of topics, written and curated by Maria Popova. If you search Brain Pickings for math, all kinds of great stuff will pop up. You can read about John ConwayPaul Erdős, Margaret WertheimBlaise Pascal, and more. You’ll find book recommendations, videos, history, and artwork galore. I particularly want to highlight Maria’s article about the trailblazing African American women who helped to put a man on the moon. Their story is told in the book Hidden Figures by Margot Lee Shetterly, and the feature film by the same name is coming soon to a theater near you!

I hope you find lots to dig into on these sites. Bon appetit!

# Coasts, Clueless Puzzles, and Beach Math Art

Ah, summertime. If it’s as hot where you are as it is here in New York, I bet this beach looks great to you, too. A huge expanse of beach all to myself sounds wonderful… And that makes me wonder – how much coastline is there in the whole world?

Interestingly, the length of the world’s coastline is very much up for debate. Just check out this Wikipedia page on coastlines, and you’ll notice that while the CIA calculates the total coastline of the world to be 356,000 kilometers, the World Resources Institute measures it to be 1,634,701! What???

Measuring the length of a coastline isn’t as simple as it might seem, because of something called the Coastline Paradox. This paradox states that as the ruler you use to measure a coastline gets shorter, the length of the coastline gets longer – so that if you used very, very tiny ruler, a coastline could be infinitely long! This excellent video by Veritasium explains the problem very well:

As Vertitasium says, many coastlines are fractals, like the Koch snowflake shown at left – never-ending, infinitely complex patterns that are created by repeating a simple process over and over again. In this case, that simple process is the waves crashing against the shore and wearing away the sand and rock. If coastlines can be infinitely long when you measure them with the tiniest of rulers, how to geographers measure coastline? By choosing a unit of measurement, making some approximations, and deciding what is worth ignoring! And, sometimes, agreeing to disagree.

Need something to read at the beach, and maybe something puzzle-y to ponder? Check out this interesting article by four mathematicians and computer scientists, including James Henle, a professor in Massachusetts. They’ve invented a Sudoku-like puzzle they call a “Clueless Puzzle,” because, unlike Sudoku, their puzzle never gives any number clues.

How does this work? These puzzles use shapes instead of numbers to provide clues. Here’s an example from the paper: Place the numbers 1 through 6 in the cells of the figure at right so that no digit appears more than once in a row or column AND so that the numbers in each region add to the same sum. The paper not only walks you through the solution to this problem, but also talks about how the mathematicians came up with the idea for the puzzles and studied them mathematically. It’s very interesting – I recommend you read it!

Finally, if you’re not much of a beach reader, maybe you’d like to make some geometrically-inspired beach art! Check out this land art by artist Andy Goldsworthy:

Or make one of these!

Happy summer, and bon appetit!