Welcome to this week’s Math Munch! For the final Thursday of May, we’ll be looking back at some of this month’s posts from our Facebook page. We’ll see some wordless videos by The Global Math Project, look at a prime number quiz game, and meet Fan Chung Graham, one of the world’s leading mathematicians.

I don’t know much about The Global Math Project, but I know James Tanton is involved, and that is always a good thing. (Remember his Exploding Dots?) Well, they’ve posted a couple of wonderful videos featuring Tanton’s “math without words.” Need I say more? See for yourself.

If you like those, here are some more math without words from Tanton’s website.

Up next is a neat little thing by Christian Lawson-Perfect from The Aperiodical. Christian bought isthisprime.com and set up a little quiz game. Click over and see for yourself how it goes… I’ll wait… click below…

It’s good practice for divisibility tests and getting your prime recognition up, but I suppose it’s not all that mathematical, is it? But Christian did something interesting. He recorded data from all the games played, and he wrote a summary of the results. I love all the charts and graphs in there. The one below shows how likely a number is to be missed by players.

Finally, I hadn’t heard of Fan Chung-Graham until I found an interview of her posted on Facebook. She is one of the world’s leading mathematicians in several fields, and though she recently retired, she still conducts some research. The interview is a little academic, but it’s still nice to get to know such a talented mathematician.

Well that wraps up the week and month. I hope you’ve found some tasty math.  Have a great week and bon appetite!

Welcome to this week’s Math Munch!

Last summer where I live, in California, there were a lot of forest fires. We’re having a big drought, and that made fires started for lots accidental of reasons– lightning, downed power lines, things like that– get much bigger than usual. I thought I’d learn a little about forest fires so that I can be a more responsible resident of my state.

And I found this great website with an awesome computer simulation that you can manipulate to experiment with the factors that lead to forest fires!

My forest fire, just starting to burn. Click on this picture to play with the simulation! (Note: It doesn’t work as well in certain browsers. I recommend Firefox.)

This site was built by Nicky Case, who studies things that mathematicians and scientists call complex systems. Basically, a complex system is some phenomenon that has a simple set of causes but unpredictable results. An environment with forest fires is a good example– a simple lightning strike in a drought-ridden forest can cause a wildfire to spread in patterns that firefighters struggle to predict. It turns out that simulations are perfect for modeling complex systems. With just a few simple program rules we can create a huge number of situations to study. Even better, we can change the rules to see what will happen if, say, the weather changes or people are more careful about where and when they set fires.

What do you think? Click the picture to see Nicky’s simulation.

You can use Nicky’s program to change the probability that trees grow, a burning tree sets its neighbors on fire, and many other factors. You can even invent your own and model them with emojis. What if there were two kinds of trees and one was more flammable than the other? What if trees grew quickly but lightning was common? As Nicky shows, simulations are useful for exploring what-if questions in complex systems. Use your imagination and explore!

Next up, have you ever heard of a scrubbing calculator? No, it’s not a calculator that doubles as a sponge. It’s a calculator that helps you solve for unknowns in equations by “scrubbing,” or approximating, the answer until you find a number that works.

Here’s how it works: Say you’re trying to solve for an unknown, like the x in the equation above (maybe for some practical reason or just because you’re doing your homework). You could do some pretty complicated algebraic manipulations so that the x alone equals some number. But what if you could make a guess and change it until the equation worked?

Click on this image to see a scrubbing calculator in action!

If your guess was too big, you’d know because the expression wouldn’t equal 768 anymore– it would equal something larger. And if you had a calculator that instantly told you the solution based on your guess, you could do this guessing and checking pretty quickly.

Well, lucky for you I found a scrubbing calculator that you can use online! It’s very simple– just type in your equation and your guess, and click on the number you want to change (most likely the guess) to make it larger or smaller. It’s useful for solving equations, like I said. But I actually find it most interesting to watch how the whole expression changes as you change one of the numbers in it. For instance, check out the Pythagorean triple calculator I built. What do you notice as you gradually change one of the numbers in the expression?

https://www.cruncher.io/?/embed/xiY1IjwUJS

Finally, I’m excited to share with you one of my favorite kinds of puzzles– Bongard problems!
A Bongard problem has two sets of pictures, with six pictures in each set. All of the pictures on the left have something in common that the pictures on the right do not. The challenge is to figure out what distinguishes the two groups of pictures.

This problem was made by Douglas Hofstadter, who introduced Bongard problems to the U.S. I haven’t figured it out yet. Can you?

I got the Bongard problems shown above from a collection of problems put together by cognitive scientist Harry Foundalis. He has almost 300 of them, some made by Mikhail Bongard himself, who developed these problems while studying how to train computers to recognize patterns.

Harry also has guidelines for how to develop your own Bongard problems. He encourages people to send their problems to him and says he might even put them up on his site!

Bon appetit!