## Processing, Pong, and Kinetic Theory

I’ve been playing around with using Processing as a way to quickly get my Calculus students doing some programming. One of my experiments was in using what I’ve learned over the past couple months about object oriented programming to make the game have multiple balls in play at once.

Once I saw how well this worked, it turned rapidly into an attempt to max out my processor. The balls have random initial locations, and ‘speeds’ distributed uniformly between -2 and 2 pixels/frame.

The pong program keeps track of the bounces off of the left and right walls, and uses this as a basic way to calculate a score. When I saw this, it looked just like a kinetic theory simulation for ideal gases, though the particles are only bouncing off of the walls, not each other. That bounce variable keeps track of the collisions with the walls – can anything cool that can be calculated just from the picture alone and the number of collisions?

Processing sketch can be found here.

## Are there too many people on this thing? (#anyqs)

Two images I want to share for the purposes of #anyqs. For those unaware, this hashtag means I want you to look at these images and let me know what mathematical questions jump out at you right away.

Once you’ve taken a moment to think about these, please send me a tweet (@emwdx) with the hashtag #anyqs letting me know what you think this is all about. That would be great if you could take a moment.

What would be even cooler, however, is if you could also take pictures of your own of these signs in elevators (or other places you might find them) as well as a little information about where it is being taken. For example, the left picture is taken in the elevator in my apartment building while the right is from the gondola that the 9th graders and I took to get down from Mount Tai on the rainy second-to-last day of the China trip.

I am especially curious to see how these signs vary between buildings, countries, and even between elevator banks within a building. I’d like to share these with students tomorrow, so please snap a quick picture and send it (or a link) my way. It hopefully goes without saying that I will give proper credit for photos that make it into the materials I use with students, and will share what comes of it with you all.

So, for the sake of an interesting idea that I think will start some cool discussions with students – skip the stairs today. Snap a picture in the elevator, and then reward yourself for your generosity (and for decision to postpone exercise for unselfish reasons) by eating a doughnut or other craved food of your choice.

## Climbing Mount Tai – #wcydwt edition

I am spending an amazing few days with students on this year’s class trip to Shandong province in China. We spent a couple days wandering around Qufu, the home of Confucius, and the location of the temple and mansion constructed for his relatives. There were some cool opportunities to think about mathematical thinking in Chinese architecture (more on that later) but nothing ready for prime time.

Today’s trek led us to the foot of Mount Tai, China’s #1 mountain for it’s cultural significance (not due to it’s height.) we decided as a group to trek up the mountain from the Heaven’s Gate which reduced the climb somewhat, but will descend the full height of the mountain in the morning after watching the sunrise.

From Wikipedia (to be replaced by my own pics when I get home, I promise.)

The realization that I might be able to do something really cool with this came after regretting that I had decided to leave two of my favorite data collection devices (heart rate monitor and hiker’s GPS) at home being unsure during packing if they would really be worth bringing. I had done this hike in March and had several conflicting reports of the exact height we climbed up and down. The students were asking me how many steps there were, and I vaguely recalled something around 7,000, but I wasn’t sure. This question actually popped out from a few different students as we passed the first set of steps. It got me thinking. Is it possible to take either one of these numbers (height or number of steps) and try to calculate or estimate the other? If the students were asking it standing at the bottom looking up, there might be a possibility they would be interested in answering it on their own if posed the right way.

I grabbed my camera and grabbed the best standard length measure I had on me: my iPhone.

(It probably isn’t necessary to say this, but this is just an example I took in the hotel.)

I took a number of pictures like the one above on way up the steps, trying to come up with a fairly random sampling of the size of stairs compared to the phone along the entire height. Through some combination of Geogebra, pencil & paper calculations, and some group discussion, I can see some height calculations for the climb coming out of this.

On the way up, there was also a perfect “answer” to this challenge posted in the form of a placard fixed to the wall that says both the vertical height and the number of steps – again, I will include a picture of this when I can transfer photos from the camera I used to take the good photos. I could see cropping this photo in a way that hides the answer, though I’m sure there is a more dramatic Act 3 to this challenge out there.

I think there is some potential here for some fun, as well as for good student discussion and writing about how close the number actually gets to the right answer. This is the second time in a week that I’ve been able to find something good that could work for a class activity, and I wanted to get the details out while still buzzed about its prospects.