It’s midterm week at school, and James Tanton threw out two interesting questions in two days. I spent a little time programming “solutions” to these problems (not solutions, just verifications for an infinitesimally small portion of the natural numbers).
Here’s my processing.org code for this problem. And here’s the output of the code, each time the sequence gets longer, it prints out the new “max” sequence length.
I didn’t use any of processing.org’s graphics but I had the prime function optimized, so it was quick work.
Here’s the python code for the “solution”. And here’s the last six lines of the output of the code. I checked all numbers under 1,000,000, and all the sequences were finite (they stopped at a multiple of 13). The starting number whose sequence ended in the largest multiple of 13 was 964,665, and the multiple of 13 had 384 digits (BIG NUMBER! There are only ~10^80 particles in the entire universe). Fun stuff.
[Edit: 1/28/2014 9:08am] Ok, ok. James asked for a proof for the second problem. Here you go
Saw this tweet yesterday:
Pretty cool. Josh Giesbrecht also did some great work with Mathematica to replicate the image.
I also replicated the image with processing.org. The (live) code can be found here.
(update 1-16-2014 11:38, image above is now lossless and will stand up to zooming.)
I happened upon this tweet when I got to work this morning:
So I watched the fantastic numberphile video Pebbling a Checkerboard. I wanted to get the kids to play the game and I didn’t have any checkers in the classroom, so I decided to program the game in Processing. Thankfully the programming went smoothly, and I finished it in time to have the Pre-Calculus class try to beat the game (it’s the day before winter break, and we just finished sequences and series). Fantastic timing.
- Goal: remove all checkers from the green prison.
- If you click on a checker, and there is space to the right and above, then that checker will disappear, and two clones will appear to the right and above.
- Theoretically this game board extends to infinity to the right and above.
The game is hosted by openprocessing.org or hosted by recursiveprocess.com. It should work in any web browser, including smartphones. If you’d like to increase the checkerboard size, just go to the openprocessing.org site and “tweak” the code. The size of the board is set on the first two lines.
From Wikipedia’s entry on Super Balls.
Wham-O Executive Vice-president Richard P. Kerr said, “Each Super Ball bounce is 92% as high as the last.
Will it ever stop bouncing?
Geometric sequences and series anybody?
Amazon review of a superball:
What’s the bounce return rate?
Fellow Empire State rep Kate Nowak requested answers to the following in her post: Tell Me Why You Blog.
1. What hooked you on reading the blogs? Was it a particular post or person? Was it an initiative by the nice MTBoS folks? A colleague in your building got you into it? Desperation?
I got hooked on reading math blogs because I was interested in becoming a better teacher and I wasn’t finding resources in other places to satisfy this desire. Math blogs put me in touch with teachers willing to try new things out and succeed, or more importantly, fail in public.
2. What keeps you coming back? What’s the biggest thing you get out of reading and/or commenting?
Confession: I don’t comment much on blogs. Maybe I use twitter as a sounding board for my opinions? Not sure why.
I keep coming back because I keep getting good stuff. The economics of this system are tough, if you people in the #mtbos stop producing good stuff, then I’m out. Thankfully, the stuff coming out has only been getting better and more interesting.
3. If you write, why do you write? What’s the biggest thing you get out of it?
Mostly I write for myself. I process things better after writing about them. This is from a guy who hates to write (or reflect). I record things on my blog first for myself; second for others. If other people find use in my blog, fantastic. But I’d still have some version of it if it were only my Mom reading it (hi Mom!).
It’s great that people find use for things I’ve posted. Just this morning I woke up to find 15+ responses on twitter talking about a post that I put up 3 years ago. Soooo cool. Just awesome. And that there’s that stupid Oreo thing. That must count for something.
4. If you chose to enter a room where I was going to talk about blogging for an hour (or however long you could stand it), what would you hope to be hearing from me? MTBoS cheerleading and/or tourism? How-to’s? Stories?
Dunno. Give me personal stories. I’m no help here.
From Tech Crunch. Must watch video.
Harvey Mudd is known as one of the most elite science, engineering and mathematics colleges in the world. But historically, its computer science department hasn’t exactly been known as a paragon of gender diversity — in 2006, only 10 percent of Harvey Mudd’s computer science majors were female.
But under Dr. Maria Klawe, the renowned computer scientist (and Microsoft board member) who joined Harvey Mudd as president in 2006, the gender ratio at Mudd’s CS department has changed dramatically. This year, fully 48 percent of the CS majors in Harvey Mudd’s junior class are female.
Yet another cool image from the Visualizing Math Blog.
I was wondering if I could recreate this graph in Desmos. Here’s what I was able to make.
It was difficult to find a way to keep the tangent line the same length, although I bet a parametric form of the line would work better than what I did.