Saturday, April 18, 2015

First grade fractals

I visited my son’s first grade class the other day, and brought along a branch I found in our yard debris pile.  The kids didn’t take long to realize the big branch was made from smaller branches, which were made from still smaller branches.  After establishing that a self-similar shape like that is known as a fractal, we set about making our own using a template I made. (The template has two equilateral triangles with vertices and midpoints marked, just to get everyone started)
sierpinski fractal activity
For this “Sierpinski gasket” fractal activity, I wanted them to follow these steps:

1. connect the midpoints of a white triangle’s sides
2. color the triangle you created in step 1.
3. Go to step 1.
sierpinski fractal activity

At the end we taped their triangles together in progressively larger groups of three.  Judging by the results, not everyone grasped the iterative process, but they seemed to have fun with the idea, which is arguably more important.

Friday, March 13, 2015

Proof by Pancake

The most epic of Pi Days occurs tomorrow, 3.14.15…

While round pancakes are somewhat rare in our house, the kids and I decided to make an exception and do some flapjack math to celebrate the occasion.

Tuesday, February 24, 2015

Friday, February 13, 2015

Fractal-heart-spiral-knot

I like how these two spirals create a series of nested hearts.  My daughter helped me add a dog, a cat, and a princess to the image.  Here’s the template I made if you want to try doing your own.
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Monday, September 8, 2014

Pancake Spirograph

I’ve been working on making spirographic pancakes lately – Spirocakes.  Here’s the latest iteration of the “Pangraph,” a ring gear that fits over the frying pan and acts just like the old Spirograph toy:

It’s time-consuming to cut out the gears, so I didn’t want to just make random ones.  It was fun to work out which gears would make the most interesting patterns and be compatible with both the 35- and 36-tooth ring gears.

I even got to make use of the program I wrote 10 years ago to draw these patterns (technically called hypotrochoids and epitrochoids), to see what kinds of patterns I could expect to see with different gear sizes.

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Friday, August 8, 2014

Graphs in the sand

I noticed this “flying ring” toy making a nice sine wave as the wind rolled it along the beach this evening. 
sine wave in the sand

It reminded me of how the wind sometimes blows plants growing in sand, causing them to trace circles.

pict0046

Sunday, August 3, 2014

Free graphing calculator emulators

Smart phones are smaller and significantly more powerful that graphing calculators, so it makes sense to use them as such.  Unfortunately, not many good calculator apps exist (in my humble opinion), so I was excited to try out a graphing calculator emulator when I upgraded my Android phone recently.  Texas Instruments is trying to restrict emulator usage to those people who actually own a real graphing calculator by requiring the ROM files to be provided by the user rather than being included with the emulator app.  I figured this shouldn’t be a problem for me, having a drawer that looks like this.
Graphing calculator emulators

But transferring a calculator ROM to a phone isn’t fun and games.  I enthusiastically began following the steps I found online, but they ended up requiring an older (32-bit) operating system.  Luckily I had an old laptop on hand, and got a little further, but kept running into problems and never did get a ROM off a calculator.  I finally resorted to the most obvious solution and Googled it. 

I tried AndieGraph first, which happily pretended to be a TI-85 and TI-86 without problems.  You can even write your own programs, but there’s no way to import other programs.  True to the original, the function plotter takes its sweet time.
Graphing calculator emulators
Next I tried Graph89, which included this interesting note in the description:

Firmware updates (*.89u, 9xu, *.v2u, *.8Xu) which are normally used to restore the operating system of your calculator can also be used as a ROM image.

Sure enough, the operating systems freely available from TI (this TI-89 download, for example) can be used with this program.  You also get the capacity to import programs and apps, change the CPU speed and display color, among other settings.  The screen is a little nicer to look at than AndieGraph’s (and plotting functions is nice and fast), but it doesn’t support the 85 or 86.  I found that the arrow keys sometimes seem to register multiple presses, which is particularly annoying when writing programs.
Graphing calculator emulators