# 10minutemath

One math teacher's musings.

## 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.

## 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.

## 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.

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

## Sunday, August 3, 2014

### Free 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.

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.

## Tuesday, June 17, 2014

### Newton’s rap battle limerick

Epic Rap Battles of History released a new classic yesterday, in which Newton battles Bill Nye. The only way to improve on this would be if Weird Al played Newton – oh yeah, he did. “To rebut,” Newton provides an equation he supposedly wrote, which is actually a silly calculus limerick:**The integral sec y dy **

**From zero to one-sixth of pi**

**Is log to base e**

**Of the square root of three**

**To the 64th power of …**

Luckily Neil deGrasse Tyson appears to finish the calculus limerick: “* i*"

## Sunday, May 18, 2014

### Cutting angles accurately

Building a playhouse for my kids, I had occasion to cut a forty degree angle in a piece of wibbly wobbly plastic. You know, the corrugated kind you put on greenhouses. I could have gotten out a protractor, marked 40Âº and extended it with a straightedge, but I suspect it could be off by a degree or two by the time the line extended to where I needed it to go. Instead, I measured one side of the triangle I would be removing from the sheet, did a little triggety-trig and came up with another side, which I could mark to the nearest 1/8-inch, which represents an accuracy of less than half a degree. Because playhouses need to be precise.