(Mathhombre) Miscellanea

Folding an ellipse.

Inspired by mathani’s nice gif this morning, I had to try in GeoGebra. Pretty happy with the result, and the marking button was a good thing to figure out, I think. It’s on GeoGebraTube for you to play with.

Infinite Gold.
The Futility Closet shares a classic Martin Gardner puzzle. I think this is a little more subtle than the more common triangle paradox. What do you think?
Here’s the sketch at GeoGebraTube. And another gif if you’re greedy or trying to figure it out.

Infinite Gold.

The Futility Closet shares a classic Martin Gardner puzzle.

I think this is a little more subtle than the more common triangle paradox. What do you think?

Here’s the sketch at GeoGebraTube. And another gif if you’re greedy or trying to figure it out.

Square Roots

Playing around with square roots this morning, inspired by a nice illustration I reblogged this morning. The reason why the construction works can be seen as that odd similarity property of right triangles that two similar can compose a third. That took me off for a while into the border spiraland and rep-tiling, but I’m back.

Sketch 1 and sketch 2 on the ‘Tube.

More with the MoKai Ninja Star.

Napoleon’s Theorem is a great traditional triangle geometry result which is in itself a great exploration of similarity. But it also generalizes beautifully.

On GeoGebraTube. See also: Cut-the-Knot’s deep exploration.

Level Curves of a Parametric

I have no idea where the idea for this came from. I think I was just thinking about designs with level curves… maybe from watching the Vi Hart on spirals recently.

In this sketch, the blue curve is parameterized by two functions of t. The red curves are spreading out at distance 1 from each previous. n = 4 makes four curves out on both sides.

Some values to try:
x(t) = t, y(t) = cubic.
x(t) = t, y(t) = 2*cos(t)
x(t) = sin(2t), y(t) = cos(t)
x(t) = sin(t), y(t) = 1.5^t

What crazy curves can you make? Are any of the designs pretty?

On GeoGebraTube
Note: the sketch can be slow - GeoGebra is doing a lot of computation!
Note 2: You might have to download this - I haven’t gotten it to work as a Student Worksheet.

Made a quick intro to motions. It’s on GGBTube. Somehow reminds me simultaneously of Jennifer Silverman and Monty Python.

Made a quick intro to motions. It’s on GGBTube. Somehow reminds me simultaneously of Jennifer Silverman and Monty Python.

GeoGebra Dotplots

Craig Winske got playing around with GeoGebra’s dotplot (his sketch), and Jon Hasenbank got ideas for more features, so…

It’s on GeoGebraTube.

Ideas for more features? Should you be able to set the center of the normal distribution?

Edit: Updated version that calculates MAD and lets you pick the mean and standard deviation.

This is an old one, but brought up again by Patrick Vennebush in a mathprank post. Wanted to dynamicize it by making the table customizable, and animating the check comparison. If you know which table is larger, see the gif below. Sketch is at GeoGebraTube.

This is an old one, but brought up again by Patrick Vennebush in a mathprank post. Wanted to dynamicize it by making the table customizable, and animating the check comparison. If you know which table is larger, see the gif below. Sketch is at GeoGebraTube.

Archimedes’ Twin Circles

From a Futility Closet post. GeoGebraTube here, think aloud about making it on the main blog.