I have an adjustable screen for my window, the kind you expand horizontally to fill up the windowsill. It’s somewhat effective at keeping bugs out of the house.
When it’s not opened all the way up, the two layers of screen overlap in the middle. Depending on the angle you are looking from, you can see some cool images.
At this angle, for example, I see a contour map of a function of several variables.
I wish I understood where the curves come from!
In honor of today’s date, 5/13/12, I honor one of my favorite triangles: the 5-12-13 triangle.
Of course, one reason this is a such a nice triangle is because it is a right. We can easily see that the side lengths satisfy the Pythagorean Theorem
Another reason I like this triangle so much is because it plays a part in another of my favorite triangles: the 13-14-15 triangle!
After having fun exploring rigid and non-rigid frames, I hung one of our indeterminate quadrilaterals up on the board. The next day, we were proving a theorem about orthodiagonal quadrilaterals, and the final step concluded that a particular quadrilateral was actually a rectangle.
I found a cute little spot to finish our proof.
This elicited a few laughs from students who appreciated the irony.
But apparently, some students in a later class did not appreciate it. They felt the need to chime in.
As a general rule I must oppose mathematical graffiti, but it’s hard not to respect their position.
This is a nice visual gallery of algebraic surfaces.
An algebraic surface is essentially a surface whose equation is a polynomial in three variables (typically x, y, and z).
Judging from Zeppelinand Zweiloch, our curator must be German. My favorites are the Dromedar and the Wigwam. Clicking on an image gives you a better look.
It’s interesting that Mobius, Wendel, and Croissant have no corresponding equation listed. Are these not algebraic surfaces?
While working on the geometry of the Platonic Solids, we spent some class time constructing them from chopsticks and marshmallows.
We had a lot of fun putting them together!
Unfortunately, the more complicated structures weren’t really strong enough to stand on their own. And after the fact, we realized that we probably shouldn’t leave marshmallows sitting around the classroom indefinitely.
But it certainly was lively way to wrap up a unit on geometric solids! You can see more pictures of the activity on my Facebook page.
