Geometry

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.