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!
All we need is some investment capital and a buyer willing to take $35 billion worth of Virgin Mobile airtime off our hands at face value.
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!
I’m not sure if this technically qualifies as a harmonograph, but the images produced by this cool apparatus definitely remind me of Lissajous curves.
The video of this device in action, from Robert Howsare, is definitely worth a look.
An interesting challenge would be to come up with the parametric equations of these curves based on the angular velocity of the two turntables, much like what can be done with actual harmonographs.
I’ve never see a restaurant go so far to ensure its customers understand the geometric and mathematical ramifications of their decisions.
Somewhere out there, the author of terribly contrived math textbook questions is saying “See! Places like this do exist!”.
