I can’t look at this lovely jellyfish without seeing a four-petal rose curve in the polar plane.
Geometry Resources Teaching
MfA Workshop — Surfaces in Space
I’m looking forward to a a workshop I’ll be running tonight at the Math for America offices on three-dimensional coordinate geometry.
This workshop will cover the basic algebraic and geometric techniques for analyzing functions and relations in x, y, and z, as well as some simple methods for building interesting surfaces in space.
Sketching in space is a favorite topic of mine, and I’m really excited to share it with a group of MfA teachers. Three-dimensional coordinate geometry is an accessible, fun, and rich area that few math teachers have experience with. But given the advances in graphing technology and the applications to 3D printing, it’s something that more people can, and should, learn about!
Geometry Photography
Math Photo: Pyramid Projection
Naturally, the geometry of this simple piece of playground equipment caught my eye, but the shadows really sparked my interest.
The shadows are the projections of the edges of this pyramid, and they form a set of angles on the ground. Notice immediately that the largest angle (the shadow formed by the “back” face) is the sum of the other three angles.
There are many other interesting questions to ask, and relationships to explore. What I was most curious about, however, is how accurately we could locate the sun in the sky based only on this information.
Geometry Photography
Math Photo: Concentric Octagons
There’s something especially appealing, and uncommon, about these concentric octagons. I like the isosceles triangles radiating outward, and the pairs of perpendicular lines that meet at the center.
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Application Appreciation Geometry Photography
Math Photo: Pothole Pentagon
I’ve read that there are over 500,000 manhole covers in New York City, but I’d never noticed these pentagonal bolts before. A nice mathematical surprise among the grit and grime.