The shadows fall like approximating rectangles under a sine curve. This brings to mind a basic approach in computing the area of curved regions: approximating the curved region with a series of flat regions, whose areas are easy to compute.
The angle of the sun makes the shadows more like approximating parallelograms, though. So we’d probably need a change-of-coordinates to complete our calculation!
I’m presenting on Desmos at today’s AMAPS meeting in New York City, and preparing my talk was an object lesson in how wonderful this technology is.
Part of my presentation demonstrates simple ways that Desmos can be a part of every high school math class: Algebra, Geometry, Trigonometry, Pre-Calculus, and Calculus. While Geogebra is generally more suitable for demonstrating and exploring geometry, Desmos certainly can be useful in that course, so I wanted to show something relevant and interesting as part of my talk. I thought, “Why not compute the circumcircle for an arbitrary triangle?”
While all the pieces of the mathematical puzzle were there for me, figuring out how to put them together in Desmos was a fun, frustrating, and worthwhile challenge. I had to play around with the basic concepts associated with perpendicular bisectors and think creatively about some mathematical problems and equations. I even ended up using the new regression feature in Desmos in a clever way!
I often get caught up in little challenges like this, and this is why Desmos is so wonderful: it provides us a mathematical makerspace. It invites us to play around, to create, to engineer, to build. And all of this happens through using the language and concepts of mathematics.
You can see my circumcircle demonstration here, and you can find more of my work in Desmos here.
I’ve always loved tree rings, in part because the word dendrochronology fascinated me a child. This lovely cross-section evokes so many mathematical ideas: concentricity, network theory, and polar representations, to name a few.
I can’t look at this lovely jellyfish without seeing a four-petal rose curve in the polar plane.
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!