Creating Rotated Solids Using GeoGebra 3D

One of the hardest Calculus topics for my students to visualize is rotating areas around an axis to create a solid. Fortunately, you can now create a great 3D representation of rotated solids using GeoGebra’s 3D app. Once you get the hang of it, it is quick and a heck of a lot easier than trying to draw them by hand!

Before I go any further, I want to give credit to Steve Phelps for posting a demo of this technique on his Twitter feed. If you are a math teacher, you really should follow him @MathTechCoach. I have learned more cool tech tricks from him than anyone else online.

Here’s my screencast illustrating how to create your very own rotated solids:

Stained Glass Mathematics, 2019 Edition

As I promised in the previous post, these are the final projects of my Mathematician As Artist students. They each researched a mathematical topic and created a design to illustrate it with stained glass. The results are pretty good, I think!

The bisector of an angle is equidistant from the sides of the angle.

The medians of a triangle intersect at a point called the centroid.

The perpendicular bisectors of a triangle intersect at a point called the circumcenter. It is the center of the circle that circumscribes the triangle.

You can construct an equilateral triangle by using two congruent circles that share a common radius.

The Four-Color Theorem states that in a map, no more than four colors are required so that no two adjacent regions have the same color.

The altitudes of a triangle meet at a point called the orthocenter.

The exterior angles of any polygon add up to 360 degrees.

If you stack right triangles so that the hypotenuse of the previous one is a leg of the next one, you create a Pythagorean Spiral.

The Two-Color case of Ramsey’s Theorem

The Mathematician As Artist, 2019 Edition

It’s Winterim again at Harpeth Hall School. This three-week interval between semesters is an opportunity for teachers and students to enjoy an alternative curriculum and pursue topics that are not often taught in a traditional course.

This year I am once again teaching my Mathematician As Artist course. We began by creating art using only a straight-edge and compass. These designs were based on a process pioneered by Dearing Wang:

Next, we constructed Voronoi Diagrams by hand. Here’s an excellent tutorial on the process. In a Voronoi Diagram, each color represents all the points that are closest to the node (the black point) within that color.

Our latest project involved using Chaoscope to create fractals. It’s an easy program for a beginner, but there are endless options for more advanced users. Here are the students’ pieces:

I will do a separate post for my students’ final projects – stained-glass windows!