Several years ago, I came across some videos by the artist Dearing Wang that showed how to create mandalas and other geometric figures using only a compass and straightedge. One of them was a figure he called a “Geometric Eye“. Drawing one by hand took hours. Using the online Desmos math app, you can create one in minutes! Here’s my screencast explaining how:
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:
I wrote a review of Big Big Train’s soon-to-be-released album, Grand Tour, and it has been posted at the Spirit of Cecilia site. It’s a terrific set of songs by one of the most talented rock groups working today.
What Hath the Train Wrought, Part I
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