# 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 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. 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.

# A Balancing Act

In Geometry, we are learning about circumcenters, orthocenters, and centroids of triangles. Geogebra is a nice tool to use to explore how the medians, perpendicular bisectors, and altitudes are concurrent respectively, regardless of the shape of the triangle.

Here is a screenshot of the centroid, which is the intersection of the medians of a triangle: Here is the circumcenter (the intersection of the perpendicular bisectors), with a circumscribed circle: And here’s the orthocenter, which is the intersection of the triangle’s altitudes: A very nice property of the centroid is that it is the exact center of gravity of a triangle. Here’s a brief video of one balancing on a paper clip: