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!


An Activity for Pi Day

Pi Day (3/14) is fast approaching. Here’s a simple Geogebra activity you can do with your math students to help them get a sense of what pi is.

In Geogebra, construct a segment, then construct the midpoint. Construct a circle using the midpoint as center, and an endpoint of the segment as a point on the circle. In the Input pane, enter Circumference(<your circle>). When you divide the circumference measurement by the diameter length, you get pi! Geogebra is dynamic, so you can change the size of the circle, but the ratio will remain constant at pi.

Here’s an interactive version for you to play with at Geogebra’s site.

Here’s a screenshot:

All of my students have TI-84 graphing calculators, so I am going to have them use their Geogebra constructions to generate 10-12 different diameters and circumferences. Then we will enter the diameters in L1, the circumferences in L2, and plot the data. We will calculate the regression line, the slope of which should approximate pi.

Happy Pi Day!

Update: This went really well in my geometry class. Here’s the data we collected –


Here’s the regression line equation (check out the value of the slope):


And here is the plot of the data and the regression line:



Coding With Processing, Part 5

Now we’re getting somewhere! In Chapter 7 of Daniel Shiffman’s Learning Processing, I learned how to define a function, which makes coding repeated objects so much easier. For this exercise, I had to define a function (named drawFlower) that drew a flower. I defined variables for the placement of each flower and the color of its petals. Here’s the result:

Here’s the code:

void setup() {
size(600, 400);

void draw() {
//Sky-blue background
background(0, 191, 255);

//For the drawFlower function, enter the x-coordinate of the flower’s center,
//the y-coordinate, and the r, g, b values for the petals.
drawFlower(100, 85, color(255, 255, 0));
drawFlower(200, 100, color(255,69,0));
drawFlower(150, 200, color(218,112,214));
drawFlower(300, 225, color(230,230,250));
drawFlower(400, 80, color(250,250,210));
drawFlower(480, 150, color(255,99,71));
drawFlower(440, 230, color(138,43,226));

void drawFlower(int centerX, int centerY, color c) {

//Draw the stem
stroke(0, 255, 100);
line(centerX, centerY + 15, centerX, centerY + 115);

//Draw the leaves
fill(0, 255, 100);
ellipse(centerX-40, centerY+40, 80, 20);
ellipse(centerX+40, centerY+40, 80, 20);

//Draw the center of the flower
ellipse(centerX, centerY, 30, 30);

//Draw the petals
ellipse(centerX, centerY+40, 20, 40);
ellipse(centerX-40, centerY, 40, 20);
ellipse(centerX+40, centerY, 40, 20);
ellipse(centerX, centerY-40, 20, 40);