The Tusi couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. With this relationship of diameters, each point on the circumference of the smaller circle actually follows a linear path as the rotation occurs. Here’s a link to a video so you can see it in motion.
Files to make your own:
SVG File:
CorelDraw 2021 File:
EPS
AI File
I learned something new by delving into the new textbook Professor Megan Raby selected for her UTeach Perspectives Class Spring Semester.
That week we would be focused on the Copernicanism and the Scientific Revolution, so anything with a math connection to astronomy would fit well. The new textbook I’m using, James Poskett’s Horizons: The Global Origins of Modern Science, integrates a lot about how Arabic astronomical observation influenced the Sci Rev.
I like to look at the pictures as well as read the text and the featured image in this chapter was similar to (not exactly) this one:
Poskett then shows and discusses Copernicus’ seminal work. This image is from another source, which makes the same conjecture – that Copernicus knew Tusi’s work and that it was important to his theory of motion of planets and stars.
There are many graphic animations, but what fun to make a real one. So we did and integrated that “gadget” into the lesson plan by giving each student a gear and and a “wheel” and an opportunity to explore what they can do.
Lecture Plan/Outline for January 30
10 min: First I will be sharing some sleuthing we did at MathHappens about mathematics related to systems of weights for balance scales. I have a balance scale with the two systems I can bring with me, base 2 and base 3. We traced the base 3 version back to Fibonacci’s Liber Aci. We’ll look at our Jumbo scale whole class and weigh some objects (cell phones as it turned out) with a base 2, English set of weights: 1 oz, 2 oz, 4oz, 8oz, 16oz. Next we’ll have a challenge to weigh something with a base 3 set of weights: 1 oz, 3 oz, 9 oz, 27 oz
5min: Next I’d like to give each student their “gadget” (big wheel, little gear and golf tee) see 1st photo. Students can explore and try to figure out what it is.
5-10 min: discuss what is this, hopefully they notice that it is the concept featured in Part I of the book. We can touch on question of invented vs discovered in math, and on attribution. Thanks to Quan Nguyen who came to share with the class her experiences finding ideas, creating CAD files and making models.
10 min: In groups and/or individual, explore ways to communicate the idea of the gadget and the concepts it relates to in Poskett’s book. Groups could have an option to select an audience (fellow student, someones grandmother, mathematician, child) for their demonstration.
15 min: Share presentations. I was thinking we could invite subsequent groups to (on the fly) incorporate something they saw in an earlier presentation that makes theirs better. So we’ll have the best at the last… maybe and hopefully no hard feelings if ideas are similar.
That’s about 50 minutes. If we run fast we can do Q&A.
