Ithaca High School Math Seminar Lesson 2-11

Date: 2023.12.06

Today we'll continue wrangling our operating systems to get us to install the Odin compiler, and possibly do some geometry calculations for a future lesson too.

If you were able to complete the previous lesson, try solving the pen-and-paper problem below. If during the previous lesson you discovered that Windows does not by default enable you to build programs (e.g. you got an error like "Windows SDK not found"), or even worse, you discovered that macOS does not even trust you enough to run programs that are not on their store, follow the installation instructions on the Odin website.

When you can finally compile and run Odin programs, finish off the previous lesson. For everyone else, we'll look into the platonic solids. The following exercises will be very useful when we begin to make 3D graphics in a later lesson.

Task: A tetrahedron lies on the xy plane in 3-dimensional Euclidean space like it would on a table. Its bottom triangle is centered at the origin, and one of its corners is located at the point (1,0,0). What are the coordinates of its other corners?

Task: Let's say we now have a dodecahedron sitting on the xy plane with bottom pentagon centered at the origin, and with one corner at (1,0,0). What are the coordinates of its other corners? Hint: perhaps a formula can be used to describe the points in sets of five...

Final task: Now consider the case of an icosahedron sitting on the xy plane with bottom triangle centered at the origin, and one of its corners is located at the point (1,0,0). What are the coordinates of its other corners?