Course 2 · Module 1
Geometry
This module covers the branch of mathematics that studies shape, size, and position. You'll see how Greek geometers turned rules of thumb for measuring land into a system that proves everything from a handful of starting assumptions, and how questioning one of those assumptions produced geometries in which triangles' angles don't add up to 180 degrees. These geometries aren't curiosities: the GPS on your phone depends on them.
Module objectives
- Explain how geometry proves results from a small set of axioms, using the Pythagorean theorem as the example.
- Describe how non-Euclidean geometries differ from Euclid's and where geometry is used today, and state one open problem.
Lessons
- Lesson 1 Geometry: Euclid's axioms, proof, and the parallel postulate You'll see how geometry grew from practical measuring into a system where every result is proved from a few starting assumptions. You'll work through a proof of the Pythagorean… 61111h 3m
- Lesson 2 Geometry: Curved space, GPS, and the packing of spheres You'll see geometries in which triangles' angles add up to more or less than 180 degrees, and why your phone's GPS has to account for the curvature of space and time. You'll also… 611111h 33m