In just two weeks, students in our Advanced Euclidean Geometry course have covered almost everything mentioned in the course description.
These topics include the Simson line, Euler line, Ceva's Theorem, a beautiful proof of Heron's formula for the area of a triangle, and more. We are off to a fast start, and class morale is high. It is delightful to have enough of a solid geometric background to be able to present and understand results that are at once mysterious, compelling, and elegant.
We have engaged with course material in a wide variety of classroom formats. Yesterday students tackled a set of questions individually before being randomly paired up as part of a review activity; the day before that they worked in larger groups to document material presented earlier in the week.
We are using Overleaf, an online collaborative LaTeX environment, as our platform for mathematical writing. We also use GeoGebra as our dynamic geometry software, which enables students to conduct explorations and create accurate diagrams on their computers. This variety of styles provides texture to the learning experience and helps to keep our classroom lively.