The purpose of this project is to create a library to store geometric objects algebraically. Geometric properties can then be easily discovered and verified algebraically by program. The coordinate system used is barycentric coordinates with respect to a triangle. In particular, such a system allows us to work with points at infinity so the entire real projective plane can be modeled.
Contributing may require a solid background in Euclidean and projective geometry (particularly Olympiad geometry), algebra, and familiarity with barycentric coordinates. Here are some resources to learn more about those:
- Evan Chen and Max Schindler's article on barycentric coordinates on Olympiad Geometry provides an overview of the technique to solve Olympiad geometry problems and the framework for this project.
- Evan Chen and Max Schindler also have written an abridged version with relevant formulas and properties for looking up.
- Circles in barycentric coordinates by Vladimir Volenec gives equations and properties of circles in barycentric coordinates.
Currently, most features of points, lines, and circles have been implemented, with homogenous integer polynomials representing the coordinates of these objects. In the most recent update, a rudimentary diagram drawing tool has been implemented with a diagram of a triangle and its nine-point-circle and Euler line contained in GeoScreen.java. Eventually, we want to build the functionalities of an app like Geogebra into it.