Analytic Geom.·Course
Analytic Geometry
Analytic geometry: coordinate systems, lines and planes, second-order curves, vector algebra
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Compute with vectors fluently.
- 02Describe lines and planes in space.
- 03Classify conics and quadric surfaces.
- 04Move between algebra and geometry.
- 05Solve geometric problems with coordinates.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~2 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Analytic Geometry [Online course]. Stoa. https://stoa.school/course/analytic-geometry
- MLA
Stoa. “Analytic Geometry.” Stoa, 2026, https://stoa.school/course/analytic-geometry.
- Chicago
Stoa. “Analytic Geometry.” Stoa. Accessed September 1, 2026. https://stoa.school/course/analytic-geometry.
§ 02 — Curriculum
5 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IVector AlgebraScalar, vector, and mixed products of vectors3 articles
18 minBegin → - M IILines and PlanesEquations of lines and planes, distances and angles3 articles
18 minBegin → - M IIIConic SectionsEllipse, hyperbola, parabola, reduction to canonical form3 articles
18 minBegin → - M IVQuadric SurfacesEllipsoids, hyperboloids, paraboloids in three-dimensional space3 articles
18 minBegin → - M VAffine and Projective TransformationsTransformations of the plane and space, invariants3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Perform operations on vectors and compute scalar and vector products.
Define and analyze lines and planes in three-dimensional space.
Classify and analyze conic sections
Study quadric surfaces and their applications
§ 04 — Practices