
3D Geometry
Entering the 3rd dimension!
Cuts Through Shapes
Surfaces of Shapes
Pieces of 3D
Introduction to Nets
Nets of a Cube
Exploring Cubes
Platonic Solids
Lines Through Cubes
3D Shortest Distance
Strings and Ants
Introduction to Cross Sections
Building Intuition
Cross Sections of Cubes
Predicting Solids
Halves of Solids
Other Fractions of Cubes
Vertices, Edges, and Faces
Uniform Vertex Configurations
Cutting Solids
Euler's Formula
Proving Euler's Formula
Duality
Course description
Explore the fundamental concepts of three-dimensional geometry: What strangely-shaped 3D pieces can result from slicing up 3D polyhedra with planes? What flat polygons can fold up into 3D shapes? If you're running around on the surface of a cube-world, what's the shortest path between two opposite corners? (The answer to this last one might surprise you.) In this course, you'll stretch problem-solving techniques from flat figures into a third-dimension and explore some mathematical ideas and techniques completely unique to 3D geometry. For example, you'll investigate and learn how to apply Euler's facet counting formula, a formula which describes a surprising algebraic relationship that relates the number of corners, edges, and faces that any polyhedron can have. To succeed at this course, you should already have some familiarity with the basics of 2D geometry. Additionally, some algebra is used in this course, but nothing beyond the level of Algebra I.
Topics covered
- Cross Sections
- Dissecting Shapes
- Distance in 3D
- Dual Polyhedra
- Euler's Formula
- Folding
- Nets
- Paths on a Surface
- Platonic Solids
- Polyhedra