3D Geometry

Entering the 3rd dimension!

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.

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1. 1

Introduction

Explore various ways of thinking about shapes in 3D.

1. Cuts Through Shapes

Think about 3D shapes by cutting them into pieces.

2. Surfaces of Shapes

Fold and fold again to transform 2D shapes into 3D.

3. Pieces of 3D

Slice, extrude and transform 3D shapes into different configurations.

2. 2

Nets and Paths

Fold and unfold 3D shapes to see how they fit together.

1. Included with

Introduction to Nets

Fold up nets to make 2D shapes into 3D. Unfold them to see how the faces relate.

2. Included with

Nets of a Cube

What nets can successfully fold up to make a cube?

3. Included with

Exploring Cubes

Explore the faces of a cube and use nets to see how they relate.

4. Included with

Platonic Solids

Discover how many of these symmetrical solids can be constructed.

3. 3

Cuts and Cross Sections

Slice 3D shapes into pieces and see what happens.

1. Included with

Introduction to Cross Sections

Think like an MRI machine as you slice through these shapes.

2. Included with

Building Intuition

How do cross sections relate to the shape they come from?

3. Included with

Cross Sections of Cubes

Explore the variety of shapes that can be obtained just by slicing up a cube.

4. Included with

Predicting Solids

Can the cross sections of a solid reveal its full shape?

4. 4

Facet Counting

Find, understand, and prove Euler's formula about the pieces of polyhedra.

1. Included with

Vertices, Edges, and Faces

Is there a pattern here?

2. Included with

Uniform Vertex Configurations

Examine polyhedra that have the same polygons in the same order at every vertex.

3. Included with