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ZingPath: Fundamental Axioms and Theorems

The Definition of Space

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Fundamental Axioms and Theorems

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Lesson Focus

The Definition of Space

Geometry

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You will discover and learn about the fundamental ideas you need to understand in order to make sound geometric conjectures and prove them.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Define three-dimensional Euclidean space.

Everything You'll Have Covered

What is three-dimensional Euclidean space?

~ The space that has infinite width, length, and height is called three-dimensional Euclidean space.

How does three-dimensional Euclidean space differ from two-dimensional Euclidean space (from planar geometry)?

~ In two-dimensional Euclidean space (i.e., in a plane) all objects may have length and width, but have no thickness. In three-dimensional Euclidean space, objects may have length, width, and thickness.

Can all physical objects be modeled by objects in three-dimensional Euclidean space? Why or why not?

~ Answers will vary. Certainly, any object with length, height, and width can be modeled by an object in three-dimensional Euclidean space. The physical objects we experience all have finite length, width, and height and thus can all be modeled by objects in three-dimensional Euclidean space.

Tutorial Details

Approximate Time 2 Minutes
Pre-requisite Concepts Students should be able to identify and define a 3-dimensional oblect, Euclidean's rule, and space.
Course Geometry
Type of Tutorial Animation
Key Vocabulary 3-dimensional, Euclidean, space