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Searching for ## Fundamental Axioms and Theorems

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Explore the full path to learning Fundamental Axioms and Theorems

Geometry

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

- Define three-dimensional Euclidean space.

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.

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 |