This animated sequence showsan antiprism from top to bottom.

This animated sequence shows an antiprism unfolding into two pyramids.

This animated sequence shows a cone from top to bottom.

This animated sequence shows a cube from top to bottom.

This animated sequence shows a cylinder from top to bottom.

This animated sequence shows an octahedron from top to bottom.

This animated sequence shows a pyramid from top to bottom.

This animated sequence shows a rectangular prism from top to bottom.

This animated sequence shows a tetrahedron from top to bottom.

This animated sequence shows a triangular prism from top to bottom.

In this program we explore the properties of three-dimensional figures. We do this in the context of two real-world applications. In the first, we look at the three-dimensional structure of Mayan pyramids. These stair-step structures provide a unique opportunity to also explore sequences and series. In the second application we look at the Shanghai Tower as an example of cylindrically shaped structures.

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We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures. This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-3d-geometry-segment-1-introduction

A Video Transcript is available for this tutorial at this Link

Note: The download is Media4Math's guide to closed captioned videos.

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Rectangular Prisms. Mayan pyramids are essentially stacks of rectangular prisms. The volume of each successive level is a percentage decrease of its lower neighbor. This introduces the notion of a geometric sequence and series, including an infinite series.

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The Shanghai Tower in China is a stack of cylindrical shapes, where each successive layer is a percentage decrease of its lower neighbor. As with the previous section, this introduces the notion of a geometric sequence and series.

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The definition of the term "Rectangular Prism."

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The formula for the Surface Area of a Sphere.

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The formula for the Surface Area of a Square Pyramid.

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The formula for the Surface Area of a Triangular Prism.

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The formula for the Surface Area of a Triangular Pyramid.

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The formula for the Volume of a Cube.

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The formula for the Volume of a Cylinder.

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The formula for the Volume of a Rectangular Prism.

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The formula for the Volume of a Square Pyramid.

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The formula for the Volume of a Triangular Prism.

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The formula for the Volume of a Triangular Pyramid.

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