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 video students learn the basics of antiprisms, in the context of New York’s Freedom Tower, which has an antiprism design. They learn the properties of antiprisms, with the focus on those with a square base.  

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In this video students learn the basics of rectangular prisms, in the context of a New York residential tower: 432 Park Avenue. They learn the properties of rectangular prisms, with and without square bases, and the architectural requirements that influence the use of both types of rectangular prisms. 

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In this video students study a real-world application of triangular prisms: The Flat Iron Building in New York City. This building is an ideal example of a real-world prism and also provides a tie-in to right triangle geometry.  This video describes the geometry of the Flat Iron Building, as well as its architecture. It includes animations that demonstrate the key features of triangular prisms. 

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In this video students learn the basics of prisms and anti prisms. They learn the properties of triangular prisms, rectangular prisms, triangular antiprisms, and rectangular antiprisms.  

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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

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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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In this program we explore the properties of quadrilaterals. We do this in the context of two real-world applications. In the first, we explore the architecture of Frank Lloyd Wright as an application of squares and rectangles; in particular, we look at his Fallingwater house. In the second application we look at a unique parallelogram-shaped building in Spain, known as the Puerta de Europa. It provides an opportunity to explore the properties of parallelograms and trapezoids.

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Stonehenge is best known as a circular structure. But it’s the post and lintel construction used that is noteworthy, and this type of construction involves quadrilateral shapes. From the familiar door frames of houses to the majestic entryways of ancient temples, post and lintel construction provides a clear introduction to the nature of quadrilaterals. This segment also describes the key concepts developed throughout the program.

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Frank Lloyd Wright’s architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure.

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The Puerta de Europa towers in Madrid bring parallelograms front and center. These tilted towers, looking like modern-day towers of Pisa seem to defy gravity, but rely on the stability brought about by its quadrilateral structure. The underlying parallelogram and trapezoidal designs are explored and analyzed.

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The definition of the term "antiprism." Note: The download is a PNG file.

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The definition of the term "prism." Note: The download is a PNG file.

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The formula for the Surface Area of a Sphere.

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To see the complete collection of Formulas, click on this link: https://media4math.com/math-formulas