Title | Description | Thumbnail Image | Curriculum Topics |
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## Circular Structures |
In this lesson students will use their basic understanding of circles to learn how circular structures are built. The example shown is that of the Roman Colosseum. Students will construct an oval shape from circular arcs to simulate the elliptical shape of the Roman Colosseum. For this lesson make sure that students have ready access to a compass, ruler, grid paper (graph paper with x-y axes marked is preferred), and pencil with an eraser. The first construction has students creating a teardrop shape from circular arcs that have overlapping points of tangency. This first construction sets up the more elaborate second construction. Students then look at a real-world application of using circular arcs to approximate the elliptical shape of the Roman Colosseum in a highly engaging video. Students analyze the architecture of the Roman Colosseum and are then shown how to build a scale model of the interior of the Colosseum. This lesson can be assigned to individual students or teams of students. The lesson can be completed in about 20 to 25 minutes. |
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## Regular Polygons |
In this module, students explore the properties of regular polygons and use their skills to construct tile patterns. Students learn about Arabesque tile patterns found throughout the Middle East. These tile patterns are based on Euclidean geometric principles. Students learn about the characteristics of polygons, including regular polygons. There are two geometric constructions, one for constructing a square and one for constructing a regular hexagon. Students need to use a compass and ruler for these activities. Students also learn the formula for calculating the sum of the interior angles of a polygon. This provides an opportunity for algebraic work in the context of geometry. This lesson addresses the high school Common Core Standards but it can also be used in an informal geometry class in middle school. |
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## Closed Captioned Video: Geometry Applications: 3D Geometry |
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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. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this Link |
3-Dimensional Figures | |

## Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 1: Introduction. |
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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 Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this Link |
3-Dimensional Figures | |

## Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 2: Pyramids |
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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. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
3-Dimensional Figures, Pyramids | |

## Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 3: Cylinders |
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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. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
3-Dimensional Figures, Cylinders | |

## Closed Captioned Video: Geometry Applications: Angles and Planes |
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In this program we explore the properties of angles and planes. We do this in the context of two real-world applications. In the first, we explore Japan's Himeji Castle and in the process learn about different types of angles and how they're used in a defensive fortification. In the second applicaiton we explore sedimentary rock layers as examples of parallel planes. We explore the Burgess Shale fossils. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Angles and Planes | |

## Closed Captioned Video: Geometry Applications: Angles and Planes, Segment 1: Introduction |
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The observatory in Arecibo, Puerto Rico provides astronomers insights into the structure of our solar system. Geometrically, the solar system relies on the plane known as the ecliptic. In studying the Earth’s orbit it is important to know that the Earth’s axis of rotation is at an angle relative to the ecliptic. This segment introduces the key themes of the program. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Angles and Planes | |

## Closed Captioned Video: Geometry Applications: Angles and Planes, Segment 2: Angles |
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Himeji castle in Japan is a marvel of architecture and a startling example of geometry and military science. The castle was used to protect samurai armies from invading forces, and the use of acute, obtuse, and right angles as part of the defense structure provide many opportunities for exploring the nature of geometric angles. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Angles and Planes | |

## Closed Captioned Video: Geometry Applications: Angles and Planes, Segment 3: Planes |
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In the Canadian Rockies, the Burgess Shale fossils provide a window to prehistoric Earth. Fossil layers are folded into sedimentary rocks. And sedimentary rocks are examples of parallel planes. This segment uses the properties of planes to analyze fossils. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Angles and Planes | |

## Closed Captioned Video: Geometry Applications: Area and Volume |
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In this program we look at applications of area and volume. We do this in the context of three real-world applications. In the first, we look at the sinking of the Titanic in the context of volume and density. In the second application we look at the glass pyramid at the Louvre Museum and calculate its surface area. In the third application we look at the Citibank Tower in New York City to study the ratio of surface area to volume to learn about heat loss in tall buildings. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Surface Area and Volume, Surface Area, Volume | |

## Closed Captioned Video: Geometry Applications: Area and Volume, Segment 1: Volume and Density. |
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The sinking of the Titanic provides an opportunity to explore volume, density, and buoyancy. Students construct a mathematical model of the Titanic to determine why it sank and what could have been done to prevent it from sinking. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Surface Area and Volume, Surface Area, Volume | |

## Closed Captioned Video: Geometry Applications: Area and Volume, Segment 2: Surface Area. |
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The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Surface Area and Volume, Surface Area, Volume | |

## Closed Captioned Video: Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume. |
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The Citibank Tower in New York City presents some unique design challenges. In addition it has to cope with a problem that all tall structure have to deal with: heat loss. By managing the ratio of surface area to volume, a skyscraper can effective manage heat loss. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Surface Area and Volume, Surface Area, Volume | |

## Closed Captioned Video: Geometry Applications: Circles |
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In this program we explore the properties of circles. We do this in the context of two real-world applications. In the first, we look at the design of the Roman Coliseum and explore how circular shapes could have been used to design this elliptical structure. In the second application we look at the Roman Pantheon, specifically its spherical dome, to see how the properties of chords and secants help clarify its unique design. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Circles, Definition of a Circle | |

## Closed Captioned Video: Geometry Applications: Circles, Segment 1: The Basics of Circles. |
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We visit Chaco Canyon in New Mexico to explore the circular kivas and in the process discover how circular buildings have been used to study the heavens. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Circles, Definition of a Circle | |

## Closed Captioned Video: Geometry Applications: Circles, Segment 2: Circles and Arcs. |
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The Roman Coliseum is a large elliptical structure. Yet, the Romans likely used circular arcs to build it. This segment explores the properties of circles and shows how arcs can be used to create elliptical shapes. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Circles, Definition of a Circle | |

## Closed Captioned Video: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles |
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The Roman Pantheon is a domed structure that shows a keen awareness of the position of the sun throughout the year. The source of light from the top of the dome allows for the exploration of chords, inscribed angles, central angles, and intercepted arcs. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this Link |
Applications of Circles, Definition of a Circle | |

## Closed Captioned Video: Geometry Applications: Coordinate Geometry |
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In this program we look at applications of coordinate geometry. We do this in the context of three real-world applications. In the first, we look at longitude and latitude as a spherical coordinate system for navigation. In the second application we look at decimal values for longitude and latitude in a two-dimensional system for locating buried treasure at sea. In the third application we look at polar coordinates in the context of Frank Lloyd Wright's design for the Guggenheim Museum. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Coordinate Geometry, Coordinate Systems | |

## Closed Captioned Video: Geometry Applications: Coordinate Geometry, Segment 1: Longitude and Latitude. |
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Greenwich, England, is the location of the Prime Meridian and offers a point of departure for a discussion of the longitude and latitude coordinate system. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this Link |
Applications of Coordinate Geometry, Coordinate Systems | |

## Closed Captioned Video: Geometry Applications: Coordinate Geometry, Segment 2: Rectangular Coordinates. |
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Centuries ago a Spanish galleon, The Atocha, sank off the coast of Florida, taking its gold treasure down with it. Aside from the technology used to recover the treasure, it was a rectangular coordinate system that made such an endeavor possible. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this Link |
Applications of Coordinate Geometry, Coordinate Systems | |

## Closed Captioned Video: Geometry Applications: Coordinate Geometry, Segment 3: Polar Coordinates. |
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The Guggenheim Museum in New York City has a spiral shape that is an example of a polar coordinate graph. This shape, found often in nature, is a way to understand the Fibonacci Sequence. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Coordinate Geometry, Coordinate Systems | |

## Closed Captioned Video: Geometry Applications: Points and Lines |
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In this program we explore the properties of points and lines. We do this in the context of two real-world applications. In the first, we go to CERN and learn about the Large Hadron Collidor. We look at how points can represent particle positions in space and look at properties of points and lines. In the second application we investigate the properties of lines in the context of city grids. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Points and Lines, Definition of a Line, Definition of a Point | |

## Closed Captioned Video: Geometry Applications: Points and Lines, Segment 1: Introduction |
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Our understanding of geometry owes much to the ancient Greeks. We visit the ancient Acropolis and explore some of its geometric secrets. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Points and Lines, Definition of a Line, Definition of a Point | |

## Closed Captioned Video: Geometry Applications: Points and Lines, Segment 2: Points |
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Geometric objects are abstractions that seem to have a connection to real world objects. In the case of a geometric point, we visit the CERN particle accelerator in Switzerland, where the smallest known subatomic particles are produced, to see how subatomic particles compare to geometric points. A mathematical analysis reveals the nature of geometric points and point-like materials objects. A Video Transcript is available for this tutorial at this Note: The download is Media4Math's guide to closed captioned videos. ## Other Closed Captioned Videos## To see the complete collection of Closed Captioned Videos, click on this
Link |
Applications of Points and Lines, Definition of a Line, Definition of a Point |