Title | Description | Thumbnail Image | Curriculum Topics |
---|---|---|---|

## Closed Captioned Video: Geometry Applications: 3D Geometry |
## DescriptionIn 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. |
3-Dimensional Figures | |

## Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 1: Introduction. |
## DescriptionWe 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: |
3-Dimensional Figures | |

## Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 2: Pyramids |
## DescriptionRectangular 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. |
3-Dimensional Figures, Pyramids | |

## Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 3: Cylinders |
## DescriptionThe 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. |
3-Dimensional Figures, Cylinders | |

## Closed Captioned Video: Geometry Applications: Angles and Planes |
## DescriptionIn 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. |
Applications of Angles and Planes | |

## Closed Captioned Video: Geometry Applications: Angles and Planes, Segment 1: Introduction |
## DescriptionThe 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. |
Applications of Angles and Planes | |

## Closed Captioned Video: Geometry Applications: Angles and Planes, Segment 2: Angles |
## DescriptionHimeji 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. |
Applications of Angles and Planes | |

## Closed Captioned Video: Geometry Applications: Angles and Planes, Segment 3: Planes |
## DescriptionIn 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. |
Applications of Angles and Planes | |

## Closed Captioned Video: Geometry Applications: Area and Volume |
## DescriptionIn 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. |
Applications of Surface Area and Volume, Surface Area, Volume | |

## Closed Captioned Video: Geometry Applications: Area and Volume, Segment 1: Volume and Density. |
## DescriptionThe 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. |
Applications of Surface Area and Volume, Surface Area, Volume | |

## Closed Captioned Video: Geometry Applications: Area and Volume, Segment 2: Surface Area. |
## DescriptionThe 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. |
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. |
## DescriptionThe 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. |
Applications of Surface Area and Volume, Surface Area, Volume | |

## Closed Captioned Video: Geometry Applications: Circles |
## DescriptionIn 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. |
Applications of Circles, Definition of a Circle | |

## Closed Captioned Video: Geometry Applications: Circles, Segment 1: The Basics of Circles. |
## DescriptionWe 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. Note: The download is Media4Math's guide to closed captioned videos. |
Applications of Circles, Definition of a Circle | |

## Closed Captioned Video: Geometry Applications: Circles, Segment 2: Circles and Arcs. |
## DescriptionThe 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. Note: The download is Media4Math's guide to closed captioned videos. |
Applications of Circles, Definition of a Circle | |

## Closed Captioned Video: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles |
## DescriptionThe 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. |
Applications of Circles, Definition of a Circle | |

## Closed Captioned Video: Geometry Applications: Coordinate Geometry |
## DescriptionIn 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. |
Applications of Coordinate Geometry, Coordinate Systems | |

## Closed Captioned Video: Geometry Applications: Coordinate Geometry, Segment 1: Longitude and Latitude. |
## DescriptionGreenwich, 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. Note: The download is Media4Math's guide to closed captioned videos. |
Applications of Coordinate Geometry, Coordinate Systems | |

## Closed Captioned Video: Geometry Applications: Coordinate Geometry, Segment 2: Rectangular Coordinates. |
## DescriptionCenturies 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. |
Applications of Coordinate Geometry, Coordinate Systems | |

## Closed Captioned Video: Geometry Applications: Coordinate Geometry, Segment 3: Polar Coordinates. |
## DescriptionThe 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. Note: The download is Media4Math's guide to closed captioned videos. |
Applications of Coordinate Geometry, Coordinate Systems | |

## Closed Captioned Video: Geometry Applications: Points and Lines |
## DescriptionIn 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. |
Applications of Points and Lines, Definition of a Line, Definition of a Point | |

## Closed Captioned Video: Geometry Applications: Points and Lines, Segment 1: Introduction |
## DescriptionOur 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. Note: The download is Media4Math's guide to closed captioned videos. |
Applications of Points and Lines, Definition of a Line, Definition of a Point | |

## Closed Captioned Video: Geometry Applications: Points and Lines, Segment 2: Points |
## DescriptionGeometric 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. |
Applications of Points and Lines | |

## Closed Captioned Video: Geometry Applications: Points and Lines, Segment 3: Lines |
## DescriptionMany cities are laid out in a rectangular grid and are examples of intersecting lines and rays. We visit the city of Houston to investigate the geometric nature of the city grid in its downtown area. We explore properties of intersecting and parallel lines and why this is the most efficient way to organize a city or community. |
Applications of Points and Lines, Definition of a Line, Definition of a Point | |

## Closed Captioned Video: Geometry Applications: Polygons |
## DescriptionIn this program we explore the properties of polygons. We do this in the context of two real-world applications. In the first, we look at Islamic tile patterns as examples of regular polygons. We explore how such intricate patterns were created using a compass and straight edge. |
Applications of Polygons |