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Title | Description | Thumbnail Image | Curriculum Topics |
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Video Transcript: Geometry Applications: Triangles, Segment 2: Triangles |
Video Transcript: Geometry Applications: Triangles, Segment 2: TrianglesThis is the transcript for the video of same title. Video contents: The Eiffel Tower includes quite a number of exposed triangular trusses. The properties of triangles are used to explore and explain the frequent use of triangular trusses in many building. In particular, isosceles and equilateral triangular trusses are explored. In addition triangle postulates and similarity are explored and analyzed. |
Applications of Triangles | |
Video Transcript: Geometry Applications: Triangles, Segment 1: Introduction |
Video Transcript: Geometry Applications: Triangles, Segment 1: IntroductionThis is the transcript for the video of same title. Video contents: The Bank of China building in Hong Kong is a dramatic example of triangular support. The notion of triangular trusses is introduced, along with the key concepts developed in the rest of the program. |
Applications of Triangles | |
Video Transcript: Geometry Applications: Triangles |
Video Transcript: Geometry Applications: TrianglesThis is the transcript for the video of same title. Video contents: In this program we explore the properties of triangle. We do this in the context of two real-world applications. In the first, we explore the triangular trusses in the Eiffel Tower and in the process learn about key properties of triangles. In the second application, we look at right-triangle-shaped sails on sail boat and why these are the ideal shape for efficient sailing. |
Applications of Triangles | |
Video Transcript: Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry |
Video Transcript: Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and SymmetryThis is the transcript for the video of same title. Video contents: The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry. |
Applications of Transformations | |
Video Transcript: Geometry Applications: Transformations, Segment 2: 3D Translations |
Video Transcript: Geometry Applications: Transformations, Segment 2: 3D TranslationsThis is the transcript for the video of same title. Video contents: Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations. |
Applications of Transformations | |
Video Transcript: Geometry Applications: Transformations, Segment 1: Translations and Rotations |
Video Transcript: Geometry Applications: Transformations, Segment 1: Translations and RotationsThis is the transcript for the video of same title. Video contents: Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced. |
Applications of Transformations | |
Video Transcript: Geometry Applications: Transformations |
Video Transcript: Geometry Applications: TransformationsThis is the transcript for the video of same title. Video contents: In this program we look at applications of transformations. We do this in the context of three real-world applications. In the first, we look at translations and rotations in the context of roller coaster rides. In the second example we look at translations in three-dimensional space in the context of cargo ships. In the third example, we look at the design of observatories to look at rotations, reflections, and symmetry. |
Applications of Transformations | |
Video Transcript: Geometry Applications: Coordinate Geometry |
Video Transcript: Geometry Applications: Coordinate GeometryThis is the transcript for the video of same title. Video contents: 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. |
Applications of Coordinate Geometry | |
Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction |
Video Transcript: Geometry Applications: 3D Geometry, Segment 1: IntroductionThis is the transcript for the video of same title. Video contents: We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Video Transcript: Geometry Applications: 3D Geometry, Segment 2: Pyramids |
Video Transcript: Geometry Applications: 3D Geometry, Segment 2: PyramidsThis is the transcript for the video of same title. Video contents: 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. |
3-Dimensional Figures and Applications of 3D Geometry | |
Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders |
Video Transcript: Geometry Applications: 3D Geometry, Segment 3: CylindersThis is the transcript for the video of same title. Video contents: 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. |
3-Dimensional Figures and Applications of 3D Geometry | |
Video Transcript: Geometry Applications: Angles and Planes |
Video Transcript: Geometry Applications: Angles and PlanesThis is the transcript for the video of same title. Video contents: 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. |
Definition of an Angle and Applications of Angles and Planes | |
Video Transcript: Geometry Applications: Angles and Planes, Segment 1: Introduction |
Video Transcript: Geometry Applications: Angles and Planes, Segment 1: IntroductionThis is the transcript for the video of same title. Video contents: 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. |
Applications of Points and Lines | |
Video Transcript: Geometry Applications: Angles and Planes, Segment 2: Angles |
Video Transcript: Geometry Applications: Angles and Planes, Segment 2: AnglesThis is the transcript for the video of same title. Video contents: 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. |
Applications of Points and Lines | |
Video Transcript: Geometry Applications: Angles and Planes, Segment 3: Planes |
Video Transcript: Geometry Applications: Angles and Planes, Segment 3: PlanesThis is the transcript for the video of same title. Video contents: 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. |
Applications of Points and Lines | |
Video Transcript: Geometry Applications: Area and Volume |
Video Transcript: Geometry Applications: Area and VolumeThis is the transcript for the video of same title. Video contents: 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. |
Applications of Surface Area and Volume | |
Video Transcript: Geometry Applications: Area and Volume, Segment 1: Volume and Density. |
Video Transcript: Geometry Applications: Area and Volume, Segment 1: Volume and Density.This is the transcript for the video of same title. Video contents: 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. |
Applications of Surface Area and Volume | |
Video Transcript: Geometry Applications: Area and Volume, Segment 2: Surface Area. |
Video Transcript: Geometry Applications: Area and Volume, Segment 2: Surface Area.This is the transcript for the video of same title. Video contents: 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. |
Applications of Surface Area and Volume | |
Video Transcript: Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume |
Video Transcript: Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to VolumeThis is the transcript for the video of same title. Video contents: 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. |
Applications of Surface Area and Volume | |
Video Transcript: Geometry Applications: Circles |
Video Transcript: Geometry Applications: CirclesThis is the transcript for the video of same title. Video contents: 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. |
Applications of Circles | |
Video Transcript: Geometry Applications: Circles, Segment 1: The Basics of Circles |
Video Transcript: Geometry Applications: Circles, Segment 1: The Basics of CirclesThis is the transcript for the video of same title. Video contents: 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. |
Applications of Circles | |
Video Transcript: Geometry Applications: Circles, Segment 2: Circles and Arcs |
Video Transcript: Geometry Applications: Circles, Segment 2: Circles and ArcsThis is the transcript for the video of same title. Video contents: 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. |
Applications of Circles | |
Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles |
Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed AnglesThis is the transcript for the video of same title. Video contents: 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. |
Applications of Circles | |
Video Transcript: Geometry Applications: 3D Geometry |
Video Transcript: Geometry Applications: 3D GeometryThis is the transcript for the video of same title. Video contents: 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. |
3-Dimensional Figures and Applications of 3D Geometry | |
Video Transcript: Geometry Applications: Coordinate Geometry, Segment 1: Longitude and Latitude |
Video Transcript: Geometry Applications: Coordinate Geometry, Segment 1: Longitude and LatitudeThis is the transcript for the video of same title. Video contents: 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. |
Applications of Coordinate Geometry |