Content Showcase: Video Library

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-area-and-volume-segment-3-ratio-surface-area-volume

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-area-and-volume-3

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles

This video includes a Teacher's Guide: https://www.media4math.com/library/geometry-applications-teachers-guide-circles

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles-segment-1-basics-circles

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles-segment-2-circles-and-arcs

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-circles-1

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles-segment-3-chords-and-inscribed-angles

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-circles-2

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-coordinate-geometry

This video includes a Teacher's Guide: https://www.media4math.com/library/geometry-applications-teachers-guide-coordinate-geometry

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-coordinate-geometry-segment-1-longitude-and-latitude

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-coordinate-geometry-1

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-coordinate-geometry-segment-2-rectangular

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-coordinate-geometry-2

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-coordinate-geometry-segment-3-polar-coordinates

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-coordinate-geometry-3

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-points-and-lines

Our understanding of geometry owes much to the ancient Greeks. We visit the ancient Acropolis and explore some of its geometric secrets.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-points-and-lines-segment-1-introduction

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-points-and-lines-segment-2-points

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-points

Many 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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-points-and-lines-segment-3-lines

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-lines

In 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. In the second application we look at composite figures, specifically in the context of the design of the Petronas Towers in Indonesia.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-polygons

The Pentagon is one of the most famous polygon-shaped buildings in the world. But why was this shape chosen over a more straightforward quadrilateral shape? We briefly explore the properties of pentagons and use this as a way of introducing the key concepts throughout the program.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-polygons-segment-1-introduction

In the ancient city of Marrakesh polygons are on display. As part of the Islamic tile work prevalent throughout the Middle Ages, Marrakesh provides an opportunity to explore the properties of polygons, and how these properties are taken advantage of in the intricate designs found throughout this fascinating city.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-polygons-segment-2-properties-polygons

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-polygons-1

The Petronas Towers in Indonesia provide an opportunity to explore the composite shapes used in the design of the towers.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-polygons-segment-3-composite-figures

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-polygons-2

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-quadrilaterals

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-quadrilaterals-segment-1-introduction

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-quadrilaterals-segment-2-squares-and-rectangles

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-quadrilaterals-1

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-quadrilaterals-segment-3-parallelograms-and

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-quadrilaterals-2

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations

Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-1-translations-and-rotations

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-transformations-1

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-2-3d-translations

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-transformations-2

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-3-rotations-reflections-and

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-transformations-3