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.

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.

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.

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.

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.

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.

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.

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.

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

Geometric objects are abstractions that seem to have a connection to real world objects.

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.

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.

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?

In the ancient city of Marrakesh polygons are on display.

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

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.

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.

Frank Lloyd Wright’s architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes.

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.

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.

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.

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.

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

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.

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.