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.

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. 

In this module students use their geometry and algebra skills to analyze a wildlife refuge in Nevada. Calculating the area, perimeter, and the ratio of the two allows students to analyze different configurations for a refuge. Specifically, they look at ways of designing a wild horse refuge, using the concepts they have learned. 

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.

We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

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.

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.

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.

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.

Himeji castle in Japan is a marvel of architecture and a startling example of geometry and military science.

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.

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.

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.

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.

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.

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.

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.