Not ready to purchase the full library of Geometry DVDs? Purchase single DVDs for $39.99.

Title

Video Segments

Contents of the DVDs

Geometry Applications DVDs: Points and Lines

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Geometry Basics: 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.

Segment 2: Points in space. 

Geometry applications: 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.

Key concepts: points, collinear points

Segment 3: Lines in space.

Geometry applications: 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.

Key concepts: lines, parallel lines, perpendicular lines, properties of parallel lines

Geometry Applications DVDs: Angles and Planes

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Geometry Basics: Angles and Planes.

Geometry applications: 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.

Segment 2: Angles.

Geometry applications: We visit Himeji castle in Japan, a marvel of architecture and military science. The use of acute, obtuse, and right angles as part of the defense structure provide many opportunities for exploring the nature of geometric angles.

Key concepts: angles, acute angles, obtuse angles, right angles, tangents to circles

Segment 3: Planes.

Geometry applications: We visit the Canadian Rockies, the Burgess Shale fossils provide a window to prehistoric Earth. This segment uses the properties of planes to analyze fossils.

Key concepts: planes, parallel planes, intersecting planes, closed figure, area

Geometry Applications DVDs: Triangles

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Geometry Basics: Triangles.

Geometry applications: The Bank of China building in Hong Kong is a dramatic example of triangular support. The notions of triangles and trusses are introduced, along with the key concepts developed in the rest of the program.

Segment 2: Triangles.

Geometry applications: We visit the Eiffel Tower to investigate its triangles. 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.

Key concepts: triangles, isosceles triangles, equilateral triangles, congruent triangles, similar triangles, S-S-S postulate

Segment 3: Right Triangles.

Geometry applications: We visit the ancient port city of Corinth in Greece allows us to explore the evolution of sailing. We explore the properties of right triangles that make triangular sails ideal.

Key concepts: right triangles, areas of a triangles, data analysis, function graphing

Geometry Applications DVDs: Quadrilaterals

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Geometry Basics: Quadrilaterals.

Geometry applications: We visit Stonehenge to study post and lintel construction, and this type of construction involves quadrilateral shapes. This segment also describes the key concepts developed throughout the program.

Segment 2: Squares and Rectangles.

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

Key concepts: quadrilaterals, squares, rectangles, analysis of diagonals and triangles

Segment 3: Parallelograms and Trapezoids.

Geometry applications: We visit the Puerta de Europa towers in Madrid to bring parallelograms front and center. The underlying parallelogram and trapezoidal designs are explored and analyzed.

Key concepts: parallelograms, trapezoids, rhombuses, analysis of diagonals and triangles

Geometry Applications DVDs: Polygons

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Geometry Basics: Polygons.

Geometry applications: We visit the Pentagon, one of the most famous polygon-shaped buildings in the world. We briefly explore the properties of pentagons and use this as a way of introducing the key concepts throughout the program.

Segment 2:

Geometry applications: We visit the ancient city of Marrakesh, where 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.

Key concepts: polygons, sum of the interior angles, analysis of triangular components, inscribed polygons, pentagons, hexagons, octagons

Segment 3: Composite Figures.

Geometry applications: We visit the Petronas Towers in Indonesia provide an opportunity to explore the composite shapes used in the design of the towers.

Key concepts: composite figures, similar figures

Geometry Applications DVDs: Circles

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: The Basics of 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.

Segment 2: Circles and Arcs. 

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.

Key concepts: circle, radius, diameter, circumference, arc

Segment 3: Chords and Inscribed Angles.

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.

Key concepts: chords, inscribed angles, central angles, intercepted arcs

Geometry Applications DVDs: 3D Geometry

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Introduction. 

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

Segment 2:

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.

Key concepts: rectangular prisms, volume, series, sequence

Segment 3: Cylinders.

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.

Key concepts: cylinders, volume, series, sequence

Geometry Applications DVDs: Area and Volume

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: 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.

Key concepts: volume, density

Segment 2: Surface Area. 

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.

Key concepts: surface area, rhombuses, similar figures, parallel lines

Segment 3: Ratio of Surface Area to Volume.

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.

Key concepts: ratio of surface area to volume, rectangular prisms, triangular prisms

Geometry Applications DVDs: Coordinate Geometry

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Longitude and Latitude. 

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.

Key concepts: longitude, latitude

Segment 2: Rectangular Coordinates. 

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.

Key concepts: Cartesian coordinates, converting latitude and longitude coordinates to rectangular coordinates

Segment 3: Polar Coordinates.

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.

Key concepts: polar coordinates, Fibonacci sequence, logarithmic spiral

Geometry Applications DVDs: Transformations

GEOMETRY APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Translations and Rotations. 

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

Key concepts: translations, rotations, vectors

Segment 2: 3D Translations. 

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.

Key concepts: translations, 3D coordinate system, data management

Segment 3: Rotations, Reflections, and Symmetry.

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.

Key concepts: rotations, reflections, symmetry