Angles and PlanesThis program treks to locations as diverse as Japan, Puerto Rico, and British Columbia to demonstrate the principles of angles, tangents to circles, parallel and perpendicular planes, and the area of 2-D figures on a plane. Angles played a key role in making Himeji Castle easy for samurai warriors to defend, and astronomers at the Arecibo Observatory build on Kepler's work with angles, planes, and ellipses to learn more about the solar system. In addition, the video uses the Burgess Shale Formation to explain the concept of intersecting planes-the reason that older fossils are sometimes found in stratified layers above, instead of below, newer fossils.