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1) Triangles
Description
Covers equilateral, isosceles, right, congruent, and similar triangles; provides examples from architecture (the Bank of China Tower, with a triangular base to help the Hong Kong skyscraper withstand typhoon winds and the Eiffel Tower in Paris). Looks at why triangles are better architectural support than rectangles or other shapes. Reveals also, why ancient merchant ships were able to go farther and faster with triangular sails, the same principle...
Description
Stonehenge is thought of as being circular, but its structure is made possible by post-and-lintel construction-vertical supports and horizontal spans that create quadrilateral forms. In this program viewers learn why most homes are also made up of quadrilaterals as the concepts of rectangles, squares, parallelograms, trapezoids, and triangles within quadrilaterals are explored. The geometry of architecture is illustrated using Frank Lloyd Wright's...
Description
The Texas Titan roller coaster hurtles riders along at a speed of 90 mph, 255 feet up in the air. And like all objects that move, its cars undergo a series of mathematical changes as they shift position. This program explores transformations, the principles that underlie the movement of a shape from one place to another. Three-dimensional transformations are made clear using containers on cargo ships as an example-the containers are efficiently stacked...
Description
The ancient Pueblo people built round ceremonial chambers at Chaco Canyon to mark the natural cycles of solstice and equinox. Like astronomers today, they knew the circular shape was ideal for tracking the progression of the Earth throughout the year. This program uses ancient structures to help define properties of circles, arcs, chords, secants, and central and inscribed angles. The video explains why the Colosseum is shaped like an ellipse instead...
Description
Marrakesh is a showcase of 12th-century Islamic art and architecture, featuring many examples of the intricate polygonal pattern called an arabesque. How did medieval artisans create this shape with such mathematical precision? This program explains compass and straightedge construction-the technique employed by the Islamic craftsmen of Marrakesh-as well as properties of regular polygons, composite figures, tessellations, and areas of polygons. The...
Description
Twice a year at Chichen Itza the sun casts a shadow on the Temple of Kulkulkan that resembles a snake descending the pyramid's steps-a curved line that is eerily similar to the descending line of x approaching infinity on the graph of the exponential function for the volume of the pyramid. In this program Mayan architecture is used to study the properties of 3-D figures, including square and rectangular pyramids, rectangular prisms, and cylinders....
Description
What are the geometric principles behind the sinking of the Titanic-and how is a ship of its size able to float in the first place? This program examines applications of area and volume, using the Titanic, the Louvre's Glass Pyramid, and New York's CitiGroup Building to illustrate the concepts of volume and density, surface area, and surface area-to-volume ratio. Knowing the proportion of the Citigroup's surface to its interior space is the first...
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