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Conic Sections: The Hyperbola

Conic Sections: The Hyperbola. Examples from the Real World. Dulles Airport         Dulles Airport, designed by Eero Saarinen, is in the shape of a hyperbolic paraboloid . The hyperbolic paraboloid is a three- dimensional curve that is a hyperbola in one cross-section, and

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Conic Sections: The Hyperbola

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  1. Conic Sections: The Hyperbola Examples from the Real World

  2. Dulles Airport         Dulles Airport, designed by Eero Saarinen, is in theshape of a hyperbolic paraboloid. The hyperbolic paraboloid is a three- dimensionalcurve that is a hyperbola in one cross-section, and a parabola in another cross section.

  3. Lampshade         A household lamp casts hyperbolic shadows on a wall.

  4. Gear transmission         Two hyperboloids of revolution can provide gear transmission between two skew axes. The cogs of each gear are a set of generating straight lines.

  5. Sonic Boom         In 1953, a pilot flew over an Air Force Baseflying faster than the speed of sound. He damaged every building on the base. As the plane moves faster than the speed of sound, you get a cone-like wave.Where the cone intersects the ground, it is an hyperbola. The sonic boom hits every point on that curve at the same time. No sound is heard outside the curve. The hyperbola is known as the "Sonic Boom Curve."

  6. Cooling Towers of Nuclear Reactors         The hyperboloid is the design standard for all nuclearcooling towers. It is structurally sound and can be built with straight steel beams.When designing these cooling towers, engineers are faced with two problems:(1) the structutre must be able to withstand high winds and (2) they should be built with as little material as possible.The hyperbolic form solves both of these problems. For a given diameter and height of a tower and a given strength, this shape requires less material than any other form. A 500 foot tower can be made of a reinforced concrete shell only six or eight inches wide. See the pictures below (this nuclear power plant is located in Indiana).

  7. Higher Ball Speed Across The Entire Face Hyperbolic Face Technology™ uses a chemical reduction process that selectively removes unwanted material for precision thickness control of the strategic hyperbolic shaping. This dramatically improves impact efficiency and produces a larger sweet spot that generates higher ball speeds across the entire face for significant distance gains on off-center hits. You'll get more consistency between the balls you hit in the center of the clubface and the balls you don't.

  8. Can you think of any hyperbolas that you may have seen?

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