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Parabolic Paranoia

Parabolic Paranoia

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Parabolic Paranoia

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  1. Parabolic Paranoia What are they good for?

  2. What exactly is it? • Parabola: “… is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.” y(x) = x2

  3. Where are all the parabolas?

  4. Where are all the parabolas? • Suspension Bridges • Parabolic Antenna • Optical Lenses • Projectile Motion

  5. Not Just A Hanging Chain • Hanging Chain= Catenary, y = Cosh(x) - 1 • Hanging Chain & Weight = Parabola, • y = x2 • Hangin’ with Mr. Cooper= Awesome show from the 90s

  6. Types of Bridges • Truss • Suspension • Beam • Arch • Cantilever • Suspension • Cable-stayed • Truss

  7. Suspension Bridges • Tibetan architect and engineer ThangtongGyalpo was the first to use the “suspension bridge” idea circa 1430 • Main parts: • Towers • Deck • Anchorage • Cables • Stringers

  8. Equation of a parabola • y = Ax2 + Bx + C • (y-k)2 = 4p(x-h) • (h, k) : Vertex of the Parabola • p| : Distance from the Vertex • p : Direction Parabola Opens • (h+p, k) when p is positive or (h, k+p) when p is negative = Focus