# Parabolic Paranoia

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Parabolic ParanoiaWhat are they good for?

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

Where are all the parabolas?

Where are all the parabolas?

Suspension Bridges Parabolic Antenna Optical Lenses Projectile Motion

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

Types of Bridges

Arch Cantilever Suspension Cable-

stayed Truss

• Truss• Suspension• Beam

Suspension Bridges

Main parts:› Towers› Deck› Anchorage› Cables› Stringers

• Tibetan architect and engineer Thangtong Gyalpo was the first to use the “suspension bridge” idea circa 1430

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