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| Image created using Geogebra © Eugene Brennan |
The parabola, a geometric shape that can be defined as the locus of points equidistant from an axis called the directrix and a point called the focus.
Parabolas
crop up everywhere in nature and in things we make. If you kick a ball
or throw a stone up at an angle into the air, the trajectory or path
traced out is in the shape of a parabola. Similarly for a jet of water
or projectile from a gun.
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| A stream of water from a jet follows a parabolic trajectory. Image courtesy GuidoB, CC BY-SA 3.0 Unported via Wikimedia Commons |
Satellite dishes, radio and optical
telescopes, flashlights and car headlamps all have parabolic reflectors
because of a useful property of the shape: Rays from the focus of the
parabola hitting the reflector are "bounced" outwards in a parallel beam
(in the case of a light, heat, microwave or sound source) and vice
versa for incoming parallel rays so they're focused on a detector (for a
satellite dish or telescope).
Parabolas are also one of the range of shapes used for the nose cones of aircraft. In this case, the shape is a 3D version of a parabola, produced by rotating it around its axis.