THE PARABOLA

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THE PARABOLA

• MA18 D
• July 11, 2003
• SECA303

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• from para beside and ballein to throw or
  cast

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A Brief History of the Parabola

• The person credited with discovering the conic
  sections is MENAECHMUS, the said tutor of
  Alexander the Great
• The terms parabola and hyperbola, however,
  were not his inventions, but were coined by
  APOLLONIUS, who studied under EUCLID.
• It is, however, suggested that the two terms are
  actually older than Apollonius himself.

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History Continued

• The famous ARCHIMEDES did much work on the
  parabola, like finding the area of a segment of a
  parabola cut off by any chord.
• Apollonius followed Archimedes in terms of work
  on the parabola. His books, Conics describes-
  what else- the conic sections. He also discussed
  the properties of parabolic mirrors, and
  developed a sundial in the shape of a conic
  section, which was more accurate than past ones.

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And Continued.

• DIOCLES, a contemporary of Apollonius, proved the
  focal property of a parabolic mirror, that is,
  parallel rays of light are brought into focus by
  it, and not by a spherical mirror.
• Later on, at the time of the renaissance, Pascal
  figured that a parabola was a projection of a
  circle.

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And History is History

• Galileo stated that projectiles follow a
  parabolic path when in motion.
• Also, he was the first to find an application of
  a parabola he used it as a graph of distances,
  since distances traveled up to any given second
  are the successive square numbers.
• Much later on, Isaac Newton worked on the
  properties of parabolic mirrors to bring parallel
  light rays to a focus.

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APPLICATIONS
A lot of them turn up in obvious places,
sometimes for a practical use, sometimes just for
fun.
Parabolas have A lot of applications.
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Guns, Cannons and other ArtilleryProjectiles
and Projectile Motion

• The path taken by objects thrown into the air is
  a parabola opening towards the source of gravity.
  A bullet fired from a gun moves in a slight
  curve, not a straight line.

• The parabola comes into play when placing aiming
  sights on a gun. The sight has to be at a certain
  height to compensate for this effect and provide
  accuracy, more so over long distances

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What you see aint what it is Optical Illusions

• There is an illusion known as the pink pig.
• The illusion is composed of a wooden box that
  seemingly has a pig on a circular mirror on its
  surface.When someone tries to get the pig,
  however, they find that their hand passes through
  the pig. Via parabolic reflectors, this illusion
  is achieved.

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How the Pink Pig Works

• The image seen outside the box are the images
  formed by 2 concave mirrors facing each other.
• The object is placed at the center of the bottom
  mirror.
• The curvature of the mirrors is such that the
  object is at the focal point of the top mirror.
• The mirrors are placed so that the focal point of
  the bottom mirror is located at the hole in the
  top of the device

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How the Pink Pig Works Contd

• When light from a point on the object hits the
  top mirror, it reflects in parallel rays. These
  rays then hit the bottom mirror and reflect so
  that they reassemble to form a point located at
  one focal length from the bottom mirror. The end
  result is that light from every point on the
  object is assembled into an image in the hole.

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London Bridge is Falling DownParabolas in
Engineering

• The main cables of suspension bridges such as the
  Golden Gate Bridge in San Francisco follow the
  form of the parabola. Proving this might require
  advanced physics and calculus, so lets just not
  ask why.

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Why make Rays converge Parabolic applications
to Manipulate Light

• A paraboloidal mirror is made by rotating a
  parabola around its axis of symmetry.
• Rays of light entering the mirror bounces off the
  side and hits the focus of the parabola. Light
  rays coming from the focus bounces off the side
  and goes out of the mirror parallel to the axis
  of symmetry.

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Light Continued..

• This property is used in flashlights and car
  headlights, where the bulb is a the focus. The
  same idea is used in radars, satellites and some
  sound systems. Again, proving this requires
  calculus, so lets just leave it there.

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Cooking With Parabolas

• Parabolic reflectors focusing heat are used as
  solar cookers.
• It basically uses a simple principle. The light
  rays merge in the focus of the parabolic dish,
  which is the grill adjustment.