Transcript of Conics Group Members Talha Zameer Zeeshan Shabbir Fiaz Ashraf M.Bilal Hammad Hassan Umair Ali.
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- Conics Group Members Talha Zameer Zeeshan Shabbir Fiaz Ashraf
M.Bilal Hammad Hassan Umair Ali
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- Conic Sections There are four conics in the conics sections
Parabolas Circles Ellipses and Hyperbolas. We see then everyday but
we just dont notice them. They appear everywhere in the world and
can be man-made or natural. The applications of conics can be seen
everyday all around us. Conics are found in architecture, physics,
astronomy and navigation. If you get lost, you can use a GPS and it
will tell where you are (a point) and it will lead you to your
destination (another point). Conics are also used to describe the
orbits of planets, moons and satellites in our universe.
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- Conic Sections A conic section (or just conic) is a curve
obtained as the intersection of a cone with a plane.
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- Parts of Conic Section CIRCLE ELLIPSE PARABOLA HYPERBOLA
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- Fiaz Ashraf Introduction
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- The conic sections were first identified by Menaechus in about
350 BC, but he used three different types of cone, taking the same
section in each, to produce the three conic sections, ellipse,
parabola and hyperbola. It was Apollonius of Perga, (c. 255170 BC)
who gave us the conic sections using just one cone. Evidence of
wheeled vehicles appears from the second half of the 4th millennium
BC. The first wheeled vehicle was invented in 3500-3350 BC.4th
millennium BC 1700 BC The Rhind Papyrus gives a method to find the
area of a circular field. The first theorems relating to circles
are attributed to Thales around 650 BC 300 BC Book III of Euclids
Element deals with the properties of circles. If we cut a cone at
different angles, then we will obtain different types of conic
section. There are four different types we can obtain.
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- The circle, where the cone is cut at right-angles to its
axis.
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- The ellipse, where the cone is cut at an oblique angle
shallower than a generator.
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- The parabola, where the cone is cut parallel to a
generator.
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- The hyperbola, where a double cone is cut at an angle steeper
than a generator.
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- Zeeshan Shabbir Circle
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- A round plane figure whose boundary (the circumference)
consists of points equidistant from a fixed point (the
centre).
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- Properties of Circle All Circles are symmetrical. All circles
do not have edges. All circles are proportionate. All line segments
starting from the middle of the circle to the circumference is
equal.
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- Real Life Applications Circle play a really large role in our
life. We just fail to realize it even through it is right in front
of us. Things that we commonly use are round. Earth, Car tires,
Coins, Man Holes, etc.
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- Real Life Application Wheels & Gears Wheel is one of the
greatest invention of all time and the basis of much of our
transportation system. Circular gears are important elements in
many of the machines we use every day, from CD players to electric
saws.
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- Real Life Application Ferris Wheel One prime example of a
circle that you can find in real life is a Ferris Wheel. All the
points along the outer rim of the wheel are equidistant from the
center.
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- Hammad Hassan Ellipse
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- A regular oval shape, traced by a point moving in a plane so
that the sum of its distances from two other points is constant, or
resulting when a cone is cut by an oblique plane which does not
intersect the base
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- Real Life Application If you tilt a glass of water, the
resulting shape of the surface of the water is also an
ellipse.
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- Real Life Applications Satellite and Planet Orbits Kepler's
first law of planetary motion is: The path of each planet is an
ellipse with the sun at one focus.
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- Football If an ellipse is rotated about the major axis, you
obtain a football. Real Life Applications
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- M. Bilal Parabola
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- A symmetrical open plane curve formed by the intersection of a
cone with a plane parallel to its side. The path of a projectile
under the influence of gravity follows a curve of this shape.
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- Real Life Applications. Heaters Heaters are sold which make use
of the relection property of the parabola. The heat source is at
the focus and heat is concentrated in parallel rays.
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- Real Life Applications. Fountains Fountains at Las Vegas
exhibit water in the shapes of parabolas.
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- Real Life Applications. Path of Football The path of an object
thrown in space is a parabola.
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- Umair Ali Hyperbola
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- A symmetrical open curve formed by the intersection of a
circular cone with a plane at a smaller angle with its axis than
the side of the cone.
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- Real Life Applications House Lamp The shadow of a lampshade or
a flashlight.
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- Real Life Applications Nuclear Reactors Cooling towers of
Nuclear Reactors.
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- Real Life Applications Shapes Most potato chips are
hyperbolic-paraboloids.
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- Thankxxx....