Ellipses By: Amanda Anthony Staci Fetterman Nicole Lloyd Ashley Morgan.
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Transcript of Ellipses By: Amanda Anthony Staci Fetterman Nicole Lloyd Ashley Morgan.
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EllipsesBy: Amanda Anthony
Staci FettermanNicole Lloyd
Ashley Morgan
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Definition
• An ellipsis is a series of three points with spaces between them(. . .) inserted into a quotation to indicate the omission of material from the original quotation.
• Example:– "His refusal to cooperate with the court and
name the source. . . resulted in a contempt citation."
Not an Ellipse!!!!!
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Formal Definition
• In mathematics, an ellipse is a plane curve that results from the intersection of a cone by
a plane in a way that produces a closed curve.
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Parts of an Ellipse
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Equations
• Point at (0,0)
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Equations
• Point at (h,k)
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History
The ellipse was first studied
by Menaechmus.
Euclid wrote about the
ellipse and it was given its
present name by Apollonius
.
The focus & directrix of an ellipse were considered by Pappus.
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HistoryKepler, in
1602, said he believed that the orbit of Mars was
oval, then he later
discovered that it was an ellipse with the sun at one focus.
In 1705 Halley showed that the comet,
which is now called after him, moved
in an elliptical orbit round
the sun.
The area of the ellipse is
πab. Ramanujan, in 1914, gave
the approximate
length
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Statistics & Finance
• In statistics, a random vector (X, Y) is jointly elliptically distributed if its iso-
density contours.– A special case is the multivariate normal
distribution.
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Multivariate Normal Distribution
• Examples
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Computer Graphics
• Drawing an ellipse as a graphics primitive is common in standard display libraries, such as the Macintosh QuickDraw API, and Direct2D on Windows.
• In 1970 Danny Cohen presented at the "Computer Graphics 1970" conference in England a linear algorithm for drawing ellipses and circles.
• In 1971, L. B. Smith published similar algorithms for all conic sections.
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Graphic Primitives
• Example–Macintosh Quick Draw
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Jack Bresenham
• Jack Bresenham at IBM is most famous for the invention of 2D drawing primitives, including line and circle drawing.
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Physics
• In the 17th century, Johannes Kepler discovered that the orbits along which the planets travel
around the Sun are ellipses with the Sun at one focus, in his first
law of planetary motion.
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Ellipses in Everyday Life
• Even though Mr. Geiswhite said that conics are only two dimensional
figures, here are some examples of three dimensional ellipse figures!!
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Continued
• Stadium
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Continued
• Oakley Logo
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Continued
• Speakers
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Continued
• Saturn
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Continued
• Buildings
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Resources
• http://en.wikipedia.org/wiki/Ellipse• http://mathworld.wolfram.com/Ellipse.html• http://math.usask.ca/emr/cir.html• http://www.mathportal.org/analytic-geometry/conic-sections
/ellipse.php• http://www.algebra.com/algebra/homework/Quadratic-relati
ons-and-conic-sections/change-this-name31623.lesson• http://www.algebralab.org/lessons/lesson.aspx?file=Algebra
_conics_ellipse.xml• http://www.purplemath.com/modules/ellipse.htm• http://www-history.mcs.st-and.ac.uk/Curves/Ellipse.html• http://britton.disted.camosun.bc.ca/jbconics.htm