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Ellipses

Ellipses. By: Amanda Anthony Staci Fetterman Nicole Lloyd Ashley Morgan. 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:

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Ellipses

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  1. Ellipses By: Amanda Anthony Staci Fetterman Nicole Lloyd Ashley Morgan

  2. 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!!!!!

  3. 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.

  4. Parts of an Ellipse

  5. Equations • Point at (0,0)

  6. Equations • Point at (h,k)

  7. History

  8. History

  9. 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.

  10. Multivariate Normal Distribution • Examples

  11. 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.

  12. Graphic Primitives • Example • Macintosh Quick Draw

  13. Jack Bresenham • Jack Bresenham at IBM is most famous for the invention of 2D drawing primitives, including line and circle drawing. 

  14. 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.

  15. 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!!

  16. Continued • Stadium

  17. Continued • Oakley Logo

  18. Continued • Speakers

  19. Continued • Saturn

  20. Continued • Buildings

  21. 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-relations-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

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