Ellipses By: Amanda Anthony Staci Fetterman Nicole Lloyd Ashley Morgan

EllipsesBy: Amanda Anthony

Staci FettermanNicole 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:– "His refusal to cooperate with the court and

name the source. . . resulted in a contempt citation."

Not an Ellipse!!!!!

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.

Parts of an Ellipse

Equations

• Point at (0,0)

Equations

• Point at (h,k)

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.

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

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.

Multivariate Normal Distribution

• Examples

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.

Graphic Primitives

• Example–Macintosh Quick Draw

Jack Bresenham

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

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.

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!!

Continued

• Stadium

Continued

• Oakley Logo

Continued

• Speakers

Continued

• Saturn

Continued

• Buildings

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