http://mathinscience.info 1

http://mathinscience.info 2

History of Conics• Appolonius of Perga, great

mathematician, was one of the first to study conic sections.

• He was the first to show all three curves.

• The early Greek astronomers thought that the planets orbited in a circular motion, however, Johannes Kepler was an astronomer who discovered the orbits of the Earth and other planets are other conic sections (i.e. ellipses).

• Newton’s analysis showed that the possible orbits are figures known as conic sections.

http://mathinscience.info 3

Gravitational Orbits• Most planets have

elliptical orbits.• Venus, however, has

such a small orbit that it appears to be circular.

• Comets have either elliptical or parabolic orbits.

• Comets with parabolic orbits pass the sun once and leave the Solar System.

• When two stars pass each other it results in a hyperbolic shape.

ellipse

hyperbola

parabola

circle

http://mathinscience.info 4

Conic Sections can be found all around us.

• Structures• Mirrors• Satellite Dishes• Orbit Paths• Etc…• Can you think of

any more?

http://mathinscience.info 5

What happened when you cut your cone?

First resulting shape: Circle

Second resulting shape: Ellipse

Third resulting shape: Parabola

Fourth resulting shape: Hyperbola

http://mathinscience.info 6

How can we define a circle?

Circle: a closed plane curve, every point of which is equidistant from a fixed point within the curve

According to Webster

http://mathinscience.info 7

How can we define an ellipse?

Ellipse:a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant : a plane section of a right circular cone that is a closed curve

According to Webster

http://mathinscience.info 8

How can we define a parabola?

Parabola: a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

According to Webster

http://mathinscience.info 9

How can we define a hyperbola?

Hyperbola:a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant

According to Webster

http://mathinscience.info 10

ReferencesConic Lesson Plan http://www.exploremath.com/activities

Power Point Background Informationhttp://mathworld.wolfram.com/ConicSection.htmlhttp://xahlee.org/SpecialPlaneCurves_dir

Historical View of Conic Sectionshttp://www.krellinst.org/UCES/archive/resources/conics/node5.html

Occurrence of the Conicshttp://ccins.camosun.bc.ca/~jbritton/jbconics.html

Newtonian Gravitation and the Laws of Keplarhttp://csep10.phys.utk.edu/astr161/lect/history/newtonkeplar.html

Drawing the Paths and Planetshttp://www.galashiels.org.uk

Orbitshttp://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/BrombacherAarnout/

OrbitsLesson/orbits_lesson_series.html