Greenwood press

CONIC SECTIONS
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Johannes Kepler (1571–1630) revolutionized astronomy when he recognized
that the motion of planets about the sun was elliptical and not circular. Working
with the detailed planetary observations of Tycho Brahe (1546–1601), Kepler
found some very slight errors in Brahe’s figures for the circular orbit of Mars. He
attempted to correct the values, but finally concluded the data was correct and
that the orbit of Mars was elliptical with the sun at one of the focal points of the
orbit. His verification of this for the other known planets of his time is known as
“Kepler’s first law.” (See Variation.)
Some comets, like Halley’s comet, follow an elliptical path around the sun
just like planets. Hence Halley’s comet “returns” to earth’s view on a regular
basis. However, some comets appear to follow parabolic or hyperbolic paths.
Once past the sun, they leave our solar system. These comets may have traced
elliptical orbits at one time, but were thrown off trajectory by a gravitational
encounter with a major planet such as Jupiter. 
Many machines contain elliptical gears. These develop a nonuniform motion
from a uniform power source. The momentary speedup or slowdown they pro-
duce is important in rotary shears, conveyers, motorcycle engines, and packag-
ing machines. 
Statisticians conceptualize plots of many variables on large numbers of sub-
jects as elliptical swarms of points. By finding the axes of such swarms, they syn-
thesize the information from many variables into important structural variables.
online sources for further exploration
Artistic views of conics
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Conics in general



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Pictures of Appollonius’s analysis


Explore conic sections dynamically


Hyperbolic mirrors

A video view of Statuary Hall in the U.S. Capitol 

Parabolic reflectors and antennas