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Sanjaya Amarasinghe
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Cutting a double-cone at different angles (each with a different eccentricity) gives us a circle, ellipse, parabola, or hyperbola. 

The eccentricity of a circle is zero.
The eccentricity of an ellipse which is not a circle is greater than zero but less than 1.
The eccentricity of a parabola is 1.
The eccentricity of a hyperbola is greater than 1.

If the eccentricity became infinite, you'd get a flat line. So you can think of eccentricity as how much any conic section deviates from a circle. And any two conic sections are similar if and only if they have the same eccentricity.

Nowadays we usually think of "conics" in mathematics as just another name for "quadratic equations". But conic sections were studied in a purely geometric sense, as shapes obtained by cutting through a cone, centuries before modern algebraic notation was invented. This animation shows a plane cutting a double cone at different angles to produce the three types of smooth conic sections—hyperbola, parabola and ellipse—as well as the degenerate conics—a single point or a pair of lines (or, just for an instant, a single line).

From: http://www.maths.adelaide.edu.au/alexander.hanysz/videos/conics_large.shtml

For ellipses and Kepler's Laws in particular, be sure to check out:
https://plus.google.com/+TomEigelsbach/posts/PyXF9bSnuLi

#math   #mathematics  
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