Keeping Things in Focus - Part 2

Some of the simplest and most well-known curves parabolas and
ellipses, which can be traced back to ancient Greece are also among
the most useful. Parabolas have a reflective property that is
employed in many of today.s solar power technologies. Mirrors with
a parabolic shape reflect all entering light to a single point
called the focus, where the solar power is converted into usable
energy. Ellipses, which have two foci, have a similar reflecting
property that is exploited in a medical procedure called
lithotripsy. Patients with kidney stones and gallstones are
positioned in a tank shaped like half an ellipse so that the stones
are at one focus. Acoustic waves sent from the other focus
concentrate all their energy on the stones, pulverizing them
without surgery. Math can sometimes throw you a curve, but that.s
not necessarily a bad thing. Parabolas and ellipses are curves
called conic sections. Another curve in this category is the
hyperbola, which may have the most profound application of all the
nature of the universe. In plane geometry, points that are a given
distance from a fixed point form a circle. In space, points that
are a given spacetime distance from a fixed point form one branch
of a hyperbola. This is not an arbitrary mandate but instead a
natural conclusion from the equations that result when the
principle of relativity is reconciled with our notions of distance
and causality. And although a great deal of time has elapsed since
the discovery of conic sections, they continue to reap benefits
today. For More Information: Practical Conic Sections: The
Geometric Properties of Ellipses, Parabolas and Hyperbolas, J. W.
Downs, 2010.