| If you slice a cone at a diagonal, you get an
ellipse:
Here's what geometrically makes an ellipse an
ellipse:
You start with the two green dots...
So, if you put two nails on a board
and put a loop of string around them...
You can draw a perfect ellipse!
Just keep the string pulled tightly.
Think
about it... That loop of string will always be the same length -- won't
it? That's what makes an
ellipse! By the way, those
green dots are called foci (the plural for focus -- it's one of those
pretentious math words that make geeks feel superior.)
These points are pretty dang
important!
In fact, our Sun lives at a
focus... All the planets orbit the Sun in elliptical paths.
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Notice how the Earth speeds up a bit when
it gets closer to the Sun?
Coooooool! (Actually, it wouldn't be
since you're closer to the Sun.)
(I exagerated this animation quite a bit
too make my point. Although our orbits are ellipses, they are much
closer to being circles.) |
I know you're pretty dang jazzed
about ellipses already (and, really, who can blame you), but, there's
more! These things have
some totally amazing reflective properties!
Check
it out: If we shoot rays
(like maybe light or sound) from one focus...
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They shoot out, reflect off the inside of
the ellipse and head straight for the other focus!
Repeat after me: Duuuuuuuuuuuude! |
This is pretty useful too --
especially with ellipsoids (3-D ellipses).
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Here's an ellipsoidal reflector spotlight. |
And what about reflecting sound?
Some
science museums have what's called "whisper rooms." The ceiling
is an ellipsoid...
If you stand at one focus... and
whisper... someone standing at the other focus will be able to hear you
over a noisy crowd!
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