Re: Questions inspired by reading Apollonius of Perga on Conic Sections
- From: Ken Pledger <ken.pledger@xxxxxxxxxxxxx>
- Date: Fri, 14 Jul 2006 11:42:02 +1200
In article <1152634908.433738.50320@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"tomhcmi" <tomhchappell@xxxxxxxxx> wrote:
In this message, I am _not_ restricting "curve" to mean "conic
section".
....
Definition: _conjugate_. A pair of axes of a curve are a pair of
_conjugate_ axes of that curve, if each of the axes in that pair
bisects every chord parallel to the other axis in the pair.
....
Question 4: Prove or give a counterexample; No axis can be conjugate to
both of two distinct other axes....
I've just realized that it's pretty obviously true. Each chord
parallel to your _first_ axis has a unique mid-point, so those
mid-points can't lie on two different lines.
Now I need some lunch. :-)
Ken Pledger.
.
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