Nice! Is there a proof this short and simple that the ellipse defined by these definitions is related to a circle by an affine transformation? The algebrist's proof of this is that both are degree-two curves that don't intersect the line at infinity, but I don't see an easy geometrical proof. On Thu, Jul 16, 2015 at 2:30 PM, Allan Wechsler <acwacw@gmail.com> wrote:
My informal proof is that if the two angles were unequal, and you shifted the contact paint along the ellipse toward the smaller angle, you'd be making the distance shorter.
On Thu, Jul 16, 2015 at 2:10 PM, Dan Asimov <asimov@msri.org> wrote:
Good point.
If we define an ellipse by the locus of points whose sum-of-distances to two given points is a fixed constant, what is the shortest proof that these two segments make equal angles with the tangent line?
(Assuming the ellipse surrounds a positive area.)
—Dan
On Jul 16, 2015, at 10:52 AM, Tom Rokicki <rokicki@gmail.com> wrote:
Let's focus on the important points here. The elliptical table is what's interesting. I'm sure Alex is eccentric and this is reflected by his choice of adjectives, but let us put away the axes because we all know he's affine fellow.
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