1) The semi-latus rectum can be geometrically interpreted as a line from a focal pt to the ellipse, drawn parallel to the minor axis. Five down, one to go:-)

2) I too couldn’t find (in the sense of “search”, not in the sense of “think hard” like Apollonius) a geometrical interpretation of the Quadratic mean of r1 and r2, though I suspect one exists.

3) A nice geometric interpretation of the six means – min, H, G, A, Q, & max – of two numbers, in the context of a circle rather than of a general ellipse, is at: http://en.wikipedia.org/w/index.php?title=File:MathematicalMeans.svg&page=1

4) Nothing major but the major you made minor should be major and the major you kept major should be minor:-)

And perhaps Florida in equal degree.

]]>Yes, I meant your polar coordinates. As one can see, my elliptology is nonexistent.

]]>Let be half the distance between the foci, the perihelion distance and the aphelion distance. Then the sum of distances to the foci at perihelion is , the sum of distances to the foci at aphelion is , and equating them gives us and .

When the planet lies on the minor axis, which bisects the line between the foci, by symmetry and Pythagoras the semi-minor axis is given by:

The nicest proof that the sum of the distances to the foci is constant involves the Dandelin spheres, and you can see it illustrated

here.

I’ll check that out and fix it if needed. Thanks!

]]>Thanks, very interesting. BTW an apparent typo in your original posting:

1) 2nd occurrence of “so the semi-major axis is”: change major to minor

Is your the same as my , i.e. the angle in polar coordinates centered at a focus of the ellipse? Or is it something else, like the angle in polar coordinates centered at the center of the ellipse? My elliptology is sort of rusty.

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