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Tree ovals: mean - ellipse, gmean - Cassini oval & hmean - ???
Has the 3-d oval a name?
And what about Generalized mean?
Solution without animation is not solution!
Solved! Go to Solution.
For the hmean (d=-1) I think it is the Cayley oval!
https://mathcurve.com/courbes2d/cayleyovale/cayleyovale.shtml
d-ellipse
d=1 - normal ellipse
d=0 - Cassini oval
d=-1 - see above (hmean)
With 3 focu
Zoom - three petals of Bernoulli lemniscate
Ellipse and Kolmogorov's ellipse
An ellipse, a Cassini oval and Point oval
The end - we have three circles at d= -1 (the harmonic oval), d=-2 (no name) and d=-3 (no name too).
What curve we have at d=3? (d=2 - a circle, d=1 - an ellipse, d=0 - a Cassini oval)
4 foci, 7 ovals. d=3, 2 (circle), 1 (elipse), 0 (Cassini oval), -1 (my oval), -2, -3.
For the hmean (d=-1) I think it is the Cayley oval!
https://mathcurve.com/courbes2d/cayleyovale/cayleyovale.shtml