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Best answer by MaxNori

For the hmean (d=-1) I think it is the Cayley oval! 

https://mathcurve.com/courbes2d/cayleyovale/cayleyovale.shtml

 

4 replies

24-Ruby IV
December 5, 2020

d-ellipse

d=1 - normal ellipse

d=0 - Cassini oval

d=-1 - see above (hmean)

Mean.png

n-ellipse.gif

24-Ruby IV
December 6, 2020

With 3 focu

3-ellipse.gif

24-Ruby IV
December 7, 2020

Zoom - three petals of Bernoulli lemniscate

3-ellipse-1.gif

24-Ruby IV
December 8, 2020

One more animation - new lemniscates!

d-lemniscate.gif

24-Ruby IV
January 3, 2021

Exponentiation oval

d-ovals-power.gif

24-Ruby IV
January 4, 2021
MaxNori10-MarbleAnswer
10-Marble
January 13, 2021

For the hmean (d=-1) I think it is the Cayley oval! 

https://mathcurve.com/courbes2d/cayleyovale/cayleyovale.shtml

 

24-Ruby IV
January 14, 2021

triginimetric ovalstriginimetric ovals

24-Ruby IV
January 14, 2021

Exponential ovalsExponential ovals