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Tree ovals - mean, gmean & hmean

ValeryOchkov
24-Ruby IV

Tree ovals - mean, gmean & hmean

Tree ovals: mean - ellipse, gmean - Cassini oval & hmean - ???

Has the 3-d oval a name?

And what about  Generalized mean?

Tree-Ovals-5cm.png

Tree-Ovals-3cm.png

Tree-Ovals-2-25cm.png

Tree-Ovals-2cm-Lemniscate of Bernoulli.png

Tree-Ovals-1-5cm.png

Solution without animation is not solution!

Tree-Ovals.gif

 

1 ACCEPTED SOLUTION

Accepted Solutions
MaxNori
5-Regular Member
(To:ValeryOchkov)

20 REPLIES 20

d-ellipse

d=1 - normal ellipse

d=0 - Cassini oval

d=-1 - see above (hmean)

Mean.png

n-ellipse.gif

With 3 focu

3-ellipse.gif

Zoom - three petals of Bernoulli lemniscate

3-ellipse-1.gif

One more animation - new lemniscates!

d-lemniscate.gif

Ellipse and Kolmogorov's ellipse

MeanKolmExp.gif

 

An ellipse, a Cassini oval and Point ovalAn ellipse, a Cassini oval and Point oval

2 foci and 7 Ovals - only rigth part.

2-Od.gif

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)

2-Od-r.gif

4 foci, 7 ovals. d=3, 2 (circle), 1 (elipse), 0 (Cassini oval), -1 (my oval), -2, -3.

4-foci-7-curves.gif

Nice too

4-HO.png

Wolfram Alpha 

Can you do it with more than 4 foci - 5, 6, 7 Etc

Seven ovals - d = 3, 2, 1, 0, -1, -2 & -3 - 4 foci

5-ellipse-OC-HO.gif

New new ovals mean, gmean and hmean(L1, 2 L2)

L-2L.gif

Triple lemniscate

3-foci-.gif

4-foci-.gif

Exponentiation oval

d-ovals-power.gif

5-ellipse-OC-HO.gif

MaxNori
5-Regular Member
(To:ValeryOchkov)

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

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

 

triginimetric ovalstriginimetric ovals

Exponential ovalsExponential ovals

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