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Tree ovals - mean, gmean & hmean

SOLVED
ValeryOchkov
Ruby I

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

Re: Tree ovals - mean, gmean & hmean

20 REPLIES 20

Re: Tree ovals - mean, gmean & hmean

d-ellipse

d=1 - normal ellipse

d=0 - Cassini oval

d=-1 - see above (hmean)

Mean.png

n-ellipse.gif

Re: Tree ovals - mean, gmean & hmean

With 3 focu

3-ellipse.gif

Re: Tree ovals - mean, gmean & hmean

Zoom - three petals of Bernoulli lemniscate

3-ellipse-1.gif

Re: Tree ovals - mean, gmean & hmean

One more animation - new lemniscates!

d-lemniscate.gif

Re: Tree ovals - mean, gmean & hmean

Ellipse and Kolmogorov's ellipse

MeanKolmExp.gif

 

Re: Tree ovals - mean, gmean & hmean

Re: Tree ovals - mean, gmean & hmean

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

Re: Tree ovals - mean, gmean & hmean

2 foci and 7 Ovals - only rigth part.

2-Od.gif

Re: Tree ovals - mean, gmean & hmean

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

Tags (1)

Re: Tree ovals - mean, gmean & hmean

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

4-foci-7-curves.gif

Re: Tree ovals - mean, gmean & hmean

Nice too

4-HO.png

Wolfram Alpha 

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

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

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

5-ellipse-OC-HO.gif

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

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

L-2L.gif

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

Triple lemniscate

3-foci-.gif

Re: Three ovals - d = 1, 0, -1, - 4 foci

4-foci-.gif

Re: Tree ovals - mean, gmean & hmean

Exponentiation oval

d-ovals-power.gif

Re: Tree ovals - mean, gmean & hmean - 5 foci

5-ellipse-OC-HO.gif

Re: Tree ovals - mean, gmean & hmean

Re: Tree ovals - mean, gmean & hmean

triginimetric ovalstriginimetric ovals

Re: Tree ovals - mean, gmean & hmean

Exponential ovalsExponential ovals

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