Golden ellipse vs golden ratio

[Jennifer]

The golden ratio for rectangles is ~1.618. Does anyone know if this also applies to ellipses, or, if not, what the "ideal" ratio is for ellipses?

I am trying to help a friend design a piece of jewelry for his wife that involves a chain of linked ovals. He would like each of the ovals to have an "ideal" shape. I've asked several jewelers. They mostly just say "whatever looks good".

One had a template with about 40-50 ovals all with different dimensions. One of the ones he drew had a ratio of 1.538 (20 mm by 13 mm), slightly less than the golden ratio. Another had a ratio of 1.667 (20 mm by 12 mm), slightly more than the golden ratio.

I did a search for "golden ellipse", but didn't find anything definitive.

The default ellipse in Visio has a ratio of 1.5 (2.25" x 1.5"), which is slightly less than 1.618. It looks a little "fat" to my eye. I put two ellipses side by side. One was 1.000 x 1.500 and the other 1.000 by 1.618. The latter looks better to my eye.

PS: I know that this is a little out of the scope of the usual post, but I'm hoping someone has some insight.

PPS: I notice that the word "Visio" is flagged as a misspelled word. 

[wapperdude]

I've never heard on golden ratio applied to ellipse, just to a rectangle.   Since googling yields nothing kinda reinforces that point.  So, yeah, I think it's a matter of taste.  So, an ellipse with height to width= golden ratio..sure, why not?!?

[bmwk100dk]

Hi Jennifer
Intriguing question.
If you google golden ratio ellipse, I think you will find what you are looking for.https://www.google.com/search?q=golden+ratio+ellipse&safe=strict&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjBldyctJDiAhXNmIsKHdyfAAsQ_AUIDigB&biw=1635&bih=884 
Good luck with the design

bmwk100dk

[Jennifer]

I actually did find that page with all of the diagrams. But I didn't see any of them that recommended one ratio over another. I also found a bunch of pages that discuss the ideal ratio for an oval-cut diamond, but I didn't think that was particularly relevant

Here's a couple of interesting pages I just found:

This one appears to recommend the golden ratio, but is mostly doing an analysis of the mathematical properties.

https://www.fq.math.ca/Scanned/12-1/huntley1.pdf

This one doesn't mention the ratio, golden or otherwise, but as a wannabe woodworker, I found it interesting.

https://www.thisiscarpentry.com/2012/03/30/the-elegant-ellipse/

I guess I'll leave it up to the jewelry designer.