APOD: Polar Ring Galaxy NGC 2685 (2014 Mar 14)

[Nitpicker]

football_shaped.png (3.59 KiB) Viewed 560 times

I did even less to turn your lens into a more realistic oval/lenticular football. But there is definitely still a need for the concept of the sharp lens shape, I just don't think it should be related to football.

(And owlice, I think you are right about lentils giving their name to the lens shape. Thank you for setting me straight.)

[Chris Peterson]

football_shaped.png

I did even less to turn your lens into a more realistic oval/lenticular football. But there is definitely still a need for the concept of the sharp lens shape, I just don't think it should be related to football.

(And owlice, I think you are right about lentils giving their name to the lens shape. Thank you for setting me straight.)

Note that either one of those shapes is quite correctly described as lenticular.

[Nitpicker]

football_shaped.png

I did even less to turn your lens into a more realistic oval/lenticular football. But there is definitely still a need for the concept of the sharp lens shape, I just don't think it should be related to football.

(And owlice, I think you are right about lentils giving their name to the lens shape. Thank you for setting me straight.)

Note that either one of those shapes is quite correctly described as lenticular.

Agreed. Also, the left one could be just as correctly described as oval, or an oval. And whilst oval and lenticular do not have precise definitions, lens does, and only the one on the right side is a lens.

[Chris Peterson]

Agreed. Also, the left one could be just as correctly described as oval, or an oval. And whilst oval and lenticular do not have precise definitions, lens does, and only the one on the right side is a lens.

Nope, both are lenses. Lenticular has a precise meaning: shaped like a lens. And when referring to shape, lens just means biconvex. There is no constraint on either symmetry or the structure of the intersection between the two curves (which need not be circular).

[Nitpicker]

Agreed. Also, the left one could be just as correctly described as oval, or an oval. And whilst oval and lenticular do not have precise definitions, lens does, and only the one on the right side is a lens.

Nope, both are lenses. Lenticular has a precise meaning: shaped like a lens. And when referring to shape, lens just means biconvex. There is no constraint on either symmetry or the structure of the intersection between the two curves (which need not be circular).

In that case, we are back to having no word for the shape of the intersection of two circles. But, nope, I think lens actually does have a precise meaning in a geometric context:
http://en.wikipedia.org/wiki/Lens_(geometry)

[Chris Peterson]

I think lens actually does have a precise meaning in a geometric context:
http://en.wikipedia.org/wiki/Lens_(geometry)

The existence of a very formal mathematical definition doesn't invalidate other, much more common definitions. Also useful, lens and lenticular are equally applicable to both 2D and 3D structures. So in the context of galaxies, they could refer to either the actual shape or to the shape in projection. (Of course, lenticular is also a galaxy classification, so there could be some confusion, given that many elliptical galaxies can be described geometrically as lenticular.)

[Nitpicker]

I think lens actually does have a precise meaning in a geometric context:
http://en.wikipedia.org/wiki/Lens_(geometry)

The existence of a very formal mathematical definition doesn't invalidate other, much more common definitions. Also useful, lens and lenticular are equally applicable to both 2D and 3D structures. So in the context of galaxies, they could refer to either the actual shape or to the shape in projection. (Of course, lenticular is also a galaxy classification, so there could be some confusion, given that many elliptical galaxies can be described geometrically as lenticular.)

It is no more formal than the definition of a square, circle, ellipse, rectangle, etc. I think the difference is that it is not as well known. See also:
http://mathworld.wolfram.com/Lens.html

Yes, "lens" certainly does have a few other meanings, but they are not relevant to my point in its context (which I didn't think I needed to explain, but it seems I did). I also think that "lenticular" and "shaped like a lens" are somewhat more relaxed descriptions than the geometric shape that is the "lens".

[Nitpicker]

Nothing to do with footballs or galaxies, just geometry ...

I must admit that, because of its other, less precise meanings, "lens" is not a brilliant name for the precise shape formed by the intersection of two planar circles. And aside from the two links I've already posted, I can't find much evidence of its use in this precise geometric way. Without concocting an ugly monster like "bi-circular-segment", I think we are only left with vesica piscis or mandorla, both of which are ancient words with religious origins, but which may be applied with validity to any intersection of two circles of the same radius. Given the choice, I would go for mandorla, as it is shorter and I like almonds more than fish guts. By extension, if the arcs had different radii, it could be called an asymmetric mandorla. Mandorla, mandorla, mandorla. I quite like it. Can anyone suggest a suitable adjective for mandorla, or even a name for a 3-D variant, which would be a volume or revolution about the radical axis (the line joining the pointy ends), not lenticular in 3-D?

[Nitpicker]

But back to footballs ... neither the 2-D nor 3-D variant of mandorla is suggested as a replacement for "football shaped", unless you specifically mean the precise shape of the mandorla. The term "football shaped", if it must be used, is best reserved for an intentionally loose description of an elongated circle or sphere. I still hold "oval" (a loose term in 2-D and 3-D) to be preferable to "football shaped" and in 2-D, it is even inclusive of lenticular shapes (no 3-D football could be correctly described as lenticular [well, maybe a partially deflated Soccer ball]).