Technical Name Of Equatorially Concentric Rings?

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Discussion Overview

The discussion revolves around the terminology for equatorially concentric rings on a sphere, particularly in relation to polar concentric rings known as lines of latitude. Participants explore whether these equatorial rings have specific names and how they relate to concepts in spherical geometry.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that polar concentric rings are called "lines of latitude," but question what equatorially concentric rings are termed.
  • One participant suggests that circles on a sphere with the same radius as the sphere are called 'great circles,' which includes the equator and poles.
  • Another participant proposes that equatorial circles could be viewed as latitudes in a different coordinate frame, but notes that these circles do not have specific names in the context of a fixed pole system.
  • There is a suggestion that small circles parallel to a meridian might have a special name, similar to how small circles parallel to the equator are known as latitudes.
  • One participant argues that small circles parallel to a meridian do not have special names because they lack the invariance provided by Earth's rotation, which gives significance to lines of latitude.
  • Another participant introduces the concept of "orthodromic" surface area in contrast to "loxodromic" surface area, suggesting that this might be a relevant consideration in the discussion of equatorial rings.

Areas of Agreement / Disagreement

Participants express differing views on whether equatorially concentric rings have specific names and the significance of these rings compared to lines of latitude. The discussion remains unresolved regarding the terminology and relevance of these equatorial rings.

Contextual Notes

Participants mention concepts such as great circles, small circles, and surface area calculations, but there are no settled definitions or consensus on the terminology for equatorially concentric rings.

KMGC
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http://math2.org/cgi-bin/mmb/server.pl?action=image&msgid=62326&fname=ringname.gif

I know that polar concentric rings are known as "lines of
latitude" or parallels, but what are equatorially concentric rings
called?--e.g., the 90° equatorially concentric ring would be a line
of longitude or meridian, but what about the other, semi-circle
rings **parallel TO A MERIDIAN**?
In terms of arcradius/radius of curvature, the "perpendicular
meridian" value is known as the "normal": Is it that a meridian is
the "prime normal", equals the 90° normal; the parallel
semi-circle/ellipse 1° away is the 89° normal, 2° away is the 88°
normal, 3° away is the 87° normal, etc., in the same way that the
equator is the 0° latitude, 1° away is the 1° latitude, etc.?
Or, as an annulus is a band bounded by two concentric rings, could
all of the rings comprising the annulus be something like
"annulobes"?

_ _ _ _ ~Kaimbridge~
 
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Any circle on a sphere that has the same radius as the sphere itself is called a 'great circle'.

That covers all circles that go through BOTH poles and the equator (and a infinite number of 'uninteresting' examples).

Is that what you were thinking of?
 
In spherical geometry or trig you could just regard your "equatorial circles" as latitudes in a different coordinate frame with poles lying on the equator of the former frame. In a system where the poles are not movable, as on the rotating earth, those circles have no specific name. A circle on the surface of the Earth which is not a great circle is called a small circle. Thus all the lines of latitude except the equator are small circles. That goes for your "equatorial" frame too - your equator is a meridian in the old frame and all meridians are great circles.
 
Right, exactly.
But, just as the small circles parallel to the equator are known as latitudes, it would, likewise, seem that small circles parallel to a meridian have a special name--even if archaic.

_ _ _ _ ~Kaimbridge~
 
No because the only reason the small circles called latitudes have names is that the Earth rotates, and rotation keeps these small circles invariant. It doesn't keep any other small circles invariant, so there isn't any special reason to study them and so they have never been named.

Why should your equatorial small circles be special? What about the small circles around me?
 
Because, if you look at my last picture ("The Spherical Cases"), "LB" and "UB" are points on the sphere (usually defined as "angular distance from equator to point")--hence, they could also be described as a point on their respective "ring".
Or, in the case of a spheroid, integrating by "ring" and "AP" ("arc path"), a whole different surface area value is found--the "orthodromic" surface area, in contrast to the more popular Authalic ("loxodromic") surface area: Given the nature of geodesics, it would seem that my "orthodromic" surface area would be the proper geodetic model, since geodetic lines equal arc paths!

_ _ _ _ ~Kaimbridge~
 

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