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difference between equator & prime meridian

truthseeker613
Posts: 464
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12/2/2012 11:23:28 PM
Posted: 4 years ago
This is more of a philosophy of mathematics / astrology question:

Why is it that the central vertical line on the globe (prime meridian) is arbitrary, but the centeral horizontal line around the globe (i.e. equator) is not?

In other words if you have a sphere, with horizontal and vertical lines, only one (or 2) horizontal line(s) can be the/a center, but there is no center when it comes to vertical lines?
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Cody_Franklin
Posts: 9,483
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12/3/2012 12:14:44 AM
Posted: 4 years ago
At 12/2/2012 11:23:28 PM, truthseeker613 wrote:
This is more of a philosophy of mathematics / astrology question:

Why is it that the central vertical line on the globe (prime meridian) is arbitrary, but the centeral horizontal line around the globe (i.e. equator) is not?

In other words if you have a sphere, with horizontal and vertical lines, only one (or 2) horizontal line(s) can be the/a center, but there is no center when it comes to vertical lines?

That isn't really a philosophy question. If you think about it graphically, the equator is just the set of points corresponding to the single set of points constituting the circumference with reference to the axis of rotation. If you imagine jamming a toothpick through a ball of clay, the toothpick represents a y-axis in three-space. Going only up and down the y-axis, tracing the surface of the sphere, there is only one set of coordinates which could correspond to its circumference. By definition, an equator is the part of a manifold's surface which intersects with a plane intersecting the axis at a particular point--the center. So, you could draw a staggering number of circles around the surface of the earth; however, taking the largest possible circle (i.e., the circumference) with respect to movement up and down the y-axis, you only have one option, which is where the plane intersects the sphere. I.e., equator.

Consider:

http://www.google.com...

Toothpick is the y-axis, and the set of all points on the x/z axes (where y is zero, obviously) create a plane of infinite size. So, if you imagine the sphere here to be a globe, and I tell you to draw lines of longitude all the way down, you'll keep increasing in size until you draw a circle of maximum circumference. This circle is located at y = 0, i.e., the spot where the plane intersects the sphere, its center, and its axis.

tl;dr Based on the definition of "equator", it could not be otherwise.