There are 360 deg in a circle, so how do you measure a sphere?

Question

Is there such a thing as square degrees, or am I asking the wrong question?

Answer 1

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Circle Formulas




Circumference = 2 • p • radius = p • diameter

Circle Area = p • r² = ¼ • p • d²

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Sphere Formulas


Sphere Surface Area = 4 • p • r² = p • d²

Sphere Volume = 4/3 • p • r³ = ( p • d³)/6

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Cylinder Formulas




Surface Area = (2 • p • r²) + (2 • p • r • height)
Where (2 • p • r² ) is the surface area of the "ends" and
(2 • p • r • height) is the lateral area (the area of the "side").

Volume = p • r² • height = ¼ • p • d² • height

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Answer 2

Solid angles are measured in steradians. Mind you, angles are also measures in radians, that is the only defintion that makes sense from a mathematical point of view. Degrees are a convenience.

But you can still measure a spere using degrees. If you check a GPS unit, you first poition yourself around the Earth through longitude, whcih goes 360 degree (actually, they like to go 180 degree east, and 180 degree west). Once you know where you are as if you were standing on the equator, then you move north or south through latitude (90 degrees north or 90 degrees south). Why not 180 North? Because you'd be coming down the other side, having passed beyond the pole.

Since Earth is essentially spherical, this system can be used for any sphere. So, you measure position by using two systems of coordiantes in degree instead of one.

But back to the measurment of a spere. There are 4 PI steradians in a sphere; so this is indeed some sort of analogue to a "square degree".

Answer 3

None of the above answers are entirely correct and neither is your question very clear.

1. There are not necessarily 360 deg in a circle. There are as many as you like. You could have 240 deg in a circle if you wished.
2. There are exactly 2*pi radians in a circle. Radian measure is true circular measure.
3. The SI unit of solid angle that, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere. There are 4 steradians in a sphere.

Answer 4

Let's start with a circle. If you measure the distance along the edge of the circle and use that as you measurement of an angle you will find that we have a concept that we scale up to a solid circle, i.e. a sphere.
So if one measures the circumerfence of a circle, one gets 2pi as the circumference of a circle with unit radius.

So If we express our angles this way, we are basically saying that this angle is an angle such that the distance along the circumference is this much.

For example an angle of pi/2 "radians" is an angle that gives us pi/2 distance along the circumference.

NOW, let's scale this up one dimension.
If we have an angle at the centre of a sphere it will create a conical thingy that ends in a circle on the surface of the sphere. This would have a surface area that is some proportion of the surface of the entire sphere.

A unit sphere (sphere with radius == 1) will have a surface area of 4pi (square units) This angle is called 4pi steradians (stere meaning solid or three dimensional).

So lesser sized cones that subtend less of the surface area of the unit sphere have their angles named by the surface area they subtend on the surface -would be a range of 0, to 2pi (for half the sphere) to 4pi for all the sphere.

I don't know if anyone ever relates this back to "degrees", so I probably have not justified myself as I have not been able to relate the measurement of solid angles to degrees, only to steradians

Answer 5

No, longitude and latitude are the best of options. The circle is 360 degrees on a FLAT PLANE but a sphere is 3D and borderless(you can only make tangents) so there would absolutely be no square degrees. You measure a sphere by volume, area, and distance between 2 points on it's surface. No square degrees here.

Answer 6

You are asking a legitimate question.
It comes down to that you want to know
the solid angle of a sphere in square degrees.
Solid angle is an angular measure
on a sphere like an arc is an angular measurement
on a circle.

The best way to go about an answer is starting with
more natural units.

For a circle, Integrate around the circle at fixed
radius from 0 to 2pi to get the simple answer of
2pi radians. Convert to degrees (multiply by 180/pi)
to get 360 degrees.

For a sphere (fixed radius) you integrate the 3d
surface element, d(cos(theta))d(phi) where cos(theta) is from
-1 to 1 and phi is from 0 to 2pi. Then you get a surface
measurement of 4pi steradians and to convert to
sq degrees (180/pi)^2 you get

41252.96 square degrees

Note that sq. degrees is an unusual unit (most people
use the steradian). But it is legitimate.

Answer 7

You would need two circles to measure points on a sphere. On Earth, we have latitude and longitude. Star Trek geeks would use Bearing and Mark. Points in space (consider it a celestial sphere) are measured by Right Ascension and Declination. In this regard, square degrees are used to measure the relative size of constellations.

Answer 8

You can measure a circle by degrees, or coordinates x (say, length),y (say, width) along the two dimensions of a circle. You measure a point on a sphere with three coordinates x, y, z (say, depth). The units of measurement could be degrees, radians, or some other distance of measurement, so long as it is consistent.

Answer 9

Any sphere still has 360 Deg radius. If I recall, to measure a sphere you first have to identify a 'plane' and then you can calculate away.

Now, this may be in basic geometry and there are some advanced calcualtions that will do more...

Answer 10

When astonomers look at the sky it can be viewed as a sphere. When locating a star they use what is known as right accension and angle of declanation. I do not believe there is such thing as square degrees.