what is the Circumference of a Great Circle of a Sphere?

Question

turingtest · Answer

what is the circumference of a regular circle?

anonymous · Answer

Just wondering....will it be set up as an integral?

anonymous · Answer

What is the Circumference of a Great Circle of a Sphere?

turingtest · Answer

no, I think this is just a straightforward geometry Q

turingtest · Answer

@MelanyN17 I read your question, can you answer mine?

anonymous · Answer

the circumference of a regular circle is: C=2(pi)r

turingtest · Answer

right
such is true for any circle, so a great circle is no different
the only thing we should perhaps point out is that r in this case is the radius of the sphere

anonymous · Answer

yes! it is! but i need to know What is the definition to the Circumference of a Great Circle of a Sphere?

turingtest · Answer

oh the definition, sorry :P

turingtest · Answer

the definition of a Great Circle is the largest circle that can be inscribed on the surface of a given sphere
for example, let's pretend what I'm about to draw is a sphere...

turingtest · Answer

|dw:1340289918780:dw|we can draw circles of various size on it....

anonymous · Answer

okay so i still don't get it

turingtest · Answer

that's cuz I'm not done explaining yet :)|dw:1340289943932:dw|these are like lines of latitude and longitude on the earth, but none of what I drew are great circles because they are not the $largest$ possible circle I can inscribe on the sphere

anonymous · Answer

:D haha okay!! sorry!!

turingtest · Answer

as opposed to|dw:1340290087478:dw|now these $are$ great circles (on the earth, though it is not a perfect sphere, the marked great circles on your globe of the earth would be the equator and the prime meridian

turingtest · Answer

how do we know that these are great circles?
1)their radius is the same as that of the sphere, which is not true in the earlier cases
2)they have the same center point as the sphere itself|dw:1340290262263:dw|

turingtest · Answer

any time we inscribe a circle on a sphere that has the same radius and center as the sphere, that is a great circle of that sphere

turingtest · Answer

you can also make them at an angle (there are infinitely many great spheres on a circle, not just the two I drew) but the drawing tool won't let me make angles ellipses very easily :(

turingtest · Answer

angled*

turingtest · Answer

|dw:1340290484936:dw|this is also a great circle (imagine it as pretty as the others; sorry I had to draw it freehand)