What is the shape of a completely flattened sphere?
102944
I think these answers are skating around what you really want. First, I don't think you mean stretch, so that it fits any shape.\n\nYou mean to 'unfold' the sphere after cutting it. Your mental imagry is a good way to see how the area of a sphere is calculated, but we wouldn't do it in a physical form since the sphere would not flatten nicely. So those who argue that it can't be done are missing the real advantage of what this question gets at. At least in my mind.\n\n\nAfter much messing around with this, the shape, after all the unfolding, is similar to two parabolas joined together.\n\nThe problem is that because the parabola like shapes don't quite make a parabola, the formulas don't quite work out. The area of a sphere is 4*pi*r^2.\n\nIf we consider them parabolas each has area (2*(pi*r)^2)/3 making the whole shape area (4*(pi*r)^2)/3. Of course this doesn't quite equal 4*pi*r^2.  Pi is roughly 3.14 and the denominator is 3. If they were to cancel in the equation, it would be correct.\n\nBecause the shapes are close, but not actual parabolas, finding the area will require calculus in order to establish that it equals 4*pi*r^2.\n\nIronically, you could use the ancient method of exhaustion to arrive at the area. I think Archimedes did this, but the method was developed by a man with your name :).\n\nHey, being a math major is useful after all.
51384
a torus or toroid. some postulate that the universe is in fact this shape
177456
Flat then you can make it curved
1011031
(m)\n\nno specific shape
316623
The most recent investigations (WMAP) about the shape (geometry) of our universe show that it is FLAT, meaning that it will expand infinitely, parallel lines never meet, etc.,.\n\nhttp://map.gsfc.nasa.gov/m_mm/mr_content.html
494502
This question is answered very well in solid geometry.\n\nOn a plane, it's a straight line.\n\nOn the surface of a sphere, it's a curved-line called a great circle.\n\nIn space, considering the curvature caused by the masses of any nearby bodies between you and the destination point, it may be a complex three-dimensional curve.
314905
Imagine a molten ball of liquid rock in space. It will take the shape of a sphere due to the gravitational pull - any other shape would be turned into a sphere by gravity over time. \n\nNow, set this sphere rotating. Due to centrifugal forces, the sphere will bulge slighty round its equator. There you have it, the shape of the Earth.
647673
Technically, it's flat, but it has a potrusion where it is separated from the vegetation at the top which looks like a point.\n\nhttp://www.vidaliaonion.org/
320204
That question makes no sense.  A ball, or sphere, is a 3-dimensional object.  A circle is a 2-dimensional object and doesn't exist in real life.  A ball is not a circle.
780074
Gravity and the spinning of the earth on it's axis... which gives you the one shape out of all possible shapes which allows for the greatest amount of surface area... the sphere.
592569
Spheroid, ovoid, globate, globular.  The most commonly used word would be egg-shaped, but I know what you mean-an egg isnt really oval, unless you are speaking about an ant egg.  I have seen ovoid used for this kind of shape more often than any other (besides "egg-shaped").\n\n*edit* an ellipsoid can also be a perfect sphere, depending on the axes.  The perfect description for a three-dimensional oval is a *prolate spheroid*, but I have never in my life heard the term until I went searching for the answer to this question.  If you follow the Wikipedia link on ellispoid to the bottom, you see that it descibes a wide range of 3D shapes, including spheres- The link to prolate spheroid shows a shape limited only to perfect 3D ovals.\n\nhttp://en.wikipedia.org/wiki/Spheroid
716964
A shape with minimum surface area for a given volume!...a round shaped ball-like mass would have minmum area of 4 pi r square for a volume 4/3 pi r cube !
465388
The Earth is round for the same reason that things don't fall off it.  Gravity is a force in the universe that attracts all forms of matter equally, this means that pieces of matter will eventually move together and form clumps, if this is happening from every direction then the most likely shape it will form is a sphere.\n\nThis gravitational attraction is pretty small.  However, the Earth is pretty big, so the combined effect of all that gravity is just enough to keep your feet firmly planted on the surface :)\n\nThere are a few other related effects that come into play, such as centrifugal force, which keeps everything spinning and moving.
266278
Oh yeah. Shape is everything. A sphere is the perfect shape for holding pressure. But the reason we dont see many spheres holding pressure is that they are also inconvenient in shape, so we have the next best thing - cylinders. LGP tanks, oxy tanks, scuba cylinders etc. Round sides even out the pressure, thats why you dont see square tanks. Also remember that when they test a tank for how well they hold pressure they fill it with water and pressurise the water, if you did this with just air, it will explode when the pressure gets too high. Thats called a hydraulic pressure test and it is marked on all pressure vessels. There is a test pressure and safe working pressure stamped in to all tanks.
1123910
Only "large" celestial objects are round. Small ones, like asteroids, can be any shape.\n\nIt is the high gravity of large objects that makes them round. As they accumulated from smaller pieces, any piece that was out of round was pulled by gravity "downhill" so the overall shape of the body is round.
431236
The celestial sphere is not a physical object but a virtual surface (an imaginary sphere, concentric and coaxial with the Earth) used by astronomers for projecting the positions of celestial objects. So, there is no definite radius, it is said to be "gigantic", just as wording convention to mean that it is big enough to contain the projection of whatever far object.\n\nLater addition: the parsec is defined by considering 1 sec parallax of an object seen from two opposite points of the Earth's orbit. So I suppose that in the parsec definition you have read, they used the wording "celestial sphere" meaning a sphere having the sun in the center and the Earth on its border. If this is true, your sphere has a radius of 1 AU (about 150 million km). But note that this is not the mainstream definition of celestial sphere.
202397
Presumably the mooon is approximately spherical for the same reason that the earth or other round celestial bodies are approximately spherical. Some comments: \n\n1. For solid bodies like the moon and the earth:\n\nThey probably formed as molten, self gravitating bodies, and the sphere is the minimum energy shape. If they rotate, hydrodynamic forces flatten them slightly, making the semimajor axis aligned with the axis of rotation shorter than the other two axes in general. \n\n2. For stars:\n\nAgain, the minimum energy configuration for many standard isolated stars is roughly spherical. If they are rotating, they might be oblate spheroids, but still close to spherical, as long as there are no other very massive bodies close to distort their shape. \n\n3. For nonspherical bodies like asteroids and comets:\n\nThese irregular chunks might have formed after some large body cooled, or not had sufficient mass for gravitational forces to constrain the shape to be spherical. \n\n4. For nonspherical stars:\n\nThere are many stars that are binaries, and the two stars are so close that their shapes are distorted (i.e., their Roche lobes are filled so they look like egg shapes, or they have accreation disks, etc). There might be other processes active that distort them away from spherical shapes. Even large close planets might distort their shapes in some cases.