from The American Heritage® Dictionary of the English Language, 5th Edition.
- noun Any of a set of objects resulting from the generalization of a two-dimensional circle and a three-dimensional sphere to n dimensions. In n-dimensional space, a hypersphere is the set of all points that are a given distance, called the radius, from a given point, called the center.
from The Century Dictionary.
- noun Equidistantial surface.
- noun In four-dimensional space, the three-dimensional quadric spaces through the intersection of X5 = 0 and where is a three-dimensional space which is met by any line of S4 in two points.
from the GNU version of the Collaborative International Dictionary of English.
- noun A mathematical object existing in more than three dimensions, analogous to the sphere in that all points on the surface are equidistant from the central point; a generalization of a sphere in more than three dimensions.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun geometry The set of all points in a given
hyperspacethat are at a given distance from a given point.
- noun sports A
zorb; the act of zorbing, entering a zorbing ball, strapping into a harness, and rolling down a hill.
from Wiktionary, Creative Commons Attribution/Share-Alike License
Sometimes the term hypersphere is used to denote the hypersolid, the portion of four-space inclosed by this locus, which is then called the boundary or hypersurface of the hypersphere.
Either that or it has something to do with the hypersphere as described by Poincaré, making the universe finite but unbounded.
Its probably more like a finite hypersphere 4-dimensional sphere-like-thing.
It is relevant to discussions between Sam, myself, Lawrence, John, and a few others earlier in the thread, considering a hypersphere universe and the merging of GR/SR/QM.
Make arbitrary Earth-style coordinates for a hypersphere.
~ Also from Joe: Kosmic Coordinates on the Kronos mandala or, the birth of a hypersphere.
If the mansion stood on a hypersphere slightly greater in diameter than the mansion grounds, a person could move from any point to any other with what, in three-space, would seem to be right angles.
For a moment, I gave off a shaking shock wave similar to what the hypersphere had done; but something was carried with it.
The shock waves the hypersphere gave off were only "sound" along one surface (hypersurface?) of the concentrically expanding ripples of pressure.
She never heard the ringing in a locked safe of the hypersphere shaking from the shock of the music of a siren.