hypersphere love

# hypersphere

## Definitions

### 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.

• noun geometry The set of all points in a given hyperspace that 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.

hyper- + sphere

## Examples

• 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.

What’s the (Dark) Matter? John 2008

• Make arbitrary Earth-style coordinates for a hypersphere.

A Dark, Misleading Force Sean 2007

• ~ 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.

Orphans of Chaos 2005

• For a moment, I gave off a shaking shock wave similar to what the hypersphere had done; but something was carried with it.

Orphans of Chaos 2005

• The shock waves the hypersphere gave off were only "sound" along one surface (hypersurface?) of the concentrically expanding ripples of pressure.

Orphans of Chaos 2005

• She never heard the ringing in a locked safe of the hypersphere shaking from the shock of the music of a siren.

Orphans of Chaos 2005