The Collaborative International Dictionary
hypersphere \hy"per*sphere\ (h[imac]"p[~e]r*sf[=e]r), n. 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.
Wiktionary
n. 1 (context geometry English) The set of all points in a given hyperspace that are at a given distance from a given point. 2 (context sports English) A zorb; the act of zorbing, entering a zorbing ball, strapping into a harness, and rolling down a hill.
Wikipedia
In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center. It is a manifold of codimension one (i.e. with one dimension less than that of the ambient space). As the radius increases the curvature of the hypersphere decreases; in the limit a hypersphere approaches the zero curvature of a hyperplane. Hyperplanes and hyperspheres are examples of hypersurfaces.
The term hypersphere was introduced by Duncan Sommerville in his discussion of models for non-Euclidean geometry. The first one mentioned is a 3-sphere in four dimensions.
Some spheres are not hyperspheres: suppose S is a sphere in E where and the space had n dimensions, then S is not a hypersphere. Similarly, any n-sphere in a proper flat is not a hypersphere. For example, a circle is not a hypersphere in three-dimensional space, but it is a hypersphere in the plane.
Usage examples of "hypersphere".
And then -- pop -- the little bubble that had been the normal world winked out of view, and Phil was alone in the hypersphere of the powerball.
Any signals he could send would circle around and around his hypersphere just like the rays of light.
He was still in a hypersphere, only it was six or seven times bigger than before.
Phil and the dog drifted around the whole hypersphere, coming to rest back at the splintered base of the oak tree with the others.
After a few minutes he came back inside the hypersphere looking very jangled.
They tripped a destruct sequence and another hypersphere of radiation blossomed beneath the skein.
The circular band of images collected by one probe as it completed one orbit of the hypersphere amounted to less than a pinprick, and even when the orbit was swept 360 degrees around the star, the sphere it traced out was about as significant, proportionately, as one shot of one location on an ordinary globe.
My belief is that though the Greater Universe may be a closed and finite hypersphere, it is not expanding, but static.
Any five points can be found on the surface of a four-dimensional hypersphere, and so on.
So, just after the Romulan War, the Starfleet Bureau of Standards and the Vulcan Science Academy arbitrarily chose the center of our galaxy as the center point of a hypersphere with .
You have bent time and space around a mass to create a hypersphere, a miniature universe.
He remembered once again how Kingsley and Tommy had gone out to the edge of the universe to create a huge bubble of space-time, warping the rim of space into a hump, curving the time-space continuum into a hypersphere that finally closed and divorced itself from the parent body, pinching off like a yeast bud to become an independent universe in the inter-space.
His exoself responded to the command, spinning his balls into hyperspheres, rebuilding his retinas as four- dimensional arrays, rewiring his visual cortex, boosting his neural model of the space around him to encompass five dimensions.
I was seeing cross sections of my body, and I saw a whole lot of different spheres that must have been sections of this hypersphere.
Caroline’s hyperspheres might take care of the energy, but we can’t be sure.