So what I REALLY "'STRICTLY "'want is a common name for disk, circle, ball, sphere, hyperball, hypersphere and perhaps even the 1D analogs of those things.
42.
Hyperbolic motions are often taken from inversive geometry : these are mappings composed of reflections in a line or a circle ( or in a hyperplane or a hypersphere for hyperbolic spaces of more than two dimensions ).
43.
"' Public hypersphere "', the new kind of " public sphere " that has come to existence globally through the use of modern information technology, digital media, and computer networks.
44.
Nonsimplicial facets only occur when " d " + 2 of the original points lie on the same " d "-hypersphere, i . e ., the points are not in general position.
45.
The first constraint defines the surface of a 3N-dimensional hypersphere of radius ( 2 " mU " ) 1 / 2 and the second is a 3N-dimensional hypercube of volume " V"
46.
In the same way the hyperspherical space of 3D rotations can be parameterized by three angles ( Euler angles ), but any such parameterization is degenerate at some points on the hypersphere, leading to the problem of gimbal lock.
47.
A particular case that has been studied is that in which the linear operator is an isometry " M " of the hypersphere ( written " S 3 " ) represented within four-dimensional Euclidean space:
48.
This behavior is matched by the set of unit quaternions : A general quaternion represents a point in a four dimensional space, but constraining it to have unit magnitude yields a three-dimensional space equivalent to the surface of a hypersphere.
49.
In computational geometry, the "'largest empty sphere "'problem is the problem of finding a hypersphere of largest radius in " d "-dimensional space whose interior does not overlap with any given obstacles.
50.
This behavior is matched by the set of unit quaternions : A general quaternion represents a point in a four-dimensional space, but constraining it to have unit magnitude yields a three-dimensional space equivalent to the surface of a hypersphere.
