Search results
Results From The WOW.Com Content Network
A torus is an orientable surface The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. The Roman surface is non-orientable.. In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". [1]
Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it.. In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1]
Although this formula provides a closed expression for the surface area, for all but very special surfaces this results in a complicated double integral, which is typically evaluated using a computer algebra system or approximated numerically. Fortunately, many common surfaces form exceptions, and their areas are explicitly known.
The radial distance upward along the zenith–axis from the point of origin to the surface of the sphere is assigned the value unity, or 1. + In this image, r appears to equal 4/6, or .67, (of unity); i.e., four of the six 'nested shells' to the surface.
Assume that f is a scalar, vector, or tensor field defined on a surface S. To find an explicit formula for the surface integral of f over S, we need to parameterize S by defining a system of curvilinear coordinates on S, like the latitude and longitude on a sphere. Let such a parameterization be r(s, t), where (s, t) varies in some region T in ...
A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.
Principal curvature directions along with the surface normal, define a 3D orientation frame at a surface point. For example, in case of a cylindrical surface, by physically touching or visually observing, we know that along one specific direction the surface is flat (parallel to the axis of the cylinder) and hence take note of the orientation ...
The concept of orientation of a curve is just a particular case of the notion of orientation of a manifold (that is, besides orientation of a curve one may also speak of orientation of a surface, hypersurface, etc.). Orientation of a curve is associated with parametrization of its points by a real variable.