Search results
Results From The WOW.Com Content Network
Some points on the torus have positive, some have negative, and some have zero Gaussian curvature. In differential geometry , the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures , κ 1 and κ 2 , at the given point: K = κ 1 κ 2 . {\displaystyle K ...
The curvature is taken to be positive if the curve turns in the same direction as the surface's chosen normal, and otherwise negative. The directions in the normal plane where the curvature takes its maximum and minimum values are always perpendicular, if k 1 does not equal k 2, a result of Euler (1760), and are called principal directions.
If it is positive then the graph has an upward concavity, and, if it is negative the graph has a downward concavity. If it is zero, then one has an inflection point or an undulation point. When the slope of the graph (that is the derivative of the function) is small, the signed curvature is well approximated by the second derivative.
A phoropter measurement of a patient reads −8.00 D sphere and −5.25 D cylinder with an axis of 85° for one eye (the notation for which is typically written as −8 −5.25×85). The phoropter measurement is made at a common vertex distance of 12 mm from the eye.
Cylindrical coordinates are useful in connection with objects and phenomena that have some rotational symmetry about the longitudinal axis, such as water flow in a straight pipe with round cross-section, heat distribution in a metal cylinder, electromagnetic fields produced by an electric current in a long, straight wire, accretion disks in ...
Green line has two intersections. Yellow line lies tangent to the cylinder, so has infinitely many points of intersection. Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3d space. An arbitrary line and cylinder may have no intersection at all.
Bessel functions for integer are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer α {\displaystyle \alpha } are obtained when solving the Helmholtz equation in spherical coordinates .
the most negative values of in a liquid flow can be summed to the cavitation number to give the cavitation margin. If this margin is positive, the flow is locally fully liquid, while if it is zero or negative the flow is cavitating or gas.