Search results
Results from the WOW.Com Content Network
Paraboloidal coordinates are three-dimensional orthogonal coordinates (,,) that generalize two-dimensional parabolic coordinates.They possess elliptic paraboloids as one-coordinate surfaces.
Standard parallels at 33°45′N/S; parallels are unequal in spacing and scale; meridians are fourth-order curves. Distortion-free only where the standard parallels intersect the central meridian. 1937 1944 Quartic authalic: Pseudocylindrical Equal-area Karl Siemon Oscar S. Adams. Parallels are unequal in spacing and scale.
The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines (in the case of a section by a tangent plane). The paraboloid is elliptic if every other nonempty plane section is either an ellipse, or a single point (in the case of a section by a tangent plane). A paraboloid is either elliptic or hyperbolic.
The scale factors for the parabolic coordinates (,) are equal = = + Hence, the infinitesimal element of area is = (+) and the Laplacian equals = + (+) Other differential operators such as and can be expressed in the coordinates (,) by substituting the scale factors into the general formulae found in orthogonal coordinates.
Solid paraboloid of revolution around z-axis: a = the radius of the base circle h = the height of the paboloid from the base cicle's center to the edge Solid ellipsoid: a, b, c = the principal semi-axes of the ellipsoid
The paraboloid of revolution obtained by rotating the safety parabola around the vertical axis is the boundary of the safety zone, consisting of all points that cannot be hit by a projectile shot from the given point with the given speed.
Hyperbolic paraboloid A model of an elliptic hyperboloid of one sheet A monkey saddle. A saddle surface is a smooth surface containing one or more saddle points.. Classical examples of two-dimensional saddle surfaces in the Euclidean space are second order surfaces, the hyperbolic paraboloid = (which is often referred to as "the saddle surface" or "the standard saddle surface") and the ...
Bathymetric charts showcase depth using a series of lines and points at equal intervals, called depth contours or isobaths (a type of contour line). A closed shape with increasingly smaller shapes inside of it can indicate an ocean trench or a seamount, or underwater mountain, depending on whether the depths increase or decrease going inward.