Search results
Results From The WOW.Com Content Network
In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci F 1 {\displaystyle F_{1}} and F 2 {\displaystyle F_{2}} are generally taken to be fixed at − a {\displaystyle -a} and + a {\displaystyle +a} , respectively, on the x ...
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system (,,) that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces , the ellipsoidal coordinate system is based on confocal quadrics .
An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
Coordinate surfaces of elliptic cylindrical coordinates. The yellow sheet is the prism of a half-hyperbola corresponding to ν=-45°, whereas the red tube is an elliptical prism corresponding to μ=1. The blue sheet corresponds to z=1.
Ellipsoidal coordinates; Elliptical distribution, in statistics; Flattening, also called ellipticity and oblateness, is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid), respectively. Focaloid, a shell bounded by two concentric, confocal ellipsoids; Geodesics on an ...
In the spherical model, for example, a triangle can be constructed with vertices at the locations where the three positive Cartesian coordinate axes intersect the sphere, and all three of its internal angles are 90 degrees, summing to 270 degrees. For sufficiently small triangles, the excess over 180 degrees can be made arbitrarily small.
Then the K-rational points of E are the points on E whose coordinates all lie in K, including the point at infinity. The set of K -rational points is denoted by E ( K ) . E ( K ) is a group, because properties of polynomial equations show that if P is in E ( K ) , then − P is also in E ( K ) , and if two of P , Q , R are in E ( K ) , then so ...
The latter relations for the x- and y-coordinates of points on the unit ellipse may be considered as generalization of the relations = , = for the coordinates of points on the unit circle. The following table summarizes the expressions for all Jacobi elliptic functions pq(u,m) in the variables ( x , y , r ) and ( φ ,dn) with r = x 2 + y ...