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In mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone. It is the spherical analog of a conic section ( ellipse , parabola , or hyperbola ) in the plane, and as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of ...
Coordinate surfaces of the conical coordinates. The constants b and c were chosen as 1 and 2, respectively. The red sphere represents r = 2, the blue elliptic cone aligned with the vertical z-axis represents μ=cosh(1) and the yellow elliptic cone aligned with the (green) x-axis corresponds to ν 2 = 2/3.
If and are zero, then is the radius of curvature and is the conic constant, as measured at the vertex (where =). The coefficients α i {\displaystyle \alpha _{i}} describe the deviation of the surface from the axially symmetric quadric surface specified by R {\displaystyle R} and K {\displaystyle K} .
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The geometry of a toric lens focuses light differently in different meridians. A meridian, in this case, is a plane that is incident with the optical axis. For example, a toric lens, when rotated correctly, could focus an object to the image of a horizontal line at one focal distance while focusing a vertical line to a separate focal distance.
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In algebraic geometry, the conic sections in the projective plane form a linear system of dimension five, as one sees by counting the constants in the degree two equations. The condition to pass through a given point P imposes a single linear condition, so that conics C through P form a linear system of dimension 4.
Now, the closing of another Kansas City Express is underway. The final day at 429 Nichols Road on the Country Club Plaza will be July 28, an employee confirmed Wednesday. Till then, everything in ...
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