Английская Википедия:Conic constant

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Ten different conic sections which open to the right from a common intersection point, at which point they have a common radius of curvature

An illustration of various conic constants

In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by <math display="block">K = -e^2, </math> where Шаблон:Math is the eccentricity of the conic section.

The equation for a conic section with apex at the origin and tangent to the y axis is <math display="block">y^2-2Rx+(K+1)x^2 = 0</math> alternately <math display="block"> x = \dfrac{y^2}{R+\sqrt{R^2-(K+1)y^2}}</math> where R is the radius of curvature at Шаблон:Math.

This formulation is used in geometric optics to specify oblate elliptical (Шаблон:Math), spherical (Шаблон:Math), prolate elliptical (Шаблон:Math), parabolic (Шаблон:Math), and hyperbolic (Шаблон:Math) lens and mirror surfaces. When the paraxial approximation is valid, the optical surface can be treated as a spherical surface with the same radius.

SomeШаблон:Which non-optical design references use the letter p as the conic constant. In these cases, Шаблон:Math.

References

• Шаблон:Cite book

Шаблон:Geometry-stub