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Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
The slant height of a right circular cone is the distance from any point on the circle of its base to the apex via a line segment along the surface of the cone. It is given by r 2 + h 2 {\displaystyle {\sqrt {r^{2}+h^{2}}}} , where r {\displaystyle r} is the radius of the base and h {\displaystyle h} is the height.
An illustration of various conic constants. In geometry, the conic constant (or Schwarzschild constant, [1] after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K.
The hypervolume of a four-dimensional pyramid and cone is = where V is the volume of the base and h is the height (the distance between the centre of the base and the apex). For a spherical cone with a base volume of =, the hypervolume is
If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =. This may also be written as V = 2 π r 3 3 ( 1 − cos φ ) , {\displaystyle V={\frac {2\pi r^{3}}{3}}(1-\cos \varphi )\,,} where φ is half the cone angle, i.e., φ is the angle between the rim of the cap and the direction ...
The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A/2 and r = 1. The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ, is the area of a spherical cap on a unit sphere
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. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (1.26, -0.78, 1.34).
An elliptic cone, a special case of a conical surface In geometry , a conical surface is a three-dimensional surface formed from the union of lines that pass through a fixed point and a space curve .