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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.
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
Taking as event p a flash of light (light pulse) at time t 0, all events that can be reached by this pulse from p form the future light cone of p, while those events that can send a light pulse to p form the past light cone of p. Given an event E, the light cone classifies all events in spacetime into 5 distinct categories:
The directrix of a conic section can be found using Dandelin's construction. Each Dandelin sphere intersects the cone at a circle; let both of these circles define their own planes. The intersections of these two parallel planes with the conic section's plane will be two parallel lines; these lines are the directrices of the conic section.
A chain hanging from points forms a catenary. The silk on a spider's web forming multiple elastic catenaries.. In physics and geometry, a catenary (US: / ˈ k æ t ən ɛr i / KAT-ən-err-ee, UK: / k ə ˈ t iː n ər i / kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field.
At moderate to bright light levels where the cones function, the eye is more sensitive to yellowish-green light than other colors because this stimulates the two most common (M and L) of the three kinds of cones almost equally. At lower light levels, where only the rod cells function, the sensitivity is greatest at a blueish-green wavelength.
The standard or unit second-order cone of dimension + is defined as + = {[] |,, ‖ ‖}. The second-order cone is also known by quadratic cone or ice-cream cone or Lorentz cone. ...