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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.
Menaechmus (Greek: Μέναιχμος, c. 380 – c. 320 BC) was an ancient Greek mathematician, geometer and philosopher [1] born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the ...
The solution of the Kepler problem in a space of uniform positive curvature is a spherical conic, with a potential proportional to the cotangent of geodesic distance. [ 5 ] Because it preserves distances to a pair of specified points, the two-point equidistant projection maps the family of confocal conics on the sphere onto two families of ...
In enumerative geometry, Steiner's conic problem is the problem of finding the number of smooth conics tangent to five given conics in the plane in general position. If the problem is considered in the complex projective plane CP 2 , the correct solution is 3264. [ 1 ]
Any plane section of an elliptic cone is a conic section. Obviously, any right circular cone contains circles. This is also true, but less obvious, in the general case (see circular section). The intersection of an elliptic cone with a concentric sphere is a spherical conic.
In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides easy ways to calculate a conic section's axis , vertices , tangents and the pole and polar relationship between points and lines of the plane determined by the conic.
More generally, when the directrix is an ellipse, or any conic section, and the apex is an arbitrary point not on the plane of , one obtains an elliptic cone [4] (also called a conical quadric or quadratic cone), [5] which is a special case of a quadric surface.
According to the definition of a parabola as a conic section, the boundary of this pink cross-section EPD is a parabola. A cross-section perpendicular to the axis of the cone passes through the vertex P of the parabola. This cross-section is circular, but appears elliptical when viewed obliquely, as is
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