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Home > Art, Film & Photography > Quadrics: Spheroid, Ellipsoid, Quadric, Hyperboloid, Paraboloid, Quadric, Cylinder, Hypercone, Conical Surface, Oblate Spheroid
Quadrics: Spheroid, Ellipsoid, Quadric, Hyperboloid, Paraboloid, Quadric, Cylinder, Hypercone, Conical Surface, Oblate Spheroid

Quadrics: Spheroid, Ellipsoid, Quadric, Hyperboloid, Paraboloid, Quadric, Cylinder, Hypercone, Conical Surface, Oblate Spheroid


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About the Book

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Spheroid, Ellipsoid, Quadric, Hyperboloid, Paraboloid, Quadric, Cylinder, Hypercone, Conical Surface, Oblate Spheroid, Prolate Spheroid, Klein Quadric. Excerpt: A circular conical surface In geometry, a ( general ) conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point the apex or vertex and any point of some fixed space curve the directrix that does not contain the apex. Each of those lines is called a generatrix of the surface. Every conic surface is ruled and developable . In general, a conical surface consists of two congruent unbounded halves joined by the apex. Each half is called a nappe, and is the union of all the half-lines that start at the apex and pass through a point of some fixed space curve. (In some cases, however, the two nappes may intersect, or even coincide with the full surface.) Sometimes the term "conical surface" is used to mean just one nappe. If the directrix is a circle C, and the apex is located on the circle's axis (the line that contains the center of C and is perpendicular to its plane), one obtains the right circular conical surface . This special case is often called a cone, because it is one of the two distinct surfaces that bound the geometric solid of that name. This geometric object can also be described as the set of all points swept by a line that intercepts a the axis line and rotates around it; or the union of all lines that intersect the axis at a fixed point p and at a fixed angle . The aperture of the cone is the angle 2 . More generally, when the directrix C is an ellipse, or any conic section, and the apex is an arbitrary point not on the plane of C, one obtains a conical quadric, which is a special case of a quadric surface . A cylindrical surface can be viewe...


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Product Details
  • ISBN-13: 9781155581705
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Spheroid, Ellipsoid, Quadric, Hyperboloid, Paraboloid, Quadric, Cylinder, Hypercone, Conical Surface, Oblate Spheroid
  • Width: 229 mm
  • ISBN-10: 1155581709
  • Publisher Date: 05 May 2010
  • Binding: Paperback
  • Spine Width: 3 mm
  • Weight: 95 gr


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