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Home > Art, Film & Photography > Birational Geometry: Conic Section, Enriques-Kodaira Classification, Blowing Up, Algebraic Curve, Surface of General Type, Flip
Birational Geometry: Conic Section, Enriques-Kodaira Classification, Blowing Up, Algebraic Curve, Surface of General Type, Flip

Birational Geometry: Conic Section, Enriques-Kodaira Classification, Blowing Up, Algebraic Curve, Surface of General Type, Flip


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 28. Chapters: Conic section, Enriques-Kodaira classification, Blowing up, Algebraic curve, Surface of general type, Flip, Kodaira dimension, Rational variety, Minimal model program, Elliptic surface, List of complex and algebraic surfaces, Cone of curves, Enriques surface, Rational surface, Rational normal curve, Canonical ring, Infinitely near point, Relative canonical model, Exceptional divisor, Iitaka dimension, Cremona group, Birational invariant, Cox-Zucker machine, Blowing down. Excerpt: In mathematics, a conic section (or just conic) is a curve obtained by intersecting a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2. It can be defined as the locus of points whose distances are in a fixed ratio to some point, called a focus, and some line, called a directrix. The three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section. The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their properties. It is believed that the first definition of a conic section is due to Menaechmus. This work does not survive, however, and is only known through secondary accounts. The definition used at that time differs from the one commonly used today in that it requires the plane cutting the cone to be perpendicular to one of the lines that generate the cone as a surface of revolution (a generatrix). Thus the shape of the conic is determined by the angle formed at the vertex of the cone (between two opposite generatrices): If the angle is acute then the conic is an ellipse; if the angle is right then the ...


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Product Details
  • ISBN-13: 9781155426242
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Weight: 73 gr
  • ISBN-10: 115542624X
  • Publisher Date: 29 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Conic Section, Enriques-Kodaira Classification, Blowing Up, Algebraic Curve, Surface of General Type, Flip
  • Width: 189 mm


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