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Topic: History
Number of pages / Number of words: 2 / 415
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(1) Real ellipsoid x /a +y /b +z /c =1

(2) Imaginary ellipsoid x /a +y /b +z /c =-1

(3) Hyperboloid of one sheet x /a +y /b -z /c =1

(4) Hyperboloid of two sheets x /a +y /b -z /c =-1

(5) Real quadric cone x /a +y /b -z /c =0

(6) Imaginary quadric cone x /a +y /b +z /c =0

(7) Elliptic paraboloid x /a +y /b +2z=0

(8) Hyperbolic paraboloid x /a -y /b +2z=0

(9) Real elliptic cylinder x /a +y /b =1

(10) Imaginary elliptic cylinder x /a +y /b =-1

(11) Hyperbolic cylinder x /a -y /b =1

(12) Real intersecting planes x /a -y /b =0

(13) Imaginary intersecting planes x /a +y /b =0

(14) Parabolic cylinder x +2y=0

(15) Real parallel planes x =1

(16) Imaginary parallel planes x =-1

(17) Coincident planes x =0

The five nondegenerate real quadrics

Figure 1: The ellipsoid (1)...


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(1) Real ellipsoid x /a +y /b +z /c =1

(2) Imaginary ellipsoid x /a +y /b +z /c =-1

(3) Hyperboloid of one sheet x /a +y /b -z /c =1

(4) Hyperboloid of two sheets x /a +y /b -z /c =-1

(5) Real quadric cone x /a +y /b -z /c =0

(6) Imaginary quadric cone x /a +y /b +z /c =0

(7) Elliptic paraboloid x /a +y /b +2z=0

(8) Hyperbolic paraboloid x /a -y /b +2z=0

(9) Real elliptic cylinder x /a +y /b =1

(10) Imaginary elliptic cylinder x /a +y /b =-1

(11) Hyperbolic cylinder x /a -y /b =1

(12) Real intersecting planes x /a -y /b =0

(13) Imaginary intersecting planes x /a +y /b =0

(14) Parabolic cylinder x +2y=0

(15) Real parallel planes x =1

(16) Imaginary parallel planes x =-1

(17) Coincident planes x =0

The five nondegenerate real quadrics

Figure 1: The ellipsoid (1)...


Essay fragment

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