Analytical Quadrics
Published on 10. July 2014
146 pages
978-1-4831-3829-9 (ISBN)
Description
Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordinates. Concerns include intersection of three planes; circular sections of central quadric; straight line; and circle at infinity. The book also discusses general quadric and classification and reduction of quadric. Discussions also focus on linear systems of quadrics and plane-coordinates. The text is a valuable reference for readers interested in the analytical geometry of three dimensions.
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B. Spain | Ian N. Sneddon
Analytical Quadrics
Book
01/1960
Reader's Digest Young Families
€60.23
Article exhausted; check different version
Content
ContentsI. Introduction1. Point Coordinates 2. Distance Between Two Points 3. Joachimsthal's Section Formula 4. Direction-Cosines 5. Direction-Ratios 6. Angle Between Two Straight Lines 7. Projections II. Plane-Straight Line8. Equation of A Plane 9. Equations of A Straight Line 10. Straight Line and Plane 11. Sign of the Expression u = ¿x + µy + vz + ¿12. Distance From A Point to A Plane 13. Pair of Planes 14. Bundle of Planes 15. Shortest Distance Between Two Skew Lines 16. Coplanar Lines 17. Rectangular Axes Related to Two Skew Lines III. Sphere18. Equation of Sphere 19. Conjugate Points 20. Pole and Polar 21. Tangent Plane and Normal Line 22. Angle of Intersection of Two Spheres 23. Radical Plane 24. Coaxal Spheres IV. Quadric Cone-Cylinder25. Quadric Cone 26. Cone With Vertex At The Origin 27. Circular Cone 28. Conditions That ¿(x,y,z) Be A Circular Cone 29. Angle Between Two Generators 30. Reciprocal Cone 31. Rectangular and Orthogonal Cones 32. Quadric Cylinder V. Central Quadric33. Central Quadric 34. Ellipsoid 35. Hyperboloid of One Sheet 36. Hyperboloid of Two Sheets 37. Polar Properties 38. Generators 39.Generators of Hyperboloid of One Sheet40.Normals41.Centre of A Section42.Axes of Central Plane Section43.Axes of Non-Central Plane SectionVI. Paraboloid44.Paraboloid45.Polar Properties46.Generators47.Generators of Hyperbolic Paraboloid48.Normals49.Centre of A Section50.Axes of Plane SectionVII. Homogeneous Coordinates51.Homogeneous Coordinates52.Point At Infinity53.Straight Line54.Plane55.Intersection of Three Planes56.Circle At Infinity57.Circular Sections of Central Quadric58.ParaboloidVIII. General Quadric59.Quadric60.Cofactor Notation61.Conjugate Points62.Pole and Polar63.Tangent Plane64.Enveloping Cone65.Generators66.Polar of A Line67.Conjugate Lines68.Conjugate Diameters69.Principal Diametral Planes70.Discriminating Cubic71.Circular Sections72.Rank of Matrix ¿IX. Transformation of Axes-Invariants73.Translation of Axes74.Invariants of A Quadratic Form Under Translation75.Rotation of Axes76.Invariants of Quadratic Form Under Rotation77.General Transformation of CoordinatesX. Classification and Reduction of Quadric78.Equation of Quadric79.Classification of Quadrics80.Central Quadric and Cone81. Paraboloid 82. Elliptic and Hyperbolic Cylinder 83. Parabolic Cylinder and Parallel Plane-Pair XI. Foci-Confocals84. Focus 85. Foci of Central Quadric 86. Foci of Paraboloid 87. Confocal Central Quadrics 88. Confocal Paraboloids XII. Linear Systems of Quadrics89. Pencil of Quadrics90. Self-Polar Tetrahedron of A Pencil of Quadrics 91. Contact of Quadrics 92. Associated Points XIII. Plane-Coordinates93. Plane-Coordinates 94. Principle of Duality 95. Quadric Envelope 96. Conic 97. Cone 98. Joachimsthal's Quadratic Equation 99. Range of Quadrics 100. Confocal Quadrics AppendicesI. Matrices II. Solutions Index
