Abstract
This chapter focuses on the general theory of quadric surfaces. The chapter discusses the transformation of rectangular coordinates in space, and reviews some general deductions based on the formulas for the transformation of coordinates. The chapter proves that if a surface is defined relative to some rectangular coordinate system by means of an algebraic equation of degree n, then relative to any other rectangular coordinate system it is again defined by an algebraic equation of degree n. The reduction to canonical form of the equation of a quadric with center at the origin is presented. Every quadratic form can be reduced to canonical form by a suitable orthogonal transformation of coordinates. The chapter reviews the invariants and classification of quadratic forms in three variables. A point S is called a center of a quadric if its equation relative to a rectangular coordinate system with origin at S contains no terms of the first degree.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
