The discussion revolves around the nature of quadratic equations involving three variables and their geometric interpretations, particularly in relation to conic sections and quadric surfaces. Participants explore whether a quadratic equation in three variables can be seen as representing a complete cone or if it describes other geometric forms.
Participants do not reach a consensus on whether a quadratic equation in three variables represents a complete cone, with multiple competing views presented regarding the nature of such equations and their geometric interpretations.
The discussion includes varying interpretations of terminology such as "quadratic equation" and "quadric surface," which may depend on specific definitions and contexts. There are also unresolved questions about the implications of having independent variables in quadratic equations.
Eventually. E.g. http://www.wolframalpha.com/input/?i=x^2+5y^2-3z^2=7 and https://en.wikipedia.org/wiki/QuadricLeo Authersh said:If a quadratic equation of two variables represents a conic section (planar intersection of a cone), then does a quadratic equation of three variables represent the complete cone?
No.Leo Authersh said:If a quadratic equation of two variables represents a conic section (planar intersection of a cone), then does a quadratic equation of three variables represent the complete cone?