Editing Algebraic geometry (section)

=== Zeros of simultaneous polynomials ===
[[File:Slanted circle.png|thumb|right|Sphere and slanted circle]]
In classical algebraic geometry, the main objects of interest are the vanishing sets of collections of [[polynomial]]s, meaning the set of all points that simultaneously satisfy one or more [[systems of polynomial equations|polynomial equations]]. For instance, the [[N-sphere|two-dimensional]] [[sphere]] of radius 1 in three-dimensional [[Euclidean space]] '''R'''<sup>3</sup> could be defined as the set of all points <math>(x, y, z)</math> with

:<math>x^2+y^2+z^2-1=0.\,</math>

A "slanted" circle in '''R'''<sup>3</sup> can be defined as the set of all points <math>(x, y, z)</math>  which satisfy the two polynomial equations

:<math>x^2+y^2+z^2-1=0,\,</math>
:<math>x+y+z=0.\,</math>