quadric

where the constants a, b, c, f, g, and h are not all zero. When the equation represents a non-empty locus, it can be reduced by translation and rotation to one of the following canonical forms:

(i) Ellipsoid:

(ii) Hyperboloid of one sheet:

(iii) Hyperboloid of two sheets:

(iv) Elliptic paraboloid:

(v) Hyperbolic paraboloid:

(vi) Quadric cone:

(vii) Elliptic cylinder:

(viii) Hyperbolic cylinder:

(ix) Parabolic cylinder:

(x) Pair of non-parallel planes:

(xi) Pair of parallel planes:

(xii) Plane:

(xiii) Line:

(xiv) Point:

Forms (i)–(v) are the non-degenerate quadrics.

• solid of revolution
• solidus
• soluble group
• solution
• solution of triangles
• solution set
• solvable by radicals
• solvable group
• sorting algorithms
• source
• source
• source
• space
• space-filling curve
• space–time
• span
• spanning set
• spanning tree
• sparse matrix
• Spearman's rank correlation coefficient
• special function
• special linear group
• special relativity
• spectral theorem
• spectrum