All surface points have a perpendicular {binormal} to osculating plane.
In three dimensions, circles {coaxial circle} can share axis.
Curves {higher curve} {higher plane curve} can have equations with degree greater than two. Defining degree-n curves requires n * (n + 3) / 2 points. Higher plane curves have inflection points, multiple points, cusps, conjugate points, genuses, and branches. One degree-m curve and one degree-n curve can intersect at m*n points.
A point and two points on a curve near the point define a circle with curvature equal to curve {osculating curve}| curvature.
Rotation about, and translation along, line makes space curve {screw curve}.
Non-intersecting curves {simple closed curve} can enclose regions. Simple closed curves {simply connected region} can surround only region points.
Curves {skew curve} {twisted curve} can go outside of plane.
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Date Modified: 2022.0225