Search Results for ""

A curve on a surface whose tangents are always in the direction of principal curvature. The equation of the lines of curvature can be written |g_(11) g_(12) g_(22); b_(11) ...

A Maurer rose is a plot of a "walk" along an n- (or 2n-) leafed rose curve in steps of a fixed number d degrees, including all cosets.

The generalization of the Schönflies theorem to n dimensions. A smoothly embedded n-hypersphere in an (n+1)-hypersphere separates the (n+1)-hypersphere into two components, ...

A conic section on which the midpoints of the sides of any complete quadrangle lie. The three diagonal points P, Q, and R also lie on this conic.

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.

The plane spanned by the normal vector N and the binormal vector B.

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

A line and a plane are parallel if they do not intersect.

There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...