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The metric ds^2=(dx^2+dy^2)/((1-x^2-y^2)^2) for the Poincaré hyperbolic disk, which is a model for hyperbolic geometry. The hyperbolic metric is invariant under conformal ...

Three concurrent homologous lines pass respectively through three fixed points on the similitude circle which are known as the invariable points.

A bistable eight-sided polyhedron discovered by Wunderlich and Schwabe (1986).

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

The length is the longest dimension of an object.

In the depiction of a row of identical columns parallel to the plane of a perspective drawing, the outer columns should appear wider even though they are farther away.

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

The plane determined by the points x_1, x_2, and x_3 and the line passing through the points x_4 and x_5 intersect in a point which can be determined by solving the four ...

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.