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The angular velocity omega is the time derivative of the angular distance theta with direction z^^ perpendicular to the plane of angular motion, omega=(dtheta)/(dt)z^^=(v)/r.

The linear fractional transformation z|->(i-z)/(i+z) that maps the upper half-plane {z:I[z]>0} conformally onto the unit disk {z:|z|<1}.

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

Two non-coincident plane angles alpha and beta in angle standard position are said to be coterminal if the terminal side of alpha is identically the same as the terminal side ...

The inner and outer spheres tangent internally to a cone and also to a plane intersecting the cone are called Dandelin spheres. The spheres can be used to show that the ...

A surface that contains two families of rulings. The only three doubly ruled surfaces are the plane, hyperbolic paraboloid, and single-sheeted hyperboloid.

If an infinite number of points in the plane are all separated by integer distances, then all the points lie on a straight line.

A field of extremals is a plane region which is simply connected by a one-parameter family of extremals. The concept was invented by Weierstrass.

A closed embedded smooth plane curve has at least four vertices, where a vertex is defined as an extremum of curvature.

The internal (external) bisecting plane of a dihedral angle of a tetrahedron divides the opposite edge in the ratio of the areas of the adjacent faces.