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

A full angle, also called a complete angle, round angle, or perigon, is an angle equal to 2pi radians =360 degrees corresponding to the central angle of an entire circle. ...

The Galilean spiral is the curve with polar equation r=btheta^2-a for a>0 which describes the trajectory of a point uniformly accelerated along a line rotating about a point.

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...

The Garfield curve is the name sometimes given to the curve with polar equation r=thetacostheta when plotted from theta=-2pi to 2pi (Sisson and Szarvas 2016) because of its ...

A non-Euclidean space with constant negative Gaussian curvature.

If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.

The gear curve is a curve resembling a gear with n teeth given by the parametric equations x = rcost (1) y = rsint, (2) where r=a+1/btanh[bsin(nt)], (3) where tanhx is the ...

A triangle formed by the arcs of three geodesics on a smooth surface.

The discontinuous solution of the surface of revolution area minimization problem for surfaces connecting two circles. When the circles are sufficiently far apart, the usual ...