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The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the the product of distances from two fixed points (-a,0) ...

The Reuleaux tetrahedron, sometimes also called the spherical tetrahedron, is the three-dimensional solid common to four spheres of equal radius placed so that the center of ...

Differential Equations

The curve given by the polar equation r=a(1-costheta), (1) sometimes also written r=2b(1-costheta), (2) where b=a/2. The cardioid has Cartesian equation ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

A 3-cusped hypocycloid, also called a tricuspoid. The deltoid was first considered by Euler in 1745 in connection with an optical problem. It was also investigated by Steiner ...

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

The 2-cusped epicycloid is called a nephroid. The name nephroid means "kidney shaped" and was first used for the two-cusped epicycloid by Proctor in 1878 (MacTutor Archive). ...

There are several sorts of graphs referred to as "star graphs" in mathematics, computer science, and information processing. The most common sort of star is the n-star graph ...