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A 4-cusped hypocycloid which is sometimes also called a tetracuspid, cubocycloid, or paracycle. The parametric equations of the astroid can be obtained by plugging in n=a/b=4 ...

The envelope of the lines connecting corresponding points on the Jacobian curve and Steinerian curve. The Cayleyian curve of a net of curves of order n has the same curve ...

The envelope of refracted rays for a given curve.

A differential ideal I on a manifold M is an ideal in the exterior algebra of differential k-forms on M which is also closed under the exterior derivative d. That is, for any ...

The links curve is the quartic curve given by the Cartesian equation (x^2+y^2-3x)^2=4x^2(2-x). (1) The area enclosed by the outer envelope is A_(envelope)=1/6(9pi+8) (2) and ...

An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

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 ...

Exterior algebra is the algebra of the wedge product, also called an alternating algebra or Grassmann algebra. The study of exterior algebra is also called Ausdehnungslehre ...