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A self-intersecting minimal surface which can be generated using the Enneper-Weierstrass parameterization with f(z) = 1 (1) g(z) = zeta. (2) Letting z=re^(iphi) and taking ...

There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means ...

An important theorem in plane geometry, also known as Hero's formula. Given the lengths of the sides a, b, and c and the semiperimeter s=1/2(a+b+c) (1) of a triangle, Heron's ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

Find the plane lamina of least area A which is capable of covering any plane figure of unit generalized diameter. A unit circle is too small, but a hexagon circumscribed on ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...

Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or ...

A band over a fixed topological space X is represented by a cover X= union U_alpha, U_alpha subset= X, and for each alpha, a sheaf of groups K_alpha on U_alpha along with ...

The skeleton of the bislit cube is the 8-vertex simple graph, illustrated above in several embeddings, which consists of a cube in which two opposite faces have polyhedron ...