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The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...

Number Theory

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in K. A nonsingular algebraic curve is an algebraic curve ...

If a points A^', B^', and C^' are marked on each side of a triangle DeltaABC, one on each side (or on a side's extension), then the three Miquel circles (each through a ...

A right strophoid is the strophoid of a line L with pole O not on L and fixed point O^' being the point where the perpendicular from O to L cuts L is called a right ...

A cyclic pentagon is a not necessarily regular pentagon on whose polygon vertices a circle may be circumscribed. Let such a pentagon have edge lengths a_1, ..., a_5, and area ...

The Jacobian of the derivatives partialf/partialx_1, partialf/partialx_2, ..., partialf/partialx_n of a function f(x_1,x_2,...,x_n) with respect to x_1, x_2, ..., x_n is ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

The 12-faced convex deltahedra also known as the Siamese dodecahedron, which is also Johnson solid J_(84). It is implemented in the Wolfram Language as ...