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An encoding is a way of representing a number or expression in terms of another (usually simpler) one. However, multiple expressions can also be encoded as a single ...

A parameterization of a minimal surface in terms of two functions f(z) and g(z) as [x(r,phi); y(r,phi); z(r,phi)]=Rint[f(1-g^2); if(1+g^2); 2fg]dz, where z=re^(iphi) and R[z] ...

An epsilon-delta definition is a mathematical definition in which a statement on a real function of one variable f having, for example, the form "for all neighborhoods U of ...

Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in the Wolfram ...

The "imaginary error function" erfi(z) is an entire function defined by erfi(z)=-ierf(iz), (1) where erf(z) is the erf function. It is implemented in the Wolfram Language as ...

The four parameters e_0, e_1, e_2, and e_3 describing a finite rotation about an arbitrary axis. The Euler parameters are defined by e_0 = cos(phi/2) (1) e = [e_1; e_2; e_3] ...

The triangle of numbers A_(n,k) given by A_(n,1)=A_(n,n)=1 (1) and the recurrence relation A_(n+1,k)=kA_(n,k)+(n+2-k)A_(n,k-1) (2) for k in [2,n], where A_(n,k) are shifted ...

The extouch triangle DeltaT_1T_2T_3 is the triangle formed by the points of tangency of a triangle DeltaA_1A_2A_3 with its excircles J_1, J_2, and J_3. The points T_1, T_2, ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...

A manifold with a Riemannian metric that has zero curvature is a flat manifold. The basic example is Euclidean space with the usual metric ds^2=sum_(i)dx_i^2. In fact, any ...