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Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

For a particular format in the IEEE 754-2008 framework, a subnormal number is a nonzero floating-point number with magnitude less than the magnitude of that formatÕs smallest ...

The pedal curve of a unit circle with parametric equation x = cost (1) y = sint (2) with pedal point (x,y) is x_p = cost-ycostsint+xsin^2t (3) y_p = ...

The cyclocevian triangle DeltaA^('')B^('')C^('') of a reference triangle DeltaABC with respect to a point P is the triangle formed by the vertices determined by the ...

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = 1/3u^3+uv^2+2(u^2-v^2). (3) The handkerchief surface has stationary points summarized in ...

A map projection given by the following transformation, x = lambda-lambda_0 (1) y = 5/4ln[tan(1/4pi+2/5phi)] (2) = 5/4sinh^(-1)[tan(4/5phi)]. (3) Here, x and y are the plane ...

According to most authors (e.g., Kelley 1955, p. 113; McCarty 1967, p. 144; Willard 1970, p. 92) a regular space is a topological space in which every neighborhood of a point ...

A complex vector bundle is a vector bundle pi:E->M whose fiber bundles pi^(-1)(m) are a copy of C^k. pi is a holomorphic vector bundle if it is a holomorphic map between ...

Consider three squares erected externally on the sides of a triangle DeltaABC. Call the centers of these squares O_A, O_B, and O_C, respectively. Then the lines AO_A, BO_B, ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...