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Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

A transformation of the form w=f(z)=(az+b)/(cz+d), (1) where a, b, c, d in C and ad-bc!=0, (2) is a conformal mapping called a linear fractional transformation. The ...

Archimedes' axiom, also known as the continuity axiom or Archimedes' lemma, survives in the writings of Eudoxus (Boyer and Merzbach 1991), but the term was first coined by ...

A chain complex is a sequence of maps ...-->^(partial_(i+1))C_i-->^(partial_i)C_(i-1)-->^(partial_(i-1))..., (1) where the spaces C_i may be Abelian groups or modules. The ...

The Riemann integral is the definite integral normally encountered in calculus texts and used by physicists and engineers. Other types of integrals exist (e.g., the Lebesgue ...

A solid of revolution is a solid enclosing the surface of revolution obtained by rotating a 1-dimensional curve, line, etc. about an axis. A portion of a solid of revolution ...

Pick three points P=(x_1,y_1), Q=(x_2,y_2), and R=(x_3,y_3) distributed independently and uniformly in a unit disk K (i.e., in the interior of the unit circle). Then the ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

Seeks to obtain the best numerical estimate of an integral by picking optimal abscissas x_i at which to evaluate the function f(x). The fundamental theorem of Gaussian ...