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Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball ...

The hyperbolic cylinder is a quadratic surface given by the equation (x^2)/(a^2)-(y^2)/(b^2)=-1. (1) It is a ruled surface. It can be given parametrically by x = asinhu (2) y ...

A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point. A ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...

A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

The limaçon trisectrix is a trisectrix that is a special case of the rose curve with n=1/3 (possibly with translation, rotation, and scaling). It was studied by Archimedes, ...

Mills' constant can be defined as the least theta such that f_n=|_theta^(3^n)_| is prime for all positive integers n (Caldwell and Cheng 2005). The first few f_n for n=1, 2, ...

The surface of revolution of the parabola which is the shape used in the reflectors of automobile headlights (Steinhaus 1999, p. 242; Hilbert and Cohn-Vossen 1999). It is a ...

The term perimeter refers either to the curve constituting the boundary of a lamina or else to the length of this boundary. The perimeter of a circle is called the ...