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Let f:A->B be a map between sets A and B. Let Y subset= B. Then the preimage of Y under f is denoted by f^(-1)(Y), and is the set of all elements of A that map to elements in ...

The Prelle-Singer method is a semi-decision procedure for solving nonlinear first-order ordinary differential equations of the form y^'=P(x,y)/Q(x,y), where P and Q are ...

The maximum and minimum of the normal curvature kappa_1 and kappa_2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the ...

A curve alpha on a regular surface M is a principal curve iff the velocity alpha^' always points in a principal direction, i.e., S(alpha^')=kappa_ialpha^', where S is the ...

A principal nth root omega of unity is a root satisfying the equations omega^n=1 and sum_(i=0)^(n-1)omega^(ij)=0 for j=1, 2, ..., n. Therefore, every primitive root of unity ...

Given n metric spaces X_1,X_2,...,X_n, with metrics g_1,g_2,...,g_n respectively, the product metric g_1×g_2×...×g_n is a metric on the Cartesian product X_1×X_2×...×X_n ...

The case of the Weierstrass elliptic function with invariants g_2=-1 and g_3=0. The half-periods for this case are L(1+i)/4 and L(-1+i)/4, where L is the lemniscate constant ...

The Pythagorean means are the three "classic" means A (the arithmetic mean), G (the geometric mean), and H (the harmonic mean) are sometimes known as the Pythagorean means. ...

A number of the form +/-sqrt(a), where a is a positive rational number which is not the square of another rational number is called a pure quadratic surd. A number of the ...

The algorithm of constructing and interpreting a quotient-difference table which allows interconversion of continued fractions, power series, and rational functions ...