Search Results for ""

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.

The recurrence relation (n-1)A_(n+1)=(n^2-1)A_n+(n+1)A_(n-1)+4(-1)^n valid for n=4, 5, ... with A(2)=0 and A(3)=1 and which solves the married couples problem (Dörrie 1965, ...

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...

Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

If a line intersects one of two parallel lines, both of which are coplanar with the original line, then it must intersect the other also. This axiom is equivalent to the ...

Given a rectangle BCDE, draw EF=DE on an extension of BE. Bisect BF and call the midpoint G. Now draw a semicircle centered at G, and construct the extension of ED which ...

A surveying problem which asks: Determine the position of an unknown accessible point P by its bearings from three inaccessible known points A, B, and C.

A spheroidal section is the curve formed by the intersection of a plane with a spheroid. A spheroidal section is either a circle (for planes parallel to an equator, i.e., ...

The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

The resultant of the vectors represented by the three radii from the center of a triangle's circumcircle to its polygon vertices is the segment extending from the ...