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A line can be specified in trilinear coordinates by parameters (l,m,n) such that the trilinear coordinates alpha:beta:gamma obey lalpha+mbeta+ngamma=0. (1) The trilinear line ...

A tetrahedron having a trihedron all of the face angles of which are right angles. The face opposite the vertex of the right angles is called the base. If the edge lengths ...

A trochoid is the locus of a point at a distance b from the center of a circle of radius a rolling on a fixed line. A trochoid has parametric equations x = aphi-bsinphi (1) y ...

A particle P is said to be undergoing uniform circular motion if its radius vector in appropriate coordinates has the form (x(t),y(t),0), where x(t) = Rcos(omegat) (1) y(t) = ...

Consider the problem of comparing two real numbers x and y based on their continued fraction representations. Then the mean number of iterations needed to determine if x<y or ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

The Weierstrass substitution is the trigonometric substitution t=tan(theta/2) which transforms an integral of the form intf(costheta,sintheta)dtheta into one of the form ...

Begin with the Yff central triangle and then parallel-displace the isoscelizers in such a way as to reduce the central triangle to a point while keeping the other three ...

Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...