Some articles on dual, number, dual numbers, numbers, dual number:
... In order to describe operations with dual quaternions, it is helpful to first consider quaternions ... a quaternion as the sum of a scalar and a vector, that is A = a0 + A, where a0 is a real number and A = A1 i + A2 j + A3 k is a three dimensional vector ... can now be used to define the quaternion product of A = a0 + A and C = c0 + C as A dual quaternion is usually described as a quaternion with dual numbers ...
... = 1 rely on the Archimedean property of the real numbers that there are no nonzero infinitesimals ... must be smaller than any positive rational number, so it must be an infinitesimal but since the reals do not contain nonzero infinitesimals, the difference ... coherent ordered algebraic structures, including various alternatives to the real numbers, which are non-Archimedean ...
... Given two dual numbers p, and q, they determine the set of z such that the Galilean angle between the lines from z to p and q is constant ... This set is a cycle in the dual number plane since the equation setting the difference in slopes of the lines to a constant is a quadratic equation in the real part of z, a ... In the Inversive ring geometry of dual numbers one encounters "cyclic rotation" as a projectivity on the projective line over dual numbers ...
Famous quotes containing the words numbers and/or dual:
“Old age equalizeswe are aware that what is happening to us has happened to untold numbers from the beginning of time. When we are young we act as if we were the first young people in the world.”
—Eric Hoffer (19021983)
“Thee for my recitative,
Thee in the driving storm even as now, the snow, the winter-day
Thee in thy panoply, thy measurd dual throbbing and thy beat
Thy black cylindric body, golden brass and silvery steel,”
—Walt Whitman (18191892)