### Some articles on *dual, number, dual numbers, numbers, dual number*:

Dual Quaternion - Formulas

... In order to describe operations with

... 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**...0.999... - In Alternative Number Systems - Infinitesimals

... = 1 rely on the Archimedean property of the real

... = 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 ...Dual Number - Geometry - Cycles

... Given two

... 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 equalizes—we 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 (1902–1983)

“Thee for my recitative,

Thee in the driving storm even as now, the snow, the winter-day

declining,

Thee in thy panoply, thy measur’d *dual* throbbing and thy beat

convulsive,

Thy black cylindric body, golden brass and silvery steel,”

—Walt Whitman (1819–1892)

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