Definition
In polar coordinates the logarithmic curve can be written as
or
with being the base of natural logarithms, and and being arbitrary positive real constants.
In parametric form, the curve is
with real numbers and .
The spiral has the property that the angle φ between the tangent and radial line at the point is constant. This property can be expressed in differential geometric terms as
The derivative of is proportional to the parameter . In other words, it controls how "tightly" and in which direction the spiral spirals. In the extreme case that the spiral becomes a circle of radius . Conversely, in the limit that approaches infinity (φ → 0) the spiral tends toward a straight half-line. The complement of φ is called the pitch.
Read more about this topic: Logarithmic Spiral
Famous quotes containing the word definition:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)