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:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)