Formula
The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor b:
or
with e being the base of natural logarithms, a being an arbitrary positive real constant, and b such that when θ is a right angle (a quarter turn in either direction):
Therefore, b is given by
The numerical value of b depends on whether the right angle is measured as 90 degrees or as radians; and since the angle can be in either direction, it is easiest to write the formula for the absolute value of (that is, b can also be the negative of this value):
- for θ in degrees;
- for θ in radians.
An alternate formula for a logarithmic and golden spiral is:
where the constant c is given by:
which for the golden spiral gives c values of:
if θ is measured in degrees, and
if θ is measured in radians.
Read more about this topic: Golden Spiral
Famous quotes containing the word formula:
“So, if we must give a general formula applicable to all kinds of soul, we must describe it as the first actuality [entelechy] of a natural organized body.”
—Aristotle (384323 B.C.)
“I feel like a white granular mass of amorphous crystalsmy formula appears to be isomeric with Spasmotoxin. My aurochloride precipitates into beautiful prismatic needles. My Platinochloride develops octohedron crystals,with a fine blue florescence. My physiological action is not indifferent. One millionth of a grain injected under the skin of a frog produced instantaneous death accompanied by an orange blossom odor.”
—Lafcadio Hearn (18501904)
“For the myth is the foundation of life; it is the timeless schema, the pious formula into which life flows when it reproduces its traits out of the unconscious.”
—Thomas Mann (18751955)