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
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