Fermat's spiral

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Fermat's spiral, . Note is graphed, in blue, and is graphed, in red

Fermat's spiral (also known as a parabolic spiral) was first discovered by Pierre de Fermat,[1] and follows the equation

in polar coordinates (the more general Fermat's spiral follows ).

It is a type of Archimedean spiral.[2]

As a parametric equation[edit]

As a parametric equation, the formula is [2][3]

Here, sgn(a) denotes the sign function of a. By parametric equation implicitization, this isn't so difficult, as can be turned into . And,

So, .

The Golden Ratio and the Golden Angle[edit]




Solar plants[edit]


See also[edit]


  1. ^ "Pierre de Fermat". Retrieved 2017-07-09. 
  2. ^ a b "Fermat's Spiral". Fermat's Spiral. Wolfram Mathworld. Retrieved 15 July 2017. 
  3. ^ "Fermat's Spiral". Geometry Atlas. Saltire Software. 2017. Retrieved 2017-07-09. 

Further reading[edit]

  • J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. pp. 31,186. ISBN 0-486-60288-5. 

External links[edit]