parabolic spirals

spiraal

A spiral is a curve in which the distance from a point to a center (pole) increases for increasing angles. Experiment:

Wind a rope around a pencil and attach the end of the rope.
Now unwind the rope holding the rope thight.
Unwinding the rope the pencil will draw a spiral.

You can describe a spiral mathematically. For the relation between the radius (= distance between pole and point) and the angle you can use different equations, each producing a slightly different shape. Here we use so-called parabolis spirals. The equation only matters to draw points on it and to illustrate the math behind sunflowerseeds.

parabolic spiral

A parabolic spiral is a curve with equation

, in which

is an angle (in radials) n defined the number of radaials.

For the spiral starts in the origin.
The bigger the angle , the closer the distance between the windings.

Note: While increasing n very much, the windings wil be so close that it becomes diffucult to distinguish them.

parabolic spirals

spiraal

parabolic spiral

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