Archimedian Spirals

Archimedian Spirals Constructed on Polargraphic Paper with Geometric Algebra

 

Single Turn Spiral

This is the trajectory of a point that travels .27... rads (unit of distance from center) every 10 of rotation from 0 to 360 , going 10 rads in the process from the center to the outside, making one turn of the spiral for the 360 rotation.

This constant increase in the distance from the center, lets call it Delta rad or D(r), here is .027.../degree, or .27... rads/ 10 counter clockwise rotation we used in this construction. Such a constant increase defines an Archimedian spiral, after the Greek mathematician, Archimedes, who studied them extensively.

Thus, the total rads, R(n), at any step n, equals the previous total, R(n-1) plus D(r), or

R(n) = R(n-1) + D(r) = n * D(r)

 

In this case of the one turn spiral,

R(n) = 36 * .277 where n=36, the total number of 10 steps taken from the initial position at 0. Thus after the 36 steps to complete the circle, 36 * .27...rads = 10 rads.

 

 

Created: 11/24/97

Updated: 12/7/97