Trying to figure out math on circular metal bender

You are describing what is known as a golden or fibonacci spiral. It occurs naturally in nature -- manifesting in examples such as nautilus shells or the stems of fiddlehead greens. You can read about them here ; https://www.intmath.com/blog/mathematics/golden-spiral-6512
and if you are comfortable in programming, can write some code to implement the formula detailed in the above or :

The Golden Spiral has the special property such that for every 1/4 turn (90° or π/2 in radians), the distance from the center of the spiral increases by the golden ratio φ = 1.6180.
 
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