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But I had the idea after investigating the geometry behind Violins to try a different approach that is along the lines of ED Leedskalnin's geometry problem of 115 degrees.. which is basically 2 radians. In other words, it's the same arc length as the diameter of the circle... in his case 260 miles. I was curious what it would look like so I laid it out in Autocad and here is the result:

I put numbers and alternated the colors to help distinguish what is going on. The 1 unit has 1 radian of arc length.. then 2 has 2 radians.. etc. There is only 6.28 radians per circle.. so I can't go further without overlapping itself. Not sure how to proceed past here. I see the violin chose to take the inverse arc from a different center point.

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