How to divide a plane circle into 360 approximately equal arcs

 I accept that one can divide a circle into 12 approximately equal arcs.

I will use the chord associated with this 1/12th arc to divide the 1/12th arc into 5 approximately equal sub arcs. 

 

Expand the circle into one with 5 times the radius. 

Mark off the 1/12th arc on the larger circle by a radial projection. 

Using the cord in the smaller circle. Mark off 5 arcs on the larger circle and the chord on the larger diameter at the circle. 

 

There will be a shortfall in the arc .

 

Project this back radially onto the smaller circle . This will mark off a 1/5th correction arc and it’s associated chord. 

 

Use this correction chord to extend the initial chord marked on the diameter.

Use this chord in the smaller circle to extend the arc , and thereby form a new chord. 

Mark this new chord on the diameter of the larger circle.

Use this chord on the larger circle to extend the initial arc there, and thereby form a new chord. Mark this off on the diameter.

I now can compare 3 corrective chords on the diameter.

 

Use the largest chord that falls short or the least chord that extends over the 1/12th arc when applied 5 times. 

 

Repeat the correction method until one is satisfied they have the best chord to divide the 1/12th arc into 5 sub arcs.

 

Project this sub arc back onto the smaller circle  to divide it into 60 approximately equal arcs. 

 

Bisect these arcs to divide the circle into 120 arcs. 

 

I will now use the chord associated to the 1/120 th arc to trisecting it. 

 

First expand this circle to one 3 times the radius.

Now use the chord to trisect the arc in the larger circle.

 

Follow the correction process above to  find the chord that trisects the 1/120th arc. 

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