How to Relate Archimedes " N - Gons "
C = S(n)/2 + S(n)/2 - For Outside Tangent Line
C = S(n)/2 + S(n)/2 - For Inside Secant Line
Refer to Book : " The Pythagorean Theorem , A 4,000 Year History "
----------------------- By : " Eli Maor "
-----------------------Ch. 4 - " Archimedes " Pg. 50 - 56
1) Construct the Square and Make a Circle in the " First Quadrant "
2) Find the Orgin of Each of the " two Circles " under Consideration and Draw them with equal distance between them as I have with their correct Radius.
3) Make sure they intersect at Lines " C " Both ; Outside and Inside as I have shown.
4) Remember this is Complex Trigonometry and " a " Distance is Independent so make sure the Radius = both " b " in Blue and " d " in Red according to the Rules
I set out in the previous two post: " Independent Axis " and " Complex Trigonometry "
5) As long as you construct this as is " d " and " b " can have any Radius so long as it was derived per my Rules that I have set Out.
6) This is a Supplement to " Complex Trigonometry " so you can see how to Apply Archimedes Principle of " N - Gons "
7) Keep " n " simple ie. 1 or 2 or multiples that work out nicely mathematically. It's your choice. At least I think so?
8) And Yes the Circle From the " First Quadrant " is Tangent but I erased it for Clarity: Construct Full Circles and Make sure all Dimensions and Intersections meet the Rules
of Geometry for this idea?
9) I was thinking even better would be to : Make both circles of any Radius that are evenly spaced to each other : Then Strike both a Tangent Line and a Secant Line
and then build the Reference Circle S(n) to those Circles with Radius " b " in Blue and " d " in Red. That may be easier because all Three Circles have to be proportionate
to each other. Just a thought on Construction of Geometry?

See the First two Post Regarding Complex Math - I have a book with both Post or
they are posted Individually
Enjoy this Mathematical Experiment which I am building the idea as I go.