Interesting post. I don't know anything about framing, etc. An engineer associate used to use hose and 2 boiler gage glasses filled with water to determine level over a distance. So, that's a thought.That is only two significant figures and less accurate. 0.0390 is better. The 1/25.4 ratio is exact to 3 figures.
I forgot. Do You understand precision vs accuracy? You can have one , the other, or both, measuring things.
I can use calculus to derive it. Don't need to memorize formulas.
I can lay out timber frame joinery with a compass, plumb bob and snap line. No rulers or squares needed, perfectly square.
Can You:
1) a Layout a perfect 1,1, root 2/45o 45o 90o knee brace and tenons, just using a compass and straight line? (A 3 4 5/30o 60o 90o brace, takes a bit more work....)
b) How about the mortices? In a post and tie beam to accept the brace you made in a above?
2) Can you layout a perfect "Star of David" using a line and a compass? Then use it to layout a perfect post,tie beam and connect them?
I can here is a hint, but then the cat is out of the bag..... Drawing copyright MP
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It's just basic geometry.........
Concerning carrying out decimal points to the nth degree, 0.039 IS exactly the same as your 0.0390.
Your 25.4 is actually 25.39.
Have you discovered the new less complicated formula for determining the area of a circle, as I have asked if anyone knew? It is very less tiresome than the common method.