What is the ratio of X to R? 11 24 2022 updated

 

And why do I ask? So, if you take a square block of wood and use a round over bit on it you form a rounded corner.  And there are different size round over bits.  Perhaps 1/4", 1/2" 3/4" and 1".  That size designation also corresponds to the radius of the round over bit.

But the question is what round over bit would you use to get the round over section equal to x over r or alternatively x over x+r?  Presuming x over x+r is a constant ratio?  Is it pie?  If not what is it?

This is one that will likely take some research.  However the old fashion interpolation way will get me fairly close to the answer I Looking for.  So a compass, a piece of paper and a ruler an do a to pencil in is where it is will start.  My radius will be 3".

May post results soon.  May not.

Ratios Derived:

X/R=.4166    or ~? 5/12

Inverse of=

X/(X+R)= .2941 or ~?5/17

Inverse of= 3.4

3X/R=1.25

Inverse of= .8

X+R/Circumference=.22547

Inverse of= 4.435

X+R/Area=.1503

Inverse of= 6.652

That 3 times the corner segment divided by the radius coming out to 1.25 is very interesting.  Is it a constant?

If so you could find an area of a circle within a square by the formula=

For convention we might call x+r max radius of square encapsulate of circle.  Mrsec.

To continue this I would need to incorporate one half of the length of square side?  But have not taken that measurement?  No, I to think somehow this can be done by starting with Square and knowing mrsec.

No time now, perhaps some other time.  Something is getting squirrelly and exhibiting latent ADHD symptoms.

No I do already know one half the length of side of said square, it is 3".  Radius at top tells me so.

But that squirrelly....

So the formula answer is 1/2 side of square times π^2= area of circle within a square.

And circumference= Whole Side Of Square Times π.

And yet none of that takes into account my coveted mrsec distance.

And for extra credit convert above ratios to comparison of a square within a circle.

Wait a minute..does one half the side of a square equal 3x/1.25??? Am I getting that right?

So therefore simply you can calc x by just knowing 1/2 side of square.

And some how in all of this can pie be factored out and my mrsec ratio take presidence.

And what comparisons can be made when I make mrsec my new radius???  Ahaaa!!!!

For example the area of a square with mrsec side times 2 versus smaller r2.

And same with Circumference.  Circ of mrsec radius compared to circ of r with r radius.

******'

Without giving the page calculations.  The area of the circle increases by the same ratio that the area of the square increases: 2.0069

Possible applications include differential rotary engine technology's.

© 2022 Thomas Paul Murphy

11/24/2022