![flower :flower:](./images/smilies/icon_flower.gif)
Re: "VH Transition" (renamed from Vertical Tansition)
My image editor had other ideas about presentation of this CAD drawing, refusing to create crisp lines in the enlarged geometry.
So, VH (Vertical Horizontal) Transition is the better title. And I see that this presentation permits easier 1:1 comparison of the squared circle with its two siblings. "Who can tell?" Maybe this 1:1 perspective has potential for revelatory guidance!
![geek :geek:](./images/smilies/icon_geek.gif)
The two red triangles and vertical line relate to trigonometry that calculates the area of the circle.
For the squared circle (copied from the May, 2012 document):
Area = (( Cos 27.597112635690604451732204752339.. ) x Diameter ) Squared
Circum. = (( Cos 27.597112635690604451732204752339.. ) x length of square's side ) x 4
The 55.194225271381208903464409504677.. degree Angle of Squaring Radii (ASR) refers to the lower vertex of a downward pointing isosceles triangle. The top horizontal side of this triangle is a portion of the top horizontal line of the circle's square.
The right half of the ASR is the angle of focus for this trigonometry:
![cheers :cheers:](./images/smilies/icon_cheers.gif)
55.194225271381208903464409504677.. x .5
= 27.597112635690604451732204752339.. ( cosine angle )
= 0.88622692545275801364908374167057.. ( cosine; Radial Pi or rPi )
= half the square root of Pi (value derived from cosine angle)
![Seeing Stars :stars:](./images/smilies/icon_stars.gif)
Here's how these wiggly numbers compare to Pi:
(selection of the 2 billion units diameter is arbitrary;
precision increases with more cosine angle digits)
![Arrow :arrow:](./images/smilies/icon_arrow.gif)
No-Pi formula for area:
A = 0.88622692545275801364908374167057
x 2000000000 = 1772453850.9055160272981674833411 squared
= 3141592653589793238.4626433832795
![Arrow :arrow:](./images/smilies/icon_arrow.gif)
Pi formula for area:
= 3141592653589793238.4626433832795 ( A = Pi x Radius squared )
![Arrow :arrow:](./images/smilies/icon_arrow.gif)
No-Pi formula for circumference:
C = 0.88622692545275801364908374167057
x 1772453850.9055160272981674833411 x 4
= 6283185307.1795864769252867665585
![Arrow :arrow:](./images/smilies/icon_arrow.gif)
Pi formula for circumference:
= 6283185307.179586476925286766559 ( C = Pi x Diameter )
Since 90 - 27.597112635690604451732204752339..
= 62.40288736430939554826779524767.. degrees,
a radius must exist that effectively squares the circle!
TMI? Tell me about it! In recent years, I've had all the Pi I want,
... but keep returning for more.
Rod