Re: "iQspiral" design
As a tee, no one needs to know that 'iQ' refers to Quadrature - not intelligence,
but it takes geometric IQ to comprehend how '8' relates to Quadrature
(serve square Pi to introduce the concept).
Geometer's secret iQ ...
A circle's square rests upon only eight points of the circle
And it takes super geometric IQ to comprehend how Pi relates to "Sweet 16"
(smallest circle-squaring right triangle that begins the inner 360 degree spiral
has precisely 1/256 the area of the triangle beginning the outer spiral).
Tasty Sqrt(2) Pi Sandwich (aka
"Pi Corral")
for circle where diameter = 2
Perimeters of squares divided ...
8.0 / 5.6568542494923801952067548968388.. enclosing/inscribed
= 1.4142135623730950488016887242097.. sqrt(2)
Circumference vs perimeters (calc up & down) ...
= 8.0 enclosing perimeter
x 1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
6.283185307179586476925286766559.. circumference = Pi(D)
/ 1.1107207345395915617539702475152.. (Pi/2)/sqrt(2)
= 5.6568542494923801952067548968388.. inscribed perimeter
Multiplier x divisor of calculated perimeters ...
1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
x 1.1107207345395915617539702475152.. (Pi/2)/sqrt(2)
= 1.4142135623730950488016887242097.. sqrt(2)
Tasty Sqrt(2) Pi Sandwich, (aka "short stack")
for circle where diameter = 2 (calc up & down):
= 2.0 circle's diameter
x 1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
1.5707963267948966192313216916398.. circumference/4
/ 1.1107207345395915617539702475152.. (Pi/2)/sqrt(2)
= 1.4142135623730950488016887242097.. side of inscribed square
1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
x 1.1107207345395915617539702475152.. (Pi/2)/sqrt(2)
= 1.4142135623730950488016887242097.. sqrt(2)
Thus, Pi is directly associated with sqrt(2).
Go Figure!
Rod