(c-b)/a tangible as a Texas Hill Country dance deck
purpose
We co-manifested this elemental algebraic calculus of Infinite-beauty into the world.
It is a many-faces union of The Pythagorean Theorem & The Golden Ratio.
It is a newfound cornucopia forged in-reaction-by experiences during a perilous age.
It is an expression of SpaceTimeScale’s no-sharp-separation ambiguities.
symbol
We choose the spiral pattern for mysticism & electromagnetism.
We choose the two-spiral pattern for the Sun & Moon balance of a Middle-Way path.
We choose rectangles over curves for the 4-directions of Unit-circle orthogonality.
We choose (b - c)/a = 10/12 = 5/6 æther for Pythagorean-triple relation to pentatonic scale.
We choose b + c = 12 feet because it is 2 feet longer than a = 10.
our process
ideal spiral
The stationary perimeter of the spiral is a fixed 144-by-120 inches frame of reference.
Coordinates on the horizontal axis (b + c “path perpendicular”) increment along the 5/6 constant’s even-powers [ (5/6)^0, (5/6)^2, (5/6)^4, … ].
Coordinates on the vertical axis (a “path parallel”) increment along the 5/6 constant’s odd-powers [ (5/6)^1, (5/6)^3, (5/6)^5, … ].
ideal dance deck
The dance deck is 144-by-144 inches, or a 12-by-12 feet surface.
With the a “path parallel” side of the spiral-border 2 feet shorter than the dance deck, the “path perpendicular” ends of the spiral include rug-like 1 foot header and footer borders.
Header, footer and cork art done by Bezuma.
actual dance deck
The actual dance deck’s floor size is more than 144 and different on all 4 sides.
A gold floor-border around 144-by-144 measurements offers an exact canvas and accentuates the rug aesthetic.
After æther^16, we corked the spiral.
interactive
measure
People can take these beams and place them on the deck, to measure if the spirals line up.
Other interactions include cutting the beams into blocks, and people can measure block-by-block.
continuation
The golden cork found at the center of the spiral is (5/6)^16 smaller than the spiral’s perimeter.
(5/6)^16 percent of 144-by-120 inches is roughly 7.79-by-6.49 inches. Here’s an image of what 7.79-by-6.49 looks like on 8.5-by-11 inches letter-sized paper:
People can print this 7.79-by-6.49 inches image and place it on top of the golden cork, converting the halted spiral into a non-halting spiral.
This is a similar idea as the continuation interaction. But rather than the golden cork or the non-halting spiral, people can fill in their own image.
For quick application of the spiral, use a stencil. This can be 3D printed or cut out of material.
double-sided cork NFT
These 18 tiles will become double-sided cork NFTs. Please visit here for the NFTs.
proportional decay offers in-frame perpetuity
natural numbers as automation
To index a non-halting pattern into a continuous count is to discretely mechanize it as finite “for-loop” processes; to count backwards is to have dipole positive and negative continuity.
unavoidable exponents
[ length, area, volume, … ] or [ position, velocity, acceleration, … ]; the index is along the exponent. These are the natural numbers within logarithmic functions.
(c-b)/a utility
(c-b)/a is the constant needed to convert a rectangle into a logarithmic function framework of a) Infinite in-frame rectangles along a projected vanishing point limit; where b) the exponents are an integer count.
A (c-b)/a algorithm has Infinite “storage blocks” as a discrete repetition of the same process. As simple a perpetuity as mechanically possible that also continuously tiles a finite plane without gaps or overlaps.
magic☆carpet (c-b)/a
https://docs.google.com/spreadsheets/d/16R3nooUIRhQe2KJod1obKanpmZ-lE95ON93TZrp9FFg/edit#gid=0
resources
https://github.com/bestape#oeis-contributions
https://zenodo.org/record/5803948
https://github.com/bestape/alchemy
https://ape.mirror.xyz/7X4RmO_wsuBTJsHnXiEC7IrCYkK3Ji0ULpHA9z5fSxQ