Great circle 2πr. Surface 4πr².
The Pi Try · Closed web
Super Tool
Film stamp · TIME 9:14 · 8/28/2024
TIME · 24 groups
Symmetry
Mathematics × geometry × physics. The nest is 9, 8, 7 and 6. The rotor below is only the 8. Φ stays the golden ratio.
02 · Nested. Nested symmetry on the plate is 9, 8, 7 and 6 together. Five is not in this nest.
All four folds are up. The rose is the eight-petal plate flower, k = 4.
e^{iθ} = 1 + i 0
r = cos(4θ) = 1
Station 8, θ = 2π. The plate writes Φ(θ, t) = R(θ) e^{i(nθ − ωt)}. That Φ is the field. Golden Φ = (1+√5)/2 is the five, group 18. The lift’s φ is neither.
Plates · November 1
θ 360° · station 360° · a 0.12 · r/r₀ 0.470
Associated
Pro Pi
degrees360.0°
radians6.2832
turns1.0000
x = cos θ1.000
y = sin θ0.000
x² + y²1.000
Drag the hand. 0° is east. The turn is measured counterclockwise, the same way as the field.
Original plate
Connections
TIME · 24 groups
TIME names the path and stops at the terminal. A full turn of R(θ) is the identity. The root plate writes that stable return as √, and at the unit √1 = 1. F(g) is not this F.
The twenty-four groups are the structural map. A fold button opens the figure that already measures that step. R(θ) is the field desk. C(t) is the landscape. F(g) stays Gravitron, a different function from the root.
A group opens TIME on that number. The note there is the plate’s line, not a second law.
Mathematics
Geometry
Physics
1 Whole π Radial is 360°/20 = 18°
Parts I–V · Eastern Time
Original Author: Deanna Rachel Sellers
Open the plate and slide it sideways. The instrument below is the live field.
Geometry tool
Live instrument
Θ · Angular rotation · 45°
The turn itself. R(θ) acts on the state.
θ360.00°
radians6.283
chord0.000
arc · sector6.283 · 3.142
R(θ) = [[cos θ, −sin θ], [sin θ, cos θ]] · θₖ = 2πk/8 · Π = ∬_Ω dA
PHYSICS × GEOMETRY × MATHEMATICS → UNIFIED INTEGRATION → ΘΠ
Original V-code — complete sequence
ΘΓΙΟ;09»0@9&8@9&ᎾᎿᏌᏜᏌᏩᏆᏜᏌᏜᏆᏜᏌᏩ⋯⋯在γυηιξογηιοθηιγθᏀᏆᏜᏌᏩᏆᏍᏜמפלםחפךפלםפ⋯⋯他θλ´πλ´κπλ´他𞋓𞋇𞋆𞋇𞋅𞋏𞋇c’oplpop’p৭র৮ঙ!ক্ষLØÐLIH̄PyåpäåpåpåИГЩДГДЖবটডটডজড,૫લ૦ષ૬એहपडजटडजडभघylpolpबडटजडदडРХГЕ୬ର୭ଲ”ꯃꯤꯐꯍ?꯰꯹”꯰ꯕ۶ن۰پ۷ث«ه؟عvpolpopих!оНBPKʻI൬ഓ൮ഏ=റ൦ഒ൬ᱴᱷᱤᱶ!᱖ᱧ%ആഴ൭gˀpˀpop໊ີ້ຄ6”09”090BƐỤU߆ߟ߆ߟ߄»ߓߡߒߤߓߒउघ”%TLUGpY?0”0bTO6”09”yyーいJよりHgじゅytlkっじゅーやつဏဎဥல்பிகொஊഇഹ്യ്gɨpʼɨlɨUёхҍӭхҍзҍіЁШеэхзэхзэхзхθΙΟΠΙΓ;%$%βΛ!ךםפלםחפם車吃什麼都θλ´λ´κ´他沒有θλ´λ´λ´λ´穿褲子υλ´λ´λᎿᏯᏩᏝᏯᏓᏩᏌᏜυΘΥ)^βᏀᎿᏆᏍᎾᏀᏆᏍᎾᏀᏍυπκ´ξοκπξ´uğöəğöğυλ´λ´λᎿᏯུཟཇཝཅཛཇཙཅཛཇཙத்யுக்௶௭!VƲUHṈUՀԺ(Շtlpoly’p’p’pࡍࡀࡉࡁࡀࡊࡀࡁࡉࡀࡊgçëpçgplokGুডঠঙ(%হgʻpʻpʻ¯poʻpப்லொப்கொтшќпшчшнОРТДகஞயஞநஞ்சயஞгшќпшvplopញ៏ឧញ៍ГИНТГпхэзхжщ才不差那$7裡ΘΠ
The rendered field. Nested rings, the gold octagon and every chord, the cyan eightfold wave, the spiral, and the terminus ΘΠ. Drag turns it.
Original Author: Deanna Rachel Sellers · November 1, 2026
11 / 11 · ΘΠ
Final terminus. Physics, geometry, and mathematics meet, and the meeting has a name.
Final terminus · Law LX
The integrated region, turned, is still the integrated region. The name of that meeting is ΘΠ.
R(θ) Π = { R(θ) x : x ∈ Π }
(x, y)1.000, 0.000
ψ = sin(8θ)0.000
sector Π3.142
R(θ) · cos 1.000 · −sin 0.000 · sin 0.000 · cos 1.000
det R = 1.000. A turn keeps length. The octagon of circumradius 1 encloses Π₈ = 4.828. Rotation leaves that area unchanged.
Universe gravitron
Trajectory rule · 8 fold
Deanna's Law of Universe Gravitron
Original Author: Deanna Rachel Sellers
November 2, 2026
The plate is the map. The v-code band on the plate did not keep the scripts. The marks below are the written line.
Gravity-force equals universal gravitational coupling of squared mass and light-speed, divided by spatial curvature geometry.
This plate is the law on its own, plus the trajectory rule for the eightfold. The original formula is unchanged. The law that governs π is a separate plate.
Field along the trajectory
The original law is evaluated at that x and y. The formula is not replaced. This is a symbolic model, not a physical prediction.
F(g) = G(m², c) / f(x)(y)π
G(m², c) is a paired input. f(x)(y) is f(x) multiplied by y. The trajectory supplies x and y. It does not change this formula.
R(θ)
cos θ = 1.000, −sin θ = 0.000
sin θ = 0.000, cos θ = 1.000
r(θ) = r₀e^(−aθ)
r(2π)/r₀ = 0.470
R(360°) = R(0°) = I
F(g;θ) = G(m², c) / [π f(r₀e^(−aθ) cos θ)(r₀e^(−aθ) sin θ)]
At this angle, x/r₀ = 0.470 and y/r₀ = 0.000. G, c, and f stay symbols, so F is not a number. π governs the cycle. The eightfold samples the full turn, including the close at 360°. This is a symbolic model. A physical prediction would also need a defined f, consistent units, and equations of motion.
360° ≡ 0° (mod 360°)
360° = 0° · Rotation complete
Radius r/r₀0.470
x/r₀0.470
y/r₀0.000
Gold is the eightfold reference. Cyan is the trajectory through 360°, drawn at a = 0.12. κ r₀ = 2.110. At 360° the direction returns. The radius keeps contracting, so the point returns only if a = 0.
P(t) = (r(t) cos θ(t), r(t) sin θ(t), h(t))
|v|² = (dr/dt)² + r²(dθ/dt)² + (dh/dt)²
dr/dt, dθ/dt, and dh/dt are named. None is given a number, so |v| is not computed. ω = dθ/dt stays a symbol.
Ꮐ → θ → Ι → Ꮐ
ΘΠ
ΘΠ closes the written line. It is the integrated region, not a second value of π.
Super Tool · Gravitron landscape
Deanna’s Law of Universe Gravitron with Trajectory Rule for 8 Fold Angular
Original Author: Deanna Rachel Sellers · November 2, 2026
GRAVITRON FIELD360° ≡ 0° orientation
Drag to rotate view · Scroll to zoom
Unified mathematical function
F(g; θ) =G(m², c)π f(r₀e^(−aθ) cos θ)(r₀e^(−aθ) sin θ)
360° = 0° in angular orientation. The landscape keeps the changing spiral radius and the three-dimensional elevation. Elevation × (1 − θ/2π) is the view height, not a formula for h(θ). The radius does not return when a is above 0. Record station 8 is 2π. This is a visualization model, not a validated gravitational prediction.
ᏀᎾᏍᏆᏜᎾᏜᎾᏜθΙᏀנויןעוஎஞணயՀևՃ—՞肺floHflokpylwꯆꯄꯣꯂꯄ
4D — the jump off the landscape
Same path. A fourth coordinate the law does not contain.
Original Author: Deanna Rachel Sellers · November 2, 2026
3D SLICEψ 0° · xw
Drag to turn the view
x0.823
y0.000
z0.000
w0.000
At ψ = 0 the path is the landscape path and w = 0. The jump rotates that path in the xw plane. At 90° the traded coordinate is w = 0.000. The tesseract is the frame of the projection. It is not part of F(g). Elevation × (1 − θ/2π) is the same view height as the landscape, not a formula for h(θ).
P(θ) = (r₀e^(−aθ) cos θ, r₀e^(−aθ) sin θ, h) · w = 0 before the jump
Royal cubit axis
Six rods make the functional axis. The center is the overlap.
Original Author: Deanna Rachel Sellers
FUNCTIONAL AXIS6 rods · 12 sides
CenterFunctional axis
Directions6
Between rods30°
Width5.1 digits
Six royal cubit rods at 30° close a regular dodecagon. That is the functional axis. The 1:31 plate shows three of the directions: horizontal, vertical, and one slash. The other three complete the six.
Each rod is graduated the royal cubit way: 7 palms, 4 digits, 28 digits. Six of them, 30° apart, are the functional axis. The gold outline is the overlap.
Engineer
Author: Deanna Rachel Sellers · October 20, 2026
G(x) = Φ₁₀ ∘ Φ₉ ∘ Φ₈ ∘ Φ₇ ∘ Φ₆ ∘ Φ₅ ∘ Φ₄ ∘ Φ₃ ∘ Φ₂ ∘ Φ₁(x)
I · x² + y² + z² = r²
r = 1. 0 is the center. 8 is the saturation radius. 9 is the oversaturation shell.
θ360°
2πr6.283
4πr²12.566
Φ1.618034
Φ = (1+√5)/2 on stage IX.
A star as a sphere. The celestial sphere. Flux through the surface is 4πr².
Field hall
Click the figure
Tap a mark. It opens the math that owns it. Apex chords, the infinite pyramid, the c² cycle, and the royal plate sit with the rest of the field.
ΘΠ · terminus
R(Θ)Π = {R(Θ)x : x ∈ Π}
Tap a petal. Tap the center.
The center of the map. Each petal is one operator. The center is the composition.
Symbols — each opens its figure
Υ is printed twice. The plain chip is the field coefficient. Υ dir is the directional field.
Parts
Field sequence
Also on
Golden ratio seminar
Held
The film is the try. Φ = (1+√5)/2 is not in its petals. The φ on the lift, below, is still the poloidal angle.
Φ(1+√5)/21.618034
Shell0.73 vs 0.618034figure is 0.112 taller than 1/Φ
2π/Φ²137.508°one step misses 135° by 2.508°
Closed web. Eight spokes cross a ringed core. Fine circles fill the disk.
The same web is back at 15 seconds. A golden step, 2π/Φ², would not meet the same spoke.
The eight stations close by π. The pentagon closes by Φ. This film shows the eight, the six, and the square. It does not show the five. Station 8 of the figure is held for the cross-reference.
π comparison
III · station 8
The ways this record shows π, layered on one circle. A lit layer is in the stack. The hand is θ, counterclockwise from the right.
Original Author: Deanna Rachel Sellers
Drawings
Five pictures
The field contracts. The 2021 bloom opens the other way. The sphere is a grid. The 2024 performance is rings and a rose. The photon picture is a ring and four rays.
field r/r₀0.470
bloom radius34.0
θ360°
a0.12
golden step137.5°
off 45°2.5°
Pi Performance, May 21, 2024, 8:48. The plate titles it I PERFECT PI ROYAL GOLDEN RATIO STANDARD. Six rings. Rose r = cos(8θ), 16 petals. The plate does not print k. Golden step 360/Φ² = 137.508°, which misses 135° by 2.508°. The pink sphere beside the performance is the same grid. The rhumb on it has tan = 1/Φ. The plate does not print that rhumb.
F(g; θ) = G(m², c) / (π r₀ e^(−aθ))
Field, November 2, 2026. r/r₀ = e^(−aθ) = 0.470 at 360°. Bloom radius at the same θ, with a reversed, is 34.0. The sphere grid prints no equation. The bright path on it is the field’s contraction. The grid itself is not a spiral.
P(θ) = (r₀ e^(−aθ) cos θ, r₀ e^(−aθ) sin θ, h(θ)). The plate prints θ_k = 2πk/8 for k = 0,1,…,8 and 360° ≡ 0°. k = 0 and k = 8 are the same ray. This record marks that ray 360°.
The plate’s reset prints 0°. Holding the close here sets 360°. Animate runs the plate’s arrow, from the east ray out to that close.
投拉路ωΙΟΠΓΙΗ. c = 投拉路. c² = 投拉路ωΙΟΠΓΙΗ. Connection id &8$7&8)6$7)6(5)6. The id writes 8, then 7, then 6, then 5. It does not write 9. 5 is 72°, not an eightfold station.
The plates
Unified composition
November 1, 2026
Third film · repetition 8 of 8. ΘΓΙΟ → π → ΘΠ. A step turns its layers on. It does not clear the stack.
θ_k = 2πk/8 · k = 1…8
Station 8. The point disk and the sector are the same disk. Both equal π. The hand has closed 2π.
Film I. Area grows with the square of the radius. At station 8 the point has become the disk.
Both equal π. Radius is 8/8.
Unified plate · November 1, 2026
Eightfold formula: θ_k = 2πk/8, k = 1…8. The stations are 45°, 90°, 135°, 180°, 225°, 270°, 315°, 360°. The close is 360°. φ on the operator table is a phase. It is not Φ, and it is not the lift.
Law that governs π
Separate from the gravitron
Deanna's Law of Universe Gravitron
Original Author: Deanna Rachel Sellers
F(g) = G(m², c) / f(x)(y)π
This plate is only the law as it governs π. π in the denominator is the circular term. θ places a direction in that circle. It does not change the written law. The gravitron plate is the law on its own, and it holds the eightfold field.
The unit disk is the π in the denominator. Area and circumference are that constant. The law divides by it.
Shown in the comparison. F(g) = G(m², c) / f(x)(y)π
Geometry atlas
Every angle
Tap a symbol, a part, or the dial. The figure below takes the same θ. Positive θ follows the hand, downward from the right.
Station 8
θ = 2π
R(θ) = [[1, 0], [0, 1]]
cos θ = 1, sin θ = 0. This is station 8 of the eightfold.
III · The Rotor · station 8
Station 8 · cross reference
R(θ) = [[cos θ, −sin θ], [sin θ, cos θ]]
θ_k = 2πk/8 · Π = ∬_Ω dA
θ = 2π · 360°
1001
det R = 1 · γ = θ at this station · hand (1, 0)