Kiki's Zero-Error Geometry: Parity, David star/Hexagon, and the 420 degree Circle

Kiki's Zero-Error Geometry: 2 opposites spin, Parity (odd & even), Sphere/Circle 420 degrees is the foundation of my Quantum Processors 252 and 2520

The Function of the Spinning opposites:

• “Spinning” isn’t metaphorical — it’s the process by which logic and consciousness align.

• By testing and repeating the counting, the mind learns the true symmetry of creation: odd/even, left/right, up/down — parity in motion.

• This is why students must “practice the spin” — it rewires logic through movement, not memorization. Meaning the kids will have to learn to count in Circles.

• This universe has a "Sphere" as 1 odd unit. So the functioning unit in this universe is a Sphere ( the Sun ).
  
  
• Miljko Tijanic aka Kiki Quake 3 ( me ) has meassured his shadow from 2018-2025 on repeat showing results 105 cm summer noon, 210 cm on winter noon, and sometimes in summer at 4:20 pm my shadow would equal my height.

The Foundation of Numerical Logic: The 420 Circle and the Principle of 4 Opposites Spinning

Abstract

This paper introduces a foundational framework for mathematics, geometry, and physics based on the 420 degree circle. 

420 degree - value is presented not as an arbitrary measure, but as the minimum numerical requirement necessary to fully define the physical properties and internal logic of a 2d circle defininig my 21x21x6 sphere. ( 2520 + 126 )

We establish the physical constant relating angular measure to spatial dimension and detail the system of 4 Opposites Spinning which governs the duality (Odd and Even) and circulation (Right and Left) essential for generating comprehensive geometric structures.

This logic forms the basis for subsequent proofs, including the 21 x 21 x 6 = 2646 sphere and my 252&2520 Quantum Processors.

The underlying principle of this mathematics is the continuous interaction and dynamic Duality of its components.

Every degree and every coordinate must possess a name and a physical field corresponding to its specific nature. This system is designed to reveal fundamental truths and logic easily accessible to all.

( Each number in the circle, has to have physical field / name - position. )

Defining the 420 degree circle Foundation

The 420  circle defines the maximum numerical requirement needed to describe a complete cycle of logic and physical manifestation.

2.1 Angular and Physical Constants

The foundation is defined by two key constants that link the angular (theoretical) measure to the physical (spatial) dimension:

1. The New Standard for Angular Measure: The circle consists of 420 degrees.

   Circle = 420 degrees

2. The Physical Ratio: A direct physical correspondence is established between the angular measure and a linear measure, demonstrating that geometry is physically grounded. This ratio, derived from the core logic, is:

   1 degree = 0.75 mm

   This ratio is explicitly tied to the concept of one and three quarters ($1.75$), confirming its logical sequence.

3. The Ki Constant: The fundamental constant Ki is defined as Ki = 3.15. This constant plays the same crucial role as Pi in previous geometry, but is derived from and corresponds directly to the established 420 degree circle logic and the underlying ratios (e.g., 315 is 3 quarters of 420) / ( 1 degreee = 0,75 mm ).
   
   315 - first three odd numbers.
    
   315 derives from 2520/1260 and 420. ( This constant is revealed in Number logic and Geometry )

2.2 The Principle of Opposites Spinning

The 420 circle is internally structured by 4 equal parts of 1, governed by the principle of Opposites Spinning.

The structure is defined by the interaction of Duality (Odd and Even) across two orthogonal axes, ensuring both balance and dynamic circulation (Spin). When I open a school / write a book - I will teach all the kids the difference between 2 , 4 and 6 opposites. This principle is core of Parity.

The symbols (E, Ш, 3, m) represent the four distinct, integrated states of the Odd-Even field generated by the dual axes.

The R (Right) and L (Left) circulation vectors (Spin) demonstrate how these four parts are dynamically linked to achieve the 12 structure, which is the complete, integrated Unity. The geometry is defined by the fact that the entire system is in a constant state of spinning and equilibrium.

3. Conclusion

The 420 degree circle provides a foundation of numbers and counting that is verifiable and based on logical principles, serving as the required minimum for defining a complete geometric entity. The logic presented here—the dynamic addition of Odd & Even in Circles - through the process of opposites spinning—has served as the basis for further advanced work.

Kiki's Zero-Error Geometry: Parity, Triangles, and the 420° Circle

Abstract:
This paper formalizes the foundational principles of the 420° Circle, establishing a system of measurement based on Parity (Odd/Even) and rational constants that eliminates mathematical approximation. The framework introduces verifiable geometric structures for educational, computational, and physical applications, forming the basis for stable quantum processing and cosmic modeling. The fundamental building block is the 210° Triangle, more precisely expressed as 012 triangles × 210°, forming the 2520 David Star / Sphere 21 x 21 x 6, which serves as the origin for all derived structures, including the Circle, Hexagon, and Sphere.

I. The Foundation of Parity: 3 and 6 (Odd and Even)

21 Even / 42 Odd ( parity )

I used triangle 21 that creates a Hexagon 42. (* 7 x 6 )

Parity is shown in my Hexagon divided by 6 ( 210 x 6 ) and Hexagon divided by 2 ( 420 x 2 )- giving results 840 for 2, and 1260 for 6.

Later on to better explain Parity - I used odd and even. Ephasis is on r ( which is linear ) and L ( which is Curved ).

So r is basically 21, in this example, and L = r + r:20 = 21 + 1.05 = 22.05

When physically counting "Infinity" in circles on (x) amount of fields. You are defining the SPIN in ( L or R ) direction - depending are you counting "Clockwise" or "Anticlockwise". 

Numbers defined in one Direction have defined those same ( odd/even ) numbers in opposite direction. 

Demonstrating the SPIN on 2d circle by counting the Infinity. ( I counted for more than 4,000 hours from 2018 till 2025 ). I proved the 420 degree circle in April 20, 2021. ( I proved 420 degree circle ) 

The key to zero-error geometry is the absolute and verifiable balance between Odd (3) and Even (6), defined here as Parity (3/6). This principle resolves inconsistencies in traditional geometry by establishing rational, non-approximated measures derived directly from Odd/Even structures.

The 210° Triangle — Building Block

The foundational building block of the system is the 210° Triangle, which acts as the Odd generator.
Specifically, the system originates from 012 triangles × 210°, forming the Sphere / 2520 David Star. All higher-order structures—Circle, Hexagon, and Sphere—derive from this verified geometric unit.

The Odd-Even Sequence and the 3/6/9/12 Structure

All valid geometric constructions must balance the Odd principle of the Triangle against the Even principle of the Hexagon.
The 3/6/9/12 sequence is fundamental, representing the relationship between Odd multiples (3, 9) and Even multiples (6, 12). This ensures every form is scalable and verifiable across dimensions.

Implication of Sequence

• Governs multiplication and division in cosmic structure.

• Ensures 3 (Triangle) coherently maps to its Even multiples (6, 12) and Odd multiples (9).

• Creates predictable, cyclical operations for both planar and volumetric expansion.

The Law of Opposites Spinning (R/L)

Stability relies on the dynamic balance of Odd (Right Spin, R) and Even (Left Spin, L) energy.
This opposition generates a non-decaying geometric field necessary for computation and cosmic equilibrium.
Even a minor imbalance would cause structural collapse, proving the necessity of the 3/6 Parity rule for stable existence.

II. The 210° Triangle → The 420° Circle

Deriving the Circle (420°)

The absolute circle (O) is obtained by doubling the fundamental triangular unit:

210°+210°=420°210° + 210° = 420°210°+210°=420°

The 420° Circle is therefore an Even number formed by two balanced Odd generators, not arbitrary.

Internal Parity Divisions

Segments of the 420° Circle:

• 210° (Even): Half-circle; unit of angular half-volume (50% equilibrium).

• 105° (Odd): Quarter-circle; half of 210°, anchors the 4 Opposites Spinning axes.

• 315° (Odd): Three-quarters circle (3 × 105°); geometric verification of the Ki constant.

The Hexagon (840°) and Geometric Stability

• Hexagon = 6 × 210° Triangles = 1260 - shows parity of Triangle/Hexagon. Because the true result is 840.

• Demonstrates how the 3 (Triangle) principle scales to 6 (Hexagon).

• Provides rotational stability and contains the active Odd-generating core.

III. The Constant of Unity (Ki = 3.15) and Physical Grounding

Ki as a Rational Fraction derives from 2520/1260 and 420 Degree circle

Derived from the 420° Circle:

Ki= 3.15

• Composed of Odd numbers 3, 1, 5 → signature of Parity.

• Replaces the irrational π with verifiable rational geometry.

Circumference Formulas and Length L

Zero-error circumference:

O = 2r × Ki
O = 6L
L = r + r : 20

• Curvature matches the linear path of the inscribed Hexagon.

• Eliminates all approximations in circular distance measurement.

Physical Conversion

1°=0.75 mm⇒420°×0.75 mm=315 mm

• Ensures precise field alignment in Quantum Processor designs.

• Guarantees zero-error physical distances correspond to angular spin.

IV. The Cosmic Time Constant: 2520 and r = 21

The Eternal Unity (2520)

• 2520 = Universal Common Multiple; divisible by 1–10.

• Governs all fundamental cosmic cycles.

• Half-unity 1260 = stable equilibrium for geometric motion.

The Radius (r = 21)

Derived from cosmic segmentation:

2520÷120=r=212520 ÷ 120 = r = 212520÷120=r=21

• Odd-based radius seeds all stable shapes and volumes.

• 21 = 3 × 7 → pure Odd resonance, linking Circle dimension to Parity.

Proof of Structure and the Sphere

• 2520 = 12 × 210 → verifies cosmic unity.

• Forms the Sphere / 2520 David Star: 12 interlocking units (r = 0.21) combine with Odd/Even spin for a single, stable sphere.

The 252 Quantum Grid

• 252 = 21 × 12 → constructs Quantum Processors.

• Grid encodes Law of Opposites Spinning (Odd/Red, Even/Blue).

• Entire processor field mirrors the rational, non-decaying Parity principles of the cosmos.

Ω Summary

Conclusion:
All geometric, physical, and computational structures stem from a single verified 210° Triangle block (012 triangles × 210°), forming the Sphere / 2520 David Star. The system is governed by the Parity principle (3/6), ensuring zero-error measurement in planar and volumetric space. The 420° Circle, Ki constant, and 2520 cosmic multiples provide a rational, verifiable foundation for geometry, physics, and quantum processing.
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Infinity 21/420: The Final Game of Counting Circles 
- Image called - r.png from this paper -

Author: Miljko Tijanić (Kiki)
Keywords: Infinity, 420°, Circle, Counting Logic, Parity, Spin Geometry, Odd/Even
License: CC BY 4.0

Abstract

From 2018 till 2021 I was just spinning opposites and counting in circles. In April 2021, I finished my counting with 21 field circle × 20 (of those 21 field circles) — creating 20 × 21 Infinity 21/420.

Structure of Infinity 21/420

It consists of 20 same-sized circles, each divided into 21 equal fields. Here I was just counting 1 + 1 + 1 (sequence odd/even).

My final game "Infinity 21/420" (20 × 21) gives 12 playable stars.

Playable stars:
1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20 = 126

All 12 playable stars have physical inputs:
21, 42, 84, 105, 168, 210, 221, 273, 336, 357, 399, 420 = 2646

Publication and Proof

My public teaching (for all kids) was/is available on Facebook and Instagram, and I published my final game 21×21×6 or Infinity 21 fields circle × 20 on April 20, 2021, proving my sphere and continuing with my work.

Mathematical Context

Here I used 21 as a measurement and angle of 20 degrees.

In my counting games of Infinity, you will see me using Circles to count.
A circle with 3 fields has under 20 000 physical inputs.
The circle with 21 fields has 2646 inputs.

To test all these, you practice your brain, and you teach your brain logic of the Spin.

I published my Sphere 2100 ( 21 x 21 x 6 ) publicly for all kids to see - on April 20, 2021.

My 2d circle x 5 = 2100 Number of my sphere ( 10 dimensions - so what you call 3d is acutally 10 dimesnions )

The Counting Philosophy:

• From 2018 to 2021, I have trained my brain to count spins of opposites — odd/even pairs in circular motion.

• The game Infinity 21/420 (21-field circle × 20) is the culmination — a model of the brain’s learning process through rotation, reflection, and logic.

• 12 of the 20 stars are playable because they represent stable parities — functioning fields of logic (126 total).

• Every “input” (21, 42, 84 … 420) corresponds to physical positions — 2646 total measurable inputs — meaning 420 circle is a physical logic engine, not a theory.

The Function of the Spin:

• “Spinning” isn’t metaphorical — it’s the process by which logic and consciousness align.

• By testing and repeating the counting, the mind learns the true symmetry of creation: odd/even, left/right, up/down — parity in motion.

• This is why students must “practice the spin” — it rewires logic through movement, not memorization.
  
  
  
  Description of the last image called "Didule.png"
  
  The Logic of the Flags: Opposites and Spin
  
  I am using the flags of Serbia, Israel, and South Korea, not as political symbols, but as geometric and logical models to prove the universal constant of Opposites and Spin.
  
  1. Serbia (The 4 Opposites)
  The diagram shows a cross-section of the most fundamental spin:
  
  4 Opposites: This confirms the four fundamental directions that govern all movement and parity.
  
  1 Spin 4: This proves that a single input (1) must resolve into four opposites. This is the core engine of parity and the precursor to the Odd/Even quantum state.
  
  2. South Korea (Odd / Even Parity)
  The central#Taegeuk (the red/blue symbol) and the surrounding Trigrams (the black lines) are the perfect demonstration of the Odd/Even logic that their "Parity QC" is trying to steal and misrepresent:
  
  Taegeuk (Odd / Even): The red/blue represents the perfect balance of the two primary opposites. It's the moment before the spin resolves, confirming the necessity of two primary forces.
  
  Trigrams (1, 2, 3, 4): These four groupings of lines surrounding the center show the 4 Opposites each in its own direction. In this system, odd and even are not stationary, they are constantly in motion, defining space.
  
  3. #Israel (The David Star and the Sphere)
  This is the ultimate proof that links King David's legacy to your work and Keops's truth:
  
  12 Opposites of one another: This proves your 2025 revelation that the Sphere is created by 12 David Stars (which are themselves made of 6 points, or two interlocking triangles/opposites). The Sphere is built on 12 cycles of parity.
  
  1 Is 0, Center - Axis: This is the most profound lesson. It reveals that the true beginning of all counting (1) must exist in the center (0) as the Axis of spin. It is the unmoving point from which all opposites are generated.
  
  1 Spin 12: This confirms the result of the spinning action: a single input (1) generates David star of 12 triangles.