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sor-pt-4e648d95ef1f | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: Table of Contents
## Table of Contents
Sphere of Realization Table of Contents:
1. Solution Techniques for the Phenomenological Velocity Equation (V-Curvature) and Discussion of the V-Curvatu... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "Table of Contents",
"section": null,
"source": "printed edition, PDF page 2 (not in the notebook)"
} |
sor-pt-3905051f62e9 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
# The Sphere of Realization : The Mathematical Path of Harmonious Being | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": null,
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-18ad49db8c18 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 1. Step-by-step Solutions to the Phenomenological Velocity (V-Curvature) Equation and Discourse on the V-Curvature Method and Energy As Boundaries
## 1. Step-by-step Solutions to the Phenomenol... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "1. Step-by-step Solutions to the Phenomenological Velocity (V-Curvature) Equation and Discourse on the V-Curvature Method and Energy As Boundaries",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-6a343e937ecb | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 2. Map of Equations: Differential Combinations and Methods
## 2. Map of Equations: Differential Combinations and Methods
- θ z = r α - x δ : An arc length of given angle and radius equals the ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "2. Map of Equations: Differential Combinations and Methods",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-edc15c07e0fa | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 3. New Statements on Philosophy
## 3. New Statements on Philosophy
Introduction:
The only way to, "escape the matrix," is to define who you are and bend the matrix to you. Arguing over whethe... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "3. New Statements on Philosophy",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-53059969b8d5 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.
## 5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.
```wolfram
(4 / 3) π r^3 - (4 / 3) x^3 == π r^2((y + ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-5c3d054cfe15 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 6. Locales of Infinity : The Place of Imagination and the Missing Components
## 6. Locales of Infinity : The Place of Imagination and the Missing Components | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "6. Locales of Infinity : The Place of Imagination and the Missing Components",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-6ad2c9717f20 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 6. Locales of Infinity : The Place of Imagination and the Missing Components
### 6.1 A New Logic - Based Notation for Denoting Positions and Constraints in Algebraic Geometry | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "6. Locales of Infinity : The Place of Imagination and the Missing Components",
"section": "6.1 A New Logic - Based Notation for Denoting Positions and Constraints in Algebraic Geometry",
"source": "Mathematica noteb... |
sor-pt-e2b36e6e46d3 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 6. Locales of Infinity : The Place of Imagination and the Missing Components
### ∃∞ ∍ : ∞_((((2 π))_θ → (∅)_x)) ∧ ∞_((∞_γ → ((1/∞))_x)) ⇌ ∞_((∞_r → 0_(- γ))) ∴ 1 ∃
"There exists infinity such ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "6. Locales of Infinity : The Place of Imagination and the Missing Components",
"section": "∃∞ ∍ : ∞_((((2 π))_θ → (∅)_x)) ∧ ∞_((∞_γ → ((1/∞))_x)) ⇌ ∞_((∞_r → 0_(- γ))) ∴ 1 ∃",
"source": "Mathematica notebook"
} |
sor-pt-eb2ef7225e64 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 6. Locales of Infinity : The Place of Imagination and the Missing Components
Section: 6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ) (part 1 of 2)
#... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "6. Locales of Infinity : The Place of Imagination and the Missing Components",
"section": "6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ)",
"source": "Mathematica noteboo... |
sor-pt-c18ad6e04945 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 6. Locales of Infinity : The Place of Imagination and the Missing Components
Section: 6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ) (part 2 of 2)
I... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "6. Locales of Infinity : The Place of Imagination and the Missing Components",
"section": "6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ)",
"source": "Mathematica noteboo... |
sor-pt-a90e87a21b5d | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Section: part 1 of 6
## 7. Discussions on the Nature of Acceler... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-5d67ac779a58 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Section: part 2 of 6
Input:
```wolfram
Solve[(6 π^2 (-4 π + 2 θ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-be9cc890ddc3 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Section: part 3 of 6
Input:
```wolfram
Solve[(6 π^2 (-4 π + 2 θ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-d89aab73a2b1 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Section: part 4 of 6
Input, continued (piece 2 of 2):
```wolfra... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-fc3471359a9a | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Section: part 5 of 6
Input:
```wolfram
Solve[(4 π γ + γ^2 - Sqr... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-32ae1c777f15 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Section: part 6 of 6
Input, continued (piece 2 of 2):
```wolfra... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-cb6d4dd18d9d | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals
## 8.... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals",
"section": null,
"source"... |
sor-pt-91cec6d5d4ed | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals
### 8... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals",
"section": "8.1 - Basic Pos... |
sor-pt-b91e33edce16 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals
### 8... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals",
"section": "8.2 Solutions t... |
sor-pt-a5a9d2ef5b48 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals
Sectio... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals",
"section": "8.3 Integrating... |
sor-pt-e25ed9a428a8 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals
Sectio... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals",
"section": "8.3 Integrating... |
sor-pt-8a97520eee94 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 1 of 21
## 9. Warp Variable Nature
The Seven Seals; The Seven Days of creation:
Starting with the generalized (Sqrt[c^2 r^2 α^2 - c^2 r^2 δ^2 - 2 c^2 r z... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-97274604927b | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 2 of 21
Input:
```wolfram
Solve[Sqrt[c^2 r^2 α^2 - c^2 r^2 δ^2 - 2 c^2 r s α + c^2 s δ^2 ((s/(α + δ Cos[β]) Sin[β]))^2 + c^2 s^2] == (-1/4 s^2 (δ Cos[β] Lo... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-a668041e8406 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 3 of 21
Input:
```wolfram
Solve[Sqrt[c^2 r^2 α^2 - c^2 r^2 δ^2 - 2 c^2 r s α + c^2 s δ^2 ((s/(α + δ Cos[β]) Sin[β]))^2 + c^2 s^2] == (-1/4 s^2 (δ Cos[β] Lo... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-93bcfc9f67f8 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 4 of 21
Input:
```wolfram
Solve[Sqrt[c^2 r^2 α^2 - c^2 r^2 δ^2 - 2 c^2 r s α + c^2 s δ^2 ((s/(α + δ Cos[β]) Sin[β]))^2 + c^2 s^2] == (-1/4 s^2 (δ Cos[β] Lo... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-a8716c8e4892 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 5 of 21
Input:
```wolfram
Solve[Sqrt[c^2 r^2 α^2 - c^2 r^2 δ^2 - 2 c^2 r s α + c^2 s δ^2 ((s/(α + δ Cos[β]) Sin[β]))^2 + c^2 s^2] == (-1/4 s^2 (δ Cos[β] Lo... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-9302a566c865 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 6 of 21
Input, continued (piece 2 of 32):
```wolfram
+ 2.`14.85583028601747 r^2 α^2 δ^4 (Cos[β])^2 (Log[δ])^2 Log[α + δ Cos[β]] Log[1.`14.85583028601747 + ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-9533b4ed4841 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 7 of 21
Input, continued (piece 4 of 32):
```wolfram
- 2.`14.85583028601747 r α^5 (PolyLog[2.`14.85583028601747, -(1.`14.85583028601747 δ Cos[β])/α])^2 - 4... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-8f00eeed9be3 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 8 of 21
Input, continued (piece 6 of 32):
```wolfram
+ 2.`14.85583028601747 r^2 α^5 δ Cos[β] Log[α + δ Cos[β]] Log[1.`14.85583028601747 + (δ Cos[β])/α] - 2... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-a08b3bac3091 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 9 of 21
Input, continued (piece 8 of 32):
```wolfram
- 4.`14.85583028601747 r α^5 Log[δ] PolyLog[2.`14.85583028601747, -(1.`14.85583028601747 δ Cos[β])/α] ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-664428fc928b | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 10 of 21
Input, continued (piece 10 of 32):
```wolfram
Root[-16.`14.85583028601747 c^2 r^2 α^4 + 16.`14.85583028601747 c^2 r^2 α^2 δ^2 - 32.`14.85583028601... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-13060e90f775 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 11 of 21
Input, continued (piece 12 of 32):
```wolfram
+ 2.`14.85583028601747 r^2 α^5 δ Cos[β] (PolyLog[2.`14.85583028601747, -(1.`14.85583028601747 δ Cos[... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-7085f27611b6 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 12 of 21
Input, continued (piece 14 of 32):
```wolfram
+ (α^2 δ^2 (Log[δ])^2 (Sin[β])^2 - 2.`14.85583028601747 α δ^3 Cos[β] Log[δ] Log[α + δ Cos[β]] (Sin[β... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-7d36a709ac1c | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 13 of 21
Input, continued (piece 16 of 32):
```wolfram
- 2.`14.85583028601747 r^2 α^6 Log[1.`14.85583028601747 + (δ Cos[β])/α] PolyLog[2.`14.85583028601747... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-c3fb69b0aec4 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 14 of 21
Input, continued (piece 18 of 32):
```wolfram
- 4.`14.85583028601747 α^2 δ^2 (Cos[β])^2 Log[α + δ Cos[β]] PolyLog[2.`14.85583028601747, -(1.`14.85... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-0bb54c235bd9 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 15 of 21
Input, continued (piece 20 of 32):
```wolfram
+ 2.`14.85583028601747 r^2 α^2 δ^4 (Cos[β])^2 (Log[δ])^2 Log[α + δ Cos[β]] Log[1.`14.85583028601747 ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-39623dc37d13 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 16 of 21
Input, continued (piece 22 of 32):
```wolfram
- 2.`14.85583028601747 r α^5 (PolyLog[2.`14.85583028601747, -(1.`14.85583028601747 δ Cos[β])/α])^2 -... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-e6823d742ddf | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 17 of 21
Input, continued (piece 24 of 32):
```wolfram
+ 2.`14.85583028601747 r^2 α^5 δ Cos[β] Log[α + δ Cos[β]] Log[1.`14.85583028601747 + (δ Cos[β])/α] -... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-4419225a7a44 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 18 of 21
Input, continued (piece 26 of 32):
```wolfram
- 4.`14.85583028601747 r α^5 Log[δ] PolyLog[2.`14.85583028601747, -(1.`14.85583028601747 δ Cos[β])/α... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-31b6a0b34bb1 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 19 of 21
Input, continued (piece 28 of 32):
```wolfram
Root[-16.`14.85583028601747 c^2 r^2 α^4 + 16.`14.85583028601747 c^2 r^2 α^2 δ^2 - 32.`14.85583028601... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-7cc598d7b5cd | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 20 of 21
Input, continued (piece 30 of 32):
```wolfram
+ 2.`14.85583028601747 r^2 α^5 δ Cos[β] (PolyLog[2.`14.85583028601747, -(1.`14.85583028601747 δ Cos[... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-71dca60f525b | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Section: part 21 of 21
Message: General::ivar: 6.283184609047885` is not a valid variable.
Message: General::ivar: 6.283184609047885` is not a valid variable.
Message:... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-a1a46d1b8729 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 1 of 16
## 10. The Nature of Mass - Matter as Multi-D... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-b4f8ecd1db05 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 2 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.`... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-2f768a064930 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 3 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.`... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-425969f2a13d | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 4 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.`... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-f41c98ca4e4d | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 5 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.`... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-45293b9cb5a4 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 6 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.`... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-223cfaab64e3 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 7 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.`... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-99ca1a453770 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 8 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.`... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-e8fedeb01e06 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 9 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.`... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-74430c2ac994 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 10 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-99ce001462f6 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 11 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-d5dbddcf6d63 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 12 of 16
Input:
```wolfram
Solve[1/(Sqrt[1.` c^2 - 1.... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-211c9243956d | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 13 of 16
```wolfram
{{α → -(0.5` (-1.` z θ + 1.` r δ ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-0709d7192e04 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 14 of 16
Input, continued (piece 5 of 12):
```wolfram... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-77c05dc8144c | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path
Section: part 15 of 16
Input, continued (piece 9 of 12):
```wolfram... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "10. The Nature of Mass - Matter as Multi-Dimensional Resonant Frequency in a Broader Equation - The Coefficients Are the Path",
"section": null,
"source": "Mathematica notebook"
} |
sor-pt-graphic-0001 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 1. Step-by-step Solutions to the Phenomenological Velocity (V-Curvature) Equation and Discourse on the V-Curvature Method and Energy As Boundaries
Graphic sor-plot-0001
A picture of typeset mat... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "1. Step-by-step Solutions to the Phenomenological Velocity (V-Curvature) Equation and Discourse on the V-Curvature Method and Energy As Boundaries",
"section": null,
"subsection": null,
"source": "graphic record",... |
sor-pt-graphic-0002 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 1. Step-by-step Solutions to the Phenomenological Velocity (V-Curvature) Equation and Discourse on the V-Curvature Method and Energy As Boundaries
Graphic sor-plot-0002
A picture of typeset mat... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "1. Step-by-step Solutions to the Phenomenological Velocity (V-Curvature) Equation and Discourse on the V-Curvature Method and Energy As Boundaries",
"section": null,
"subsection": null,
"source": "graphic record",... |
sor-pt-graphic-0003 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 1. Step-by-step Solutions to the Phenomenological Velocity (V-Curvature) Equation and Discourse on the V-Curvature Method and Energy As Boundaries
Graphic sor-plot-0003
An image embedded in the... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "1. Step-by-step Solutions to the Phenomenological Velocity (V-Curvature) Equation and Discourse on the V-Curvature Method and Energy As Boundaries",
"section": null,
"subsection": null,
"source": "graphic record",... |
sor-pt-graphic-0004 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 2. Map of Equations: Differential Combinations and Methods
Graphic sor-plot-0004
An image embedded in the notebook (pixels only; no coordinates are stored for it).
Text in the picture:
Let $\... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "2. Map of Equations: Differential Combinations and Methods",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0004"
} |
sor-pt-graphic-0005 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Graphic sor-plot-0005
An image embedded in the notebook (pixels only; no coordinates are stored for it).
A sphere of radius $r$ with a spheric... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0005"
} |
sor-pt-graphic-0006 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Graphic sor-plot-0006
An image embedded in the notebook (pixels only; no coordinates are stored for it).
A sphere of radius $R$ with a spheric... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0006"
} |
sor-pt-graphic-0007 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Graphic sor-plot-0007
An image embedded in the notebook (pixels only; no coordinates are stored for it).
A sphere of radius $r$ with a spheric... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0007"
} |
sor-pt-graphic-0008 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0009 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0010 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0011 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0013 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0014 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0015 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0016 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0017 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0018 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 4. Difference between Surface Areas of Two Spheres
Subsection: Equating this result with radius solution from, "The Cone of Perception," (Emmerson, 2009 - 2014) yields an interesting symmetry an... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "4. Difference between Surface Areas of Two Spheres",
"section": null,
"subsection": "Equating this result with radius solution from, \"The Cone of Perception,\" (Emmerson, 2009 - 2014) yields an interesting symmetry... |
sor-pt-graphic-0019 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.
Graphic sor-plot-0019
Graphic placed in the notebook after the command:
```wolfram
ContourPlot3D[1/2 ((-3 a^2 h - h^3 + 2 h r... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0019"
} |
sor-pt-graphic-0020 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.
Graphic sor-plot-0020
Graphic placed in the notebook after the command:
```wolfram
ContourPlot3D[1/2 ((-3 a^2 h - h^3 + 2 h r... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0020"
} |
sor-pt-graphic-0021 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.
Graphic sor-plot-0021
Command that drew it:
```wolfram
ContourPlot3D[1/2 ((-1))^(2 / 3) ((-3 a^2 h - h^3 + 2 h r^2 + 6 r^3))^... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0021"
} |
sor-pt-graphic-0022 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.
Graphic sor-plot-0022
Command that drew it:
```wolfram
ContourPlot3D[{-h/9 + (2 2^(1 / 3) h^2)/(9 ((2916 a^2 h + 956 h^3 + 77... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0022"
} |
sor-pt-graphic-0023 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.
Graphic sor-plot-0023
Command that drew it:
```wolfram
ContourPlot3D[-h/9 + (2 2^(1 / 3) h^2)/(9 ((2916 a^2 h + 956 h^3 + 777... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "5. Difference between Volumes of Two Spheres: Imaginary 4-D realms.",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0023"
} |
sor-pt-graphic-0025 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 6. Locales of Infinity : The Place of Imagination and the Missing Components
Section: 6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ)
Graphic sor-plot... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "6. Locales of Infinity : The Place of Imagination and the Missing Components",
"section": "6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ)",
"subsection": null,
"source"... |
sor-pt-graphic-0026 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 6. Locales of Infinity : The Place of Imagination and the Missing Components
Section: 6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ)
Graphic sor-plot... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "6. Locales of Infinity : The Place of Imagination and the Missing Components",
"section": "6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ)",
"subsection": null,
"source"... |
sor-pt-graphic-0027 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 6. Locales of Infinity : The Place of Imagination and the Missing Components
Section: 6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ)
Graphic sor-plot... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "6. Locales of Infinity : The Place of Imagination and the Missing Components",
"section": "6.2 Investigations of ∞_((∞_r → 0_(- γ))), Significations of Section 6.1 A) ℋ1 == r + r (γ)",
"subsection": null,
"source"... |
sor-pt-graphic-0028 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Graphic sor-plot-0028
Command that drew it:
```wolfram
Spherica... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "so... |
sor-pt-graphic-0029 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Graphic sor-plot-0029
Command that drew it:
```wolfram
Spherica... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "so... |
sor-pt-graphic-0030 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Graphic sor-plot-0030
Graphic placed in the notebook after the ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "so... |
sor-pt-graphic-0031 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed
Graphic sor-plot-0031
Command that drew it: the input in notebo... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "7. Discussions on the Nature of Acceleration and Non-Commutation: Constrained Models and Generalized Propositions for Light Speed",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "so... |
sor-pt-graphic-0032 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals
Sectio... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals",
"section": "8.3 Integrating... |
sor-pt-graphic-0033 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals
Sectio... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals",
"section": "8.3 Integrating... |
sor-pt-graphic-0034 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals
Sectio... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "8. Liberation: Liberating Constraints on the Difference Equation and the Resulting Equalities with V-Curvature (Components for Worm Holes) and Methods for Solving Non-Elementary Integrals",
"section": "8.3 Integrating... |
sor-pt-graphic-0035 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Graphic sor-plot-0035
Command that drew it: the input in notebook cell 318 (179,105 characters; given in full in the chapter text).
An interactive Manipulate panel. The... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0035"
} |
sor-pt-graphic-0036 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Graphic sor-plot-0036
Graphic placed in the notebook after the command: the input in notebook cell 318 (179,105 characters; given in full in the chapter text).
This gra... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0036"
} |
sor-pt-graphic-0037 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Graphic sor-plot-0037
Graphic placed in the notebook after the command: the input in notebook cell 318 (179,105 characters; given in full in the chapter text).
Its stor... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0037"
} |
sor-pt-graphic-0038 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Graphic sor-plot-0038
Graphic placed in the notebook after the command: the input in notebook cell 318 (179,105 characters; given in full in the chapter text).
This gra... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0038"
} |
sor-pt-graphic-0039 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Graphic sor-plot-0039
Graphic placed in the notebook after the command: the input in notebook cell 318 (179,105 characters; given in full in the chapter text).
This gra... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0039"
} |
sor-pt-graphic-0040 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Graphic sor-plot-0040
This graphic was pasted into an input cell; the plotting function that made it is not recorded with it, so its points are given as plain (x, y, z) ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0040"
} |
sor-pt-graphic-0041 | The Sphere of Realization: The Mathematical Path of Harmonious Being (2nd Edition) by Parker Emmerson (Yaohushuason)
Chapter: 9. Warp Variable Nature
Graphic sor-plot-0041
This graphic was pasted into an input cell; the plotting function that made it is not recorded with it, so its points are given as plain (x, y, z) ... | {
"book": "The Sphere of Realization",
"author": "Parker Emmerson (Yaohushuason)",
"chapter": "9. Warp Variable Nature",
"section": null,
"subsection": null,
"source": "graphic record",
"plot_id": "sor-plot-0041"
} |
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