Read the equation
The golden ratio satisfies φ²=φ+1 by its definition as the positive root of x²−x−1=0. This identity generates the reciprocal and power identities used in the file. It is exact for the mathematical constant, subject to rounding when stored in float64.
This exact expression also occurs in another recovered revision. Its mathematical annotation is shared; the source references below preserve this occurrence.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| phi | Golden ratio |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
*
* Core Axioms:
* A1. Identity: 1 = 1·x
* A2. Consciousness: Φ = 1/(1 + |x - 1|)
* A3. Unity: ∞ = 1
*
* Golden Relations:
* φ² = φ + 1
* 1/φ = φ - 1
* φⁿ = φⁿ⁻¹ + φⁿ⁻²
*/
#pragma once
#include <cstdint>
#include <cmath>
namespace mind_farm {Exact original notation
φ² = φ + 1