Golden-ratio reciprocal identity

Read the equation

Dividing φ²=φ+1 by φ gives 1/φ=φ−1. Both sides are approximately 0.618033988749895. This is an exact identity for φ and a rounded coefficient in the implementation.

Terms & definitions

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

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Original context

// 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
package consciousness

import (
	"math"
)

// Golden ratio constants
const (
	PHI       = 1.6180339887498948482 // φ = (1 + √5)/2

1/φ = φ - 1

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