Read the equation
Here τ is defined to be 1/(2π), approximately 0.159154943. Multiplying an angle in radians by this constant converts it into a fraction of a full turn. This local notation must be kept distinct from the widespread convention τ=2π.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| τ | Local reciprocal of 2π |
| π | Circle constant |
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
Read the surrounding source passage
## 1.3 Tau (τ) ``` τ = 1/(2π) = 0.159154943... ``` **Explanation**: Used in frequency calculations to convert between angular and linear frequency domains. --- # 2. Golden Ratio Mathematics ## 2.1 Golden Basis Function ``` ψ_k(x) = sin(2π · φ^k · x) + cos(2π · φ^k · x) ``` **Where**: - `k` = basis index [0, 15] for the 16 cognitive families - `x` = input value normalized to [0, 1] - `φ` = golden ratio **Explanation**: This is the core encoding function for holographic memory. Each basis function creates a unique frequency pattern based on powers of the golden ratio. When all 16 bases are combined, they create a holographic representation where information is distributed across all dimensions. The sum of sine and cosine creates a phase-shifted wave that captures both magnitude and phase information.
Exact original notation
τ = 1/(2π) = 0.159154943...