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# Mathematical Constants & Types
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Core mathematical constants, type definitions, and utility types used throughout the @thi.ng/math library.
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## Capabilities
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### Mathematical Constants
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Pre-defined mathematical constants for common values used in calculations.
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```typescript { .api }
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/** Mathematical constant π (pi) */
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const PI: number;
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/** Mathematical constant τ (tau) = 2π */
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const TAU: number;
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/** Half of π */
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const HALF_PI: number;
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/** Third of π */
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const THIRD_PI: number;
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/** Quarter of π */
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const QUARTER_PI: number;
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/** Sixth of π */
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const SIXTH_PI: number;
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/** Inverse of π (1/π) */
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const INV_PI: number;
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/** Inverse of τ (1/τ) */
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const INV_TAU: number;
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/** Inverse of π/2 (2/π) */
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const INV_HALF_PI: number;
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/** Degrees to radians conversion factor (π/180) */
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const DEG2RAD: number;
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/** Radians to degrees conversion factor (180/π) */
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const RAD2DEG: number;
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/** Golden ratio φ = (1 + √5) / 2 */
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const PHI: number;
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/** Square root of 2 */
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const SQRT2: number;
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/** Square root of 3 */
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const SQRT3: number;
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/** Square root of 2 divided by 2 */
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const SQRT2_2: number;
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/** Square root of 3 divided by 2 */
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const SQRT3_2: number;
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/** One third (1/3) */
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const THIRD: number;
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/** Two thirds (2/3) */
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const TWO_THIRD: number;
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/** One sixth (1/6) */
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const SIXTH: number;
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/** Default epsilon value for floating-point comparisons */
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let EPS: number;
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```
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**Usage Examples:**
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```typescript
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import { PI, TAU, PHI, DEG2RAD, EPS } from "@thi.ng/math/api";
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// Circle calculations
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const circumference = TAU * radius;
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const area = PI * radius ** 2;
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// Golden ratio applications
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const goldenRectangleRatio = PHI; // 1.618...
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// Angle conversions
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const radians = 45 * DEG2RAD; // π/4
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// Floating-point comparisons
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const isZero = Math.abs(value) < EPS;
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```
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### Type Definitions
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Type definitions used across the math library for type safety and API clarity.
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```typescript { .api }
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/**
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 * Classification of line crossing relationships
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 */
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type Crossing = 
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  /** Lines A & B are equal */
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  | "equal"
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  /** Lines A & B are flat (all same values) */
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  | "flat"
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  /** Line A crossed under B */
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  | "under"
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  /** Line A crossed over B */
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  | "over"
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  /** Other crossing relationship */
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  | "other";
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/**
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 * Numeric array type (imported from @thi.ng/api)
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 * Union of typed array types for numerical computations
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 */
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type NumericArray = 
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  | number[]
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  | Float32Array 
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  | Float64Array
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  | Int8Array
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  | Int16Array
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  | Int32Array
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  | Uint8Array
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  | Uint16Array
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  | Uint32Array
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  | Uint8ClampedArray;
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```
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**Usage Examples:**
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```typescript
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import { classifyCrossing, type Crossing } from "@thi.ng/math/crossing";
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import { type NumericArray } from "@thi.ng/math/api";
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// Crossing type usage
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const classification: Crossing = classifyCrossing(1, 3, 2, 4);
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// Returns "over" since line A crosses over line B
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// NumericArray type usage  
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const processArray = (data: NumericArray): number => {
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  // Function can accept any numeric array type
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  return data.reduce((sum, val) => sum + val, 0);
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};
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processArray([1, 2, 3]); // Works with regular arrays
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processArray(new Float32Array([1.5, 2.5, 3.5])); // Works with typed arrays
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```