/**
 * A class that contains various mathematical constants.
 */
export  class Constants {
    /**
     * A small value used for comparing floating-point numbers.
     * Can be used for precision comparisons in mathematical calculations.
     */
    static readonly DELTA: number = 1e-12;

    /**
     * The mathematical constant pi (approximately 3.14159).
     * Can be used for calculations involving circles, angles, and trigonometry.
     */
    static readonly PI: number = Math.PI;

    /**
     * The mathematical constant tau, which is equal to 2 * pi (approximately 6.28318).
     * Can be used as a more convenient representation of the circle constant.
     */
    static readonly TAU: number = 6.2831853071795865;

    /**
     * The mathematical constant e (approximately 2.71828).
     * Can be used for calculations involving exponential growth and decay.
     */
    static readonly E: number = Math.E;

    /**
     * The square root of 5 (approximately 2.23607).
     * Can be used in calculations involving the golden ratio and Fibonacci numbers.
     */
    static readonly SQRT5: number = 2.2360679774997897;

    /**
     * The square root of 3 (approximately 1.73205).
     * Can be used in calculations involving equilateral triangles and hexagons.
     */
    static readonly SQRT3: number = 1.7320508075688772;

    /**
     * The square root of 2 (approximately 1.41421).
     * Can be used in calculations involving right triangles and diagonal lengths.
     */
    static readonly SQRT2: number = Math.SQRT2;

    /**
     * The square root of 1/2 (approximately 0.70711).
     * Can be used in calculations involving scaling and normalization.
     */
    static readonly SQRT1_2: number = Math.SQRT1_2;

    /**
     * The twelfth root of 12 (approximately 1.05946).
     * Can be used in calculations involving musical intervals and pitch ratios.
     */
    static readonly TWELFTH_SQRT12: number = 1.0594630943592953;

    /**
     * The cube root of 3 (approximately 1.44225).
     * Can be used in calculations involving exponential functions and logarithms.
     */
    static readonly CSQRT3: number = 1.4422495703074084;

    /**
     * The cube root of 2 (approximately 1.25992).
     * Can be used in calculations involving exponential functions and logarithms.
     */
    static readonly CSQRT2: number = 1.2599210498948732;

    /**
     * The super golden ratio (approximately 1.46557).
     * Can be used in calculations involving aesthetics and design.
     */
    static readonly SUPER_GOLDEN_RATIO: number = 1.4655712318767680;

    /**
     * The golden ratio (approximately 1.61803).
     * Can be used in calculations involving aesthetics, design, and proportions.
     */
    static readonly GOLDEN_RATIO: number = 1.6180339887498948;

    /**
     * The silver ratio (approximately 2.41421).
     * Can be used in calculations involving aesthetics, design, and proportions.
     */
    static readonly SILVER_RATIO: number = 2.414213562373095;
}