gamma_1_2_squared.rs

gamma_1_2_squared.rs

// Verbose Script: Corrected Floating-Point Comparison

fn main() {
    // ----------------------------------------------------
    // 1. Define Constants
    // ----------------------------------------------------

    const PI: f64 = std::f64::consts::PI;
    let gamma_one_half: f64 = PI.sqrt();
    
    println!("--- Initial Mathematical Fact ---");
    println!("Gamma(1/2) (Simulated) = {:.16}", gamma_one_half);
    println!("Square Root of Pi          = {:.16}", PI.sqrt());
    println!("---------------------------------");
    
    // ----------------------------------------------------
    // 2. Perform the Squaring Operation
    // ----------------------------------------------------

    // LHS: (Gamma(1/2))^2 = (sqrt(PI))^2. The result might hold a slight rounding error.
    let lhs_squared: f64 = gamma_one_half.powi(2);

    // RHS: PI (the original constant)
    let rhs_squared: f64 = PI;

    // ----------------------------------------------------
    // 3. Print the Resulting Equation
    // ----------------------------------------------------

    println!("\n--- Resulting Equation After Squaring Both Sides ---");
    
    println!("LHS: (Gamma(1/2))^2 = {:.16}", lhs_squared);
    println!("RHS: pi            = {:.16}", rhs_squared);

    // ----------------------------------------------------
    // 4. Robust Comparison
    // ----------------------------------------------------
    
    const TOLERANCE: f64 = 1e-15; // A more appropriate fixed tolerance for high-precision math
    
    println!("\n--- Conclusion ---");
    // Check for equality using a reasonable tolerance.
    if (lhs_squared - rhs_squared).abs() < TOLERANCE {
        println!("The squared LHS and RHS are equal within tolerance of {}.", TOLERANCE);
        println!("The resulting equation is mathematically verified: (Gamma(1/2))^2 = pi");
    } else {
        println!("Error: The calculated values do not match (even with tolerance).");
    }
}

https://play.rust-lang.org/?version=stable&mode=debug&edition=2024&gist=c60f8e78ef58d25b493ce6abd987dd8d