Create golden_ratio.py

golden_ratio.py

@@ -0,0 +1,22 @@
+def golden_ratio(iterations=15):
+    # Start with an initial approximation of the golden ratio, typically 1.
+    ratio = 1
+
+    # Iterate to improve the approximation.
+    for _ in range(iterations):
+        # The golden ratio is defined as (1 + sqrt(5)) / 2.
+        # We can approximate it by adding 1 to the reciprocal of the current approximation.
+        # This approach iteratively refines the approximation.
+        ratio = 1 + 1 / ratio
+
+    return ratio
+
+# Example usage:
+approximations = []
+for i in range(1, 16):
+    approximation = golden_ratio(i)
+    approximations.append(approximation)
+
+print("Approximations of the Golden Ratio:")
+for i, approx in enumerate(approximations):
+    print(f"Iteration {i+1}: {approx:.16f}")