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import numpy as np
import matplotlib.pyplot as plt
# cool things about the golden ratio, just like facts,
e1 = "(φ ≈ 1.618)"
print("""
the golden spiral, derived from the golden ratio ""","<yellow>" +e1+ "</yellow>",""", is found throughout nature, art, architecture, and even human behavior, its a visually appealing pattern that has captured the imagination of people for centuries""")
# its applications to life
print("""
yep, would love to show you some of its applications in life! here are some of its applications i found in books on webpages:
""")
ap1 = "its applications in nature:"
ex1 = """snails: the most famous natural example is the spiral shape of shells, such as the nautilus shell
the spiral grows outward in a pattern that closely follows the golden spiral, with each turn of the spiral representing a growth ratio of approximately 1.618
this helps the organism grow in a compact and efficient way while maintaining structural integrity
flower petals: Many flowers exhibit a Fibonacci pattern, a close approximation of the golden ratio, in the number of petals or the arrangement of seeds
for instance, sunflowers, pinecones, and pineapples all display spiral patterns that resemble the golden spiral
hurricanes and galaxies: hurricanes, spiral galaxies, and certain types of weather patterns also display the shape of a spiral
these patterns form as the energy distribution follows the spirals exponential growth, optimizing the systems dynamics"""
print("<blue>"+ap1+"</blue>",
"<green>"+ex1+"</green>")
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OUTPUT
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