Beneath the surface of the natural world lies a symphony of mathematical patterns that govern everything from the arrangement of petals on a flower to the spirals of distant galaxies. These patterns are not human inventions but discoveries—an intrinsic language of the universe that reveals itself through numbers, shapes, and relationships. Consider the Fibonacci sequence, where each number is the sum of the two preceding ones. This progression appears in the branching of trees, the arrangement of leaves, the curve of waves, and even the breeding patterns of rabbits. The sequence leads to the golden ratio—approximately 1.618—a proportion that seems to please the human eye and appears in everything from…