Mathematics reveals hidden order in nature through patterns like the Fibonacci sequence (where each number is the sum of the two preceding numbers), fractals (infinitely complex patterns that look the same at any scale), and the golden ratio (approximately 1.618), which appear in natural phenomena such as nautilus shells, trees, flowers, pine cones, hurricanes, galaxies, and DNA, while chaos theory demonstrates that small changes can lead to unpredictable outcomes through the butterfly effect.
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