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The Fibonacci method and the golden section method are both techniques for optimization, particularly in finding the minimum or maximum of a unimodal function on a closed interval. The Fibonacci method uses a sequence of numbers to progressively narrow down the interval based on function evaluations at specific points, while the golden section method utilizes the golden ratio to determine the points at which the function is evaluated, ensuring a more efficient reduction of the interval. The Fibonacci method is more structured and relies on the Fibonacci sequence, whereas the golden section method is based on the properties of the golden ratio, which offers a more continuous approach to optimization. Both methods aim to converge on an optimal solution, but their strategies and mathematical foundations differ.

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