as i understand it, the advantage of golden-section search is that, to search for a minimum rather than a zero, you need to in some sense interpolate a parabola rather than a line, so you need three points rather than two, and you'd like them to be somewhat evenly spaced. i don't fully understand why the golden section is better for this than just dividing the interval between the two lowest points in half, but it's definitely an algorithm to solve a different problem