Why is the golden ratio considered beautiful by many?

The golden ratio is often presented as if it automatically makes anything beautiful, but the real story is more careful. The golden ratio is: $$\varphi=\frac{1+\sqrt5}{2}\approx 1.618.$$ It appears naturally in some mathematical patterns, especially Fibonacci ratios. That part is real. But the claim that humans universally prefer golden-ratio rectangles is much weaker. Some studies find mild preferences; others do not. In art and architecture, people also tend to notice examples that fit the story and ignore examples that do not. So a balanced answer is: - $\varphi$ is mathematically elegant, - it appears in some natural and geometric settings, - it can produce pleasing proportions, - but many popular claims about it are exaggerated after the fact. Beauty in design usually comes from balance, contrast, rhythm, context, and function, not one magic number.