Question

The Golden Ratio refers to \(\underline{\hspace{3cm}}\).

• A. $1:\sqrt{2}$
• B. $2:(1 + \sqrt{5})$
• C. $1:1$
• D. $16:9$

Hint:

The Golden Ratio $\phi = \frac{1+\sqrt{5}}{2}$ is valued for its natural aesthetic balance and appears in art, nature, and geometry.

Answer 1

The Correct Option is B

The Golden Ratio, denoted by the Greek letter $\phi$ (phi), is one of the most famous proportions in art, architecture, design, and nature. It is defined mathematically by the equation \[ \phi = \frac{1 + \sqrt{5}}{2}. \] This value is approximately $1.618$, and it arises from a geometric division of a line segment such that the ratio of the whole to the larger part equals the ratio of the larger part to the smaller. When expressed as a proportion, one common way of writing it is: \[ 1 : \phi \text{ or equivalently } 2 : (1 + \sqrt{5}). \] The Golden Ratio has appeared throughout history—from the Parthenon in Greece, to Renaissance paintings, to naturally occurring spirals in sunflowers and shells. The other options represent well-known ratios, but none of them correspond to the Golden Ratio: $1:\sqrt{2}$ corresponds to the paper size standard; $1:1$ represents perfect symmetry; $16:9$ is the modern screen aspect ratio. Therefore, the only correct ratio representing the Golden Ratio is option (B).