Which ratio discovered by Pythagoras is known for providing a visually pleasing appearance in art and architecture?

The ratio known for providing a visually pleasing appearance in art and architecture is the Golden section, often referred to as the Golden ratio. This ratio, approximately equal to 1.618, has been appreciated since antiquity for its aesthetic appeal and harmony in design. It is derived from the division of a line into two parts so that the ratio of the whole line to the longer part is equal to the ratio of the longer part to the shorter part, embodying a mathematical elegance that resonates with human perception.

The Golden section has been extensively used by artists and architects throughout history, from classical antiquity to the Renaissance and even in modern design. Its application can be seen in various forms, such as in the proportions of buildings, the layout of paintings, and the arrangement of elements within a composition, creating a sense of balance and beauty.

In contrast, while arithmetic and geometric proportions are fundamental concepts in mathematics, they do not carry the same aesthetic significance associated with the Golden section. The term "grid" typically refers to a structural framework used for organization in design or layout but lacks the specific properties of beauty and proportion that characterize the Golden ratio.