Goldschnitt

Goldschnitt, or the golden section, is a mathematical proportion long associated with aesthetic balance. It is defined by a line divided into two parts so that the whole is to the larger part as the larger part is to the smaller part. The ratio is φ, approximately 1.618. Equivalently, if a and b are the two parts with a ≤ b, then (a+b)/b = b/a = φ.

Historically, the concept appears in discussions of classical art and architecture and is popularly called Goldener Schnitt in German. It is tied to the golden rectangle, a rectangle whose side ratio is φ; when a square is removed, the remaining rectangle is again golden. The notion also relates to the golden spiral, which can be drawn by quarter circles within successive golden rectangles. φ can be approximated by the ratios of successive Fibonacci numbers, which converge to the same value as the sequence progresses.

Applications of the Goldschnitt occur in visual composition, architecture, and design, where it is used as a guideline for balance, proportion, and hierarchy. Designers may employ the golden rectangle or the spiral to guide placement of elements, and the Fibonacci sequence provides a practical approximation for constructing proportions. In practice, adherence to φ is not universal and is often one among several principles used to structure work.

Criticism notes that there is no universal or invariant aesthetic rule validated across cultures or contexts. The term Goldschnitt is sometimes used descriptively in modern discourse and marketing, and its historical use is occasionally overstated in popular accounts.