Zilverhoudingen

Zilverhoudingen, also known as silver ratios, are a family of irrational numbers that are related to the silver ratio, often denoted by the Greek letter delta (δ). The primary silver ratio is defined as 1 + sqrt(2). This number is approximately 2.414. Like the golden ratio, the silver ratio appears in various mathematical contexts, including geometry and number theory.

The silver ratio has a recursive property. If you take a rectangle with sides in the silver ratio, and cut off a square, the remaining rectangle will also have sides in the silver ratio. This is analogous to how the golden ratio behaves. The silver ratio is also related to the Pell numbers, a sequence of integers similar to the Fibonacci numbers. The ratio of consecutive Pell numbers approaches the silver ratio.

Other members of the silver ratio family exist, often represented as 1 + n*sqrt(2), where n is an integer. These ratios share some of the geometric and number-theoretic properties of the primary silver ratio, though they are less commonly encountered. The silver ratio and its relatives are distinct from the golden ratio, which is defined as (1 + sqrt(5))/2. While both are irrational and possess repeating geometric properties, their numerical values and related sequences differ. The study of silver ratios falls within the broader field of irrational numbers and their mathematical applications.