Degrau

Degrau is a term used in Portuguese and other languages to refer to a single step of a staircase. In architectural and construction contexts, a degrau is the horizontal surface a person steps on, called the tread, and its vertical face, the riser, which rises to the next level. Stairs are designed to provide safe ascent and descent, with the size and shape of degraus governed by building codes and ergonomic guidelines. The function of degraus is to translate vertical height into a sequence of shallow climbs, enabling access between different levels of a structure. Variations exist across regions and types of stairs.

In mathematics and related fields, degrau can refer to a step function, also called a Heaviside function in many contexts. A degrau (step) function is piecewise constant, remaining at one value until a threshold and then jumping to another value, creating a graph of horizontal steps. A common example is the unit step function u(t), which is 0 for t < 0 and 1 for t ≥ 0. Step functions model instantaneous changes and are widely used in signal processing, control theory, and systems analysis.

Other uses and considerations: The concept of a degrau appears in descriptions of thresholds, levels, or progressions in various disciplines. In design and safety, the size and proportion of steps influence accessibility, including compliance with accessibility standards. The term generally conveys a progression from one level to another, whether in physical space, mathematical representations, or abstract systems.