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In mathematical analysis, the staircase paradox is a pathological example showing that limits of curves do not necessarily preserve their length. [1] It consists of a sequence of "staircase" polygonal chains in a unit square , formed from horizontal and vertical line segments of decreasing length, so that these staircases converge uniformly to ...
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
An animated cobweb diagram of the logistic map = (), showing chaotic behaviour for most values of >. A cobweb plot , known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions , such as the logistic map .
A building's surface detailing, inside and outside, often includes decorative moulding, and these often contain ogee-shaped profiles—consisting (from low to high) of a concave arc flowing into a convex arc, with vertical ends; if the lower curve is convex and higher one concave, this is known as a Roman ogee, although frequently the terms are used interchangeably and for a variety of other ...
A staircase or stairway is one or more flights of stairs leading from one floor to another, and includes landings, newel posts, handrails, balustrades, and additional parts. [5] In buildings, stairs is a term applied to a complete flight of steps between two floors. A stair flight is a run of stairs or steps
The graph of the Cantor function on the unit interval. In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous.It is a notorious counterexample in analysis, because it challenges naive intuitions about continuity, derivative, and measure.
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, ...
Stairway with skylight. A stairwell or stair room is a room in a building where a stair is located, and is used to connect walkways between floors so that one can move in height. [1] Collectively, a set of stairs and a stairwell is referred to as a staircase or stairway.