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He did not realize that his figure was a continuous flight of stairs while drawing, but the process enabled him to trace his increasingly complex designs step by step. When M.C. Escher's Ascending and Descending was sent to Reutersvärd in 1961, he was impressed but didn't like the irregularities of the stairs (2 × 15 + 2 × 9).
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.
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 category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain.
To see how this number arises, consider the real one-parameter map =.Here a is the bifurcation parameter, x is the variable. The values of a for which the period doubles (e.g. the largest value for a with no period-2 orbit, or the largest a with no period-4 orbit), are a 1, a 2 etc.
Algebraic link diagram for the Borromean rings. The vertical dotted black midline is a Conway sphere separating the diagram into 2-tangles. In knot theory, the Borromean rings are a simple example of a Brunnian link, a link that cannot be separated but that falls apart into separate unknotted loops as soon as any one of its components is ...
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 ...