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A number of generalisations [25] [26] [27] of the notion of a word-representable graph are based on the observation by Jeff Remmel that non-edges are defined by occurrences of the pattern 11 (two consecutive equal letters) in a word representing a graph, while edges are defined by avoidance of this pattern. For example, instead of the pattern ...
The honeycomb is a well-known example of tessellation in nature with its hexagonal cells. [82] In botany, the term "tessellate" describes a checkered pattern, for example on a flower petal, tree bark, or fruit. Flowers including the fritillary, [83] and some species of Colchicum, are characteristically tessellate. [84]
In combinatorial mathematics and theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation.Any permutation may be written in one-line notation as a sequence of entries representing the result of applying the permutation to the sequence 123...; for instance the sequence 213 represents the permutation on three elements that swaps elements 1 and 2.
For example, any sequence of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns. [23] Gravity is a source of ubiquitous scientific patterns or patterns of observation. The sun rising and falling pattern each day results from the rotation of the earth while in ...
For example, . is a very general pattern, [a-z] (match all lower case letters from 'a' to 'z') is less general and b is a precise pattern (matches just 'b'). The metacharacter syntax is designed specifically to represent prescribed targets in a concise and flexible way to direct the automation of text processing of a variety of input data, in a ...
The recursive nature of some patterns is obvious in certain examples—a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. Similarly, random fractals have been used to describe/create many highly irregular real-world objects, such as coastlines and mountains.
Like the pattern blocks, the interlocking cubes provide a concrete experience for students to identify, extend, and create patterns. The difference is that a student can also physically decompose a pattern by the unit. For example, if a student made a pattern train that followed this sequence:
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
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