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Simplexity is a neologism which proposes a possible complementary relationship between complexity and simplicity.. One of the first formally published instances of the word was in the journal 'Childhood Education' (1924), in the article it appears to be used to discuss education and psychology related issues.
A simplicial 3-complex. In mathematics, a simplicial complex is a structured set composed of points, line segments, triangles, and their n-dimensional counterparts, called simplices, such that all the faces and intersections of the elements are also included in the set (see illustration).
[1] [2] The term is generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts. The study of these complex linkages at various scales is the main goal of complex systems theory.
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Thomas Kuhn argues that as science progresses, explanations tend to become more complex before a paradigm shift offers radical simplification. [9] For example, when modeling the flight of an aircraft, we could embed each mechanical part of the aircraft into our model and would thus acquire an almost white-box model of the system.
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Similarly, if is a complex semisimple Lie algebra, every finite-dimensional representation of is a sum of irreducibles. [10] Weyl's original proof of this used the unitarian trick : Every such g {\displaystyle {\mathfrak {g}}} is the complexification of the Lie algebra of a simply connected compact Lie group K {\displaystyle K} .
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