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In mathematics, a Young tableau (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties.
Mathematical visualization is used throughout mathematics, particularly in the fields of geometry and analysis. Notable examples include plane curves , space curves , polyhedra , ordinary differential equations , partial differential equations (particularly numerical solutions, as in fluid dynamics or minimal surfaces such as soap films ...
In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal (e.g., mental construct) and external (e.g., graph). Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate ...
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
These sets can be used to define a plane dual structure. Interchange the role of "points" and "lines" in C = (P, L, I) to obtain the dual structure. C ∗ = (L, P, I ∗), where I ∗ is the converse relation of I. C ∗ is also a projective plane, called the dual plane of C. If C and C ∗ are isomorphic, then C is called self-dual.
Example of a grouped (clustered) bar chart, one with horizontal bars. A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent.
The researcher would then plot the data in a scatter plot, assigning "lung capacity" to the horizontal axis, and "time holding breath" to the vertical axis. [ citation needed ] A person with a lung capacity of 400 cl who held their breath for 21.7 s would be represented by a single dot on the scatter plot at the point (400, 21.7) in the ...
so the exponential map applied to the ε-axis covers only half the "circle". Let z = a + bε. If a ≠ 0 and m = b / a , then z = a(1 + mε) is the polar decomposition of the dual number z, and the slope m is its angular part. The concept of a rotation in the dual number plane is equivalent to a vertical shear mapping since (1 + pε)(1 ...