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In such a 2D diagram of a 3D coordinate system, the z-axis would appear as a line or ray pointing down and to the left or down and to the right, depending on the presumed viewer or camera perspective. In any diagram or display, the orientation of the three axes, as a whole, is arbitrary.
Cartesian diagram, a construction in category theory; Cartesian geometry, now more commonly called analytic geometry; Cartesian morphism, formalisation of pull-back operation in category theory; Cartesian oval, a curve; Cartesian product, a direct product of two sets; Cartesian product of graphs, a binary operation on graphs
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A representation of a three-dimensional Cartesian coordinate system. In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point.
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.
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On the other hand, the representation of an object in a diagram may be overly specific and properties that are true in the diagram may not be true for the object the diagram represents. [7]: 48 A diagram may act as a means of cognitive extension allowing reasoning to take place on the diagram based on which constraints are similar. [7]: 50
In geometry, a Schlegel diagram is a projection of a polytope from into through a point just outside one of its facets. The resulting entity is a polytopal subdivision of the facet in R d − 1 {\textstyle \mathbb {R} ^{d-1}} that, together with the original facet, is combinatorially equivalent to the original polytope.