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Consider a polygon in the complex plane.
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Consider and polygon
Consider a polygon P and a triangle T, with one edge in common with P. Assume Pick's theorem is true for both P and T separately ; we want to show that it is also true to the polygon PT obtained by adding T to P. Since P and T share an edge, all the boundary points along the edge in common are merged to interior points, except for the two endpoints of the edge, which are merged to boundary points.
Consider region D in the plane: a unit circle or general polygon — the asymptotics of the problem, which are the interesting aspect, aren't dependent on the exact shape.
Consider the non-convex polygon P shown in the figure, which is formed from a regular hexagon by adding projections on two of its sides and matching indentations on three sides.
Consider and complex
Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.
In Consider Phlebas it is noted that Minds still find humans fascinating, especially their odd ability to sometimes achieve similarly advanced reasoning as their much more complex machine brains.
Consider the complex Hilbert space L < sup > 2 </ sup >( R ), and the operator which multiplies a given function by x:
Consider the Gram – Schmidt process applied to the columns of the full column rank matrix, with inner product ( or for the complex case ).
A fundamental part of ` Abdul-Bahá's teachings on evolution is the belief that all life came from the same origin: " the origin of all material life is one ..." He states that from this sole origin, the complete diversity of life was generated: " Consider the world of created beings, how varied and diverse they are in species, yet with one sole origin " He explains that a slow, gradual process led to the development of complex entities:
Consider for example any compact connected complex manifold M: any holomorphic function on it is locally constant by Liouville's theorem.
Consider a complex, real-world problem, like those of marketing or making policies for a nation, where there are many governing factors, and most of them cannot be expressed as numerical time series data, as one would like to have for building mathematical models.
Consider a once-punctured elliptic curve, given as the locus D of complex points satisfying, where and is a complex number.
Consider a d < sup > 6 </ sup > octahedral complex ( example IrBr < sub > 6 </ sub >< sup > 3 -</ sup >).
Consider and plane
Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.
Consider a planar projection of each knot and suppose these projections are disjoint. Find a rectangle in the plane where one pair of sides are arcs along each knot but is otherwise disjoint from the knots.
Consider a point in a continuum under a state of plane stress, or plane strain, with stress components and all other stress components equal to zero ( Figure 7. 1, Figure 8. 1 ).
Consider a set of points R ( R is a vector depicting a point in a Bravais lattice ) constituting a Bravais lattice, and a plane wave defined by:
Consider the illustration, depicting a plane intersecting a cone to form an ellipse ( the interior of the ellipse is colored light blue ).
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