Consider an equilateral triangle with three spins, one on each vertex.

Consider an arbitrary triangle with sides a, b, c and with corresponding

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.

The Bertrand paradox goes as follows: Consider an equilateral triangle inscribed in a circle.

Consider again the illustration to the right, where it is known that c, e, b + d, and the triangle area A are integers.

Consider fitting a line: for each data point the product of the vertical and horizontal residuals equals twice the area of the triangle formed by the residual lines and the fitted line.

Consider a triangle ABC Let D be the midpoint of, E be the midpoint of, F be the midpoint of, and O be the centroid.

Consider a triangle ABC.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

Consider, for example, the implication this has for plane rotations.

Consider the plane spanned by and, where is a ket in the subspace perpendicular to.

Consider an open subset U of the complex plane C. Let a be an element of U, and f: U

Consider the special case in which the axis of rotation lies in the xy plane.

Consider two points A and B in two dimensional plane flow.

Consider two dimensional plane flow within a Cartesian coordinate system.

Consider a sphere B of radius 1 and a plane P touching B at the South Pole S of B.

Consider now the Minkowski plane: R < sup > 2 </ sup > equipped with the metric

Consider the ( Euclidean ) complex plane equipped with the metric

* Consider a uniform layer of fluid over an infinite horizontal plane.

Consider a " small " light source located on-axis in the object plane of the lens.

Consider a plane with a compact arrangement of spheres on it.

Consider a pair of parallel lines in an affine plane A.

Consider the example of moving along a curve γ ( t ) in the Euclidean plane.

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 ).

Consider two proof masses vibrating in plane ( as in the MEMS gyro ) at frequency.

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 an inertial observer in Minkowski spacetime who encounters a sandwich plane wave.

Consider a plane wave where all perturbed quantities vary as exp ( i ( kx-ωt )).

Consider adopting a system of holidays in which time off is granted with an eye to minimum inconvenience to the operation of the plant.

Consider a shear field with a height of H and a cross-sectional area of A opposed by a manometer with a height of H ( referred to the same base as H ) and a cross-sectional area of A.

Consider the assembly of a car: assume that certain steps in the assembly line are to install the engine, install the hood, and install the wheels ( in that order, with arbitrary interstitial steps ); only one of these steps can be done at a time.

* Consider a set with three elements, A, B, and C. The following operation:

Consider a speech signal reduced to packets, and forced to share a link with bursty data traffic ( traffic with some large data packets ).

Consider a complete orthonormal system ( basis ),, for a Hilbert space H, with respect to the norm from an inner product.

Consider the real line with its ordinary topology.

( Consider 1 / 0, which is defined with the value of infinity, vs. 0 / 0, which is undefined.

Consider a physical system that acts as a linear filter, such as a system of springs and masses, or an analog electronic circuit that includes capacitors and / or inductors ( along with other linear components such as resistors and amplifiers ).

Fundamental group: Consider the category of pointed topological spaces, i. e. topological spaces with distinguished points.

Consider a collection of particles performing a random walk in one dimension with length scale and time scale.

< li > Consider the group ( Z < sub > 6 </ sub >, +), the integers from 0 to 5 with addition modulo 6.

* The Infinite Moment ( 1961 ) ( US edition of Consider Her Ways, with two stories dropped, two others added )

Consider the following example ( in Kwakw ' ala, sentences begin with what corresponds to an English verb ):

Consider a test apparatus consisting of a closed and well insulated cylinder equipped with a piston.

Consider two noninteracting systems and, with respective Hilbert spaces and.

Consider as above systems and each with a Hilbert space,.

Consider two ISPs, A and B, which each have a presence in New York, connected by a fast link with latency 5 ms ; and which each have a presence in London connected by a 5 ms link.

Consider the following: if the typical user is searching with term " A ", would they also want resources tagged with term " B "?

Again we start with a C < sup >∞</ sup > manifold, M, and a point, x, in M. Consider the ideal, I, in C < sup >∞</ sup >( M ) consisting of all functions, ƒ, such that ƒ ( x ) = 0.

Consider a linear differential equation with constant coefficients

Consider the time series of an independent variable and a dependent variable, with observations sampled at discrete times.