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 a triangle in the plane with unequal sides.

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

Consider a wave packet as a function of position x and time t: α ( x, t ).

Consider a wave function that is a sum of many waves, however, we may write this as

Consider a traveling transverse wave ( which may be a pulse ) on a string ( the medium ).

Consider this wave as traveling

Consider a light wave propagating along the z principal axis polarised such the electric field of the wave is parallel to the x-axis.

Consider solutions in which a fixed wave form ( given by f ( X )) maintains its shape as it travels to the right at phase speed c. Such a solution is given by ( x, t )

Consider the net electric field E produced by a light wave of frequency ω together with an external electric field E < sub > 0 </ sub >:

Consider, for example, a two element array spaced apart by one-half the wavelength of an incoming RF wave.

Consider a second order partial differential equation in three variables, such as the two-dimensional wave equation

Consider the unitary form defined above for the DFT of length N, where

* Consider now L = Q ( ³ √ 2, ω ), where ω is a primitive third root of unity.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

Consider Peter Unger's example of a cloud ( from his famous 1980 paper, " The Problem of the Many "): it's not clear where the boundary of a cloud lies ; for any given bit of water vapor, one can ask whether it's part of the cloud or not, and for many such bits, one won't know how to answer.

Consider, also, that all English speakers often pronounce ' Z ' where ' S ' is spelled, almost always when a noun ending in a voiced consonant or a liquid is pluralized, for example " seasons ", " beams ", " examples ", etc.

Consider the case where the far end of the cable is shorted ( that is, it is terminated into zero ohms impedance ).

Consider a quantum ensemble of size N with occupancy numbers n < sub > 1 </ sub >, n < sub > 2 </ sub >,..., n < sub > k </ sub > corresponding to the orthonormal states, respectively, where n < sub > 1 </ sub >+...+ n < sub > k </ sub >

We say that the number x is a periodic point of period m if f < sup > m </ sup >( x ) = x ( where f < sup > m </ sup > denotes the composition of m copies of f ) and having least period m if furthermore f < sup > k </ sup >( x ) ≠ x for all 0 < k < m. We are interested in the possible periods of periodic points of f. Consider the following ordering of the positive integers:

Consider a database that records customer orders, where an order is for one or more of the items that the enterprise sells.

Consider the simple experiment where a fair coin is tossed four times.

Consider a number n > 0 in base b ≥ 2, where it is written in standard notation with k + 1 digits a < sub > i </ sub > as:

: Example: Consider a scenario where a legitimate party called Alice encrypts messages using the cipher-block chaining mode.

Consider for example, the sharing of food in some hunter-gatherer societies, where food-sharing is a safeguard against the failure of any individual's daily foraging.

Consider the simple case of two-body system, where object A is moving towards another object B which is initially at rest ( in any particular frame of reference ).

Consider a 10 year mortgage where the principal amount P is $ 200, 000 and the annual interest rate is 6 %.

Consider a simple banking application where two users have access to the funds in a particular account.

Consider the polynomial ring R, and the irreducible polynomial The quotient space is given by the congruence As a result, the elements ( or equivalence classes ) of are of the form where a and b belong to R. To see this, note that since it follows that,,, etc.

Consider a random walk on the number line where, at each step, the position ( call it x ) may change by + 1 ( to the right ) or-1 ( to the left ) with probabilities:

Consider a system where the gun and shooter have a combined mass M and the bullet has a mass m. When the gun is fired, the two systems move away from one another with new velocities V and v respectively.

Consider a circuit where R, L and C are all in parallel.

Consider an MDCT with 2N inputs and N outputs, where we divide the inputs into four blocks ( a, b, c, d ) each of size N / 2.

Consider for example the same task as above but with an array consisting of 1000 numbers instead of 100, and where all numbers have the value 1.

Consider the physical model of the citizenship of human beings in the early 21st century, where about 30 % are Indian and Chinese citizens, about 5 % are American citizens, about 1 % are French citizens, and so on.

Consider a social network, where the graph ’ s vertices represent people, and the graph ’ s edges represent mutual acquaintance.