If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.

If the coordinates represent spatial positions ( displacements ), it is common to represent the vector from the origin to the point of interest as.

If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different.

If a spatial extra dimension is of radius R, the invariant mass of such standing waves would be M < sub > n </ sub > = nh / Rc with n an integer, h being Planck's constant and c the speed of light.

If there were a single Earth revolving at some distance from the center of space, the universe's center of balance would not coincide with its spatial center.

If the Hamiltonian is not an explicit function of time, the equation is separable into its spatial and temporal parts.

If the true spatial extent of activation, that is the spread of the cluster of voxels simultaneously active, matches the width of the filter used, this process improves the signal-to-noise ratio.

If you ignore the effects of gravity, then there are ten basic ways of doing such shifts: translation through time, translation through any of the three dimensions of space, rotation ( by a fixed angle ) around any of the three spatial axes, or a boost in any of the three spatial directions.

If we assume that equation ( 1 ) represents a flowing medium of constant area, we can sub-divide the spatial domain,, into finite volumes or cells with cell centres indexed as.

If a simple rotation is only in the three space dimensions, i. e. about a plane that is entirely in space, then this rotation is the same as a spatial rotation in three dimensions.

If they are both in surface-wave and resonator mode, they can exhibit a high degree of spatial localisation.

If p spatial dimensions satisfy the Neumann boundary condition, then the string endpoint is confined to move within a p-dimensional hyperplane.

If a Dp-brane is embedded in a spacetime of d spatial dimensions, the brane carries ( in addition to its Maxwell field ) a set of d-p massless scalars ( particles which do not have polarizations like the photons making up light ).

If the person has difficulty with spatial concepts, such as ' over ', ' under ', ' here ' and ' there ', he or she may have arithmetic difficulties, have difficulty understanding word problems and instructions, or have difficulties using words.

If the spatial scale is large compared to the Debye length, the oscillations are only weakly modified by the pressure term, but at small scales the pressure term dominates and the waves become dispersionless with a speed of.

If d is the number of spatial dimensions, we can represent a point by the vector

If they all fit individually, it must have simply been that the spatial relationship was incorrect, and the abutment that was sectioned from the pontic must now be reattached to the pontic according to the newly confirmed spatial relationship.

If the wind white forcing is zonally uniform it should generate a red spectrum in which h variance increase with the period and reaches a constant amplitude at lower frequencies without decadal and interdecadal peaks, however low frequencies atmospheric circulation tends to be dominated by fixed spatial patterns so that wind forcing is not zonally uniform, if the wind forcing is zonally sinusoidal then decadal peaks occurs due to resonance of the forced basin-scale Rossby waves.

If all species are identical in their spatial interactions, then the interaction matrix is circulant.

If you think about how spatial and time translations, rotations and boosts work, these relations are intuitive ( except for the central extension ).

If space is necessary to distinguish objects, then deficits in explicit access to spatial information located in the master map leads to the inability to perceive more than one object at a time.

If one also removes the second postulate (" a line can be extended indefinitely ") then elliptic geometry arises, where there is no parallel through a point outside a line, and in which the interior angles of a triangle add up to more than 180 degrees.

If the viewing distance is large compared with the separation of the slits ( the far field ), the phase difference can be found using the geometry shown in the figure below right.

If not stated otherwise, this article considers symmetry groups in Euclidean geometry, but the concept may also be studied in wider contexts ; see below.

If a photographic plate or another 2-D optical sensor is located within the scattered light field without a lens, a speckle pattern is obtained whose characteristics depend on the geometry of the system and the wavelength of the laser.

The later invention of non-Euclidean geometry does not resolve this question ; for one might as well ask, " If given the axioms of Riemannian geometry, can an omnipotent being create a triangle whose angles do not add up to more than 180 degrees?

If the geometric diagram does not intersect major physical points in the image, the result is what Skinner calls " unanchored geometry.

If G arises as the group of units of a ring A, then an inner automorphism on G can be extended to a projectivity on the projective space over A by inversive ring geometry.

If the final geometry is obtained using a usually simple-shaped electrode which is moved along several directions and is possibly also subject to rotations, often the term EDM milling is used.

If the curvature is exactly zero, then the local geometry is flat ; if it is positive, then the local geometry is spherical, and if it is negative then the local geometry is hyperbolic.

If the local geometry has constant curvature, the global geometry is very constrained, as described in Thurston geometries.

If the geometry of the universe is not compact, then it is infinite in extent with infinite paths of constant direction that, generally do not return and the space has no definable volume, such as the Euclidean plane.

If all axioms defining a class of algebras are identities, then the class of objects is a variety ( not to be confused with algebraic variety in the sense of algebraic geometry ).

* If π < sub > 1 </ sub >( M ) is virtually nilpotent but not virtually abelian then the geometric structure on M is nil geometry, and M is compact.

* If π < sub > 1 </ sub >( M ) is virtually solvable but not virtually nilpotent then the geometric structure on M is sol geometry, and M is compact.

If the geometry of the body is fixed and in case of symmetric flight ( β = 0 and Q = 0 ), pressure and friction coefficients are functions depending on:

If not properly managed ( through outlet piping geometry ) or accounted for ( by structural reinforcement of downstream components ), the resulting pulsations can cause fluid cavitation and / or damage to components downstream of the blower.

If the antipodal points were considered to be distinct, as in spherical geometry, then uniqueness would be violated, e. g., the lines of longitude on the Earth's surface all pass through both the north pole and the south pole.

If superposition is to be considered a valid method of geometric proof, all of geometry would be full of such proofs.

If any of the lines is removed from the plane, along with the points on that line, the resulting geometry is the affine plane of order 2.

If the axiom set is not categorical ( so that there is more than one model ) one has the geometry / geometries debate to settle.