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 spatial geometry is spherical, the topology is compact.

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.

If the moral code were flouted, the proper balance of the universe would be upset, and the disastrous result could be floods, plague, or famine.

If this is true, then the universe today looks just as it did millions of years ago and as it will look millions of years hence, even though the universe is expanding.

If the universe is flat, there must be an additional component making up 73 % ( in addition to the 23 % dark matter and 4 % baryons ) of the energy density of the universe.

* If one refuses to sit down and make a move, one cannot be checkmated ( in relation to Russell's belief about the existence of the universe ).

If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made.

If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would ( by definition ) be outside the observable universe, it is difficult to imagine ( much less construct ) experiments to test this hypothesis.

If this sounds indulgent, it allows simultaneity, absolute space and time and a deterministic universe ( along with decoherence theory ) whilst the status-quo permits time travel / causality paradoxes, subjectivity in the measurement process and multiple universes.

If the entire volume of the observable universe ( taken to be 3 × 10 < sup > 80 </ sup > m < sup > 3 </ sup >) were packed solid with fine dust particles about 1. 5 micrometres in size, then the number of different ways of ordering these particles ( that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered ) would be approximately one googolplex.

If the universe is static and populated by an infinite number of stars, any sight line from Earth must end at the ( very bright ) surface of a star, so the night sky should be completely bright.

If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell between 2, 000, 000, 000 to 2, 000, 000, 001 light years away.

If, on the other hand, the conception taken as the foundation of the system is that the great inclusive unity is the world itself, or the universe, God is swallowed up in that unity, which may be designated nature.

If one adds two whole parts the result is one whole and if one whole is subtracted from another whole the result is another whole-it means there is one whole universe and it is all prevaded by " Him ". Since the universe has come forth from the Divine, all things and beings are sacred and must be treated so in human thought and action.

If God in some sense knows ahead of time what will happen, then events in the universe are effectively predetermined from God's point of view.

If the energy density is positive, the associated negative pressure will drive an accelerated expansion of the universe, as observed.

If the universe is described by an effective local quantum field theory down to the Planck scale, then we would expect a cosmological constant of the order of.

If this type of energy were to exist, it would cause a big rip in the universe due to the growing energy density of dark energy which would cause the expansion of the universe to increase at a faster-than-exponential rate.

If there are as many monkeys as there are particles in the observable universe ( 10 < sup > 80 </ sup >), and each types 1, 000 keystrokes per second for 100 times the life of the universe ( 10 < sup > 20 </ sup > seconds ), the probability of the monkeys replicating even a short book is nearly zero.

If one assumes that all of the universe consists of protons and neutrons, the density of the universe is such that much of the currently observed deuterium would have been burned into helium-4.

If α were > 0. 1, stellar fusion would be impossible and no place in the universe would be warm enough for life as we know it.

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.