Help


[permalink] [id link]
+
Page "Charts on SO(3)" ¶ 1
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Every and improper
Every rotation is the result of reflecting in an even number of reflections in hyperplanes through the origin, and every improper rotation is the result of reflecting in an odd number.
( Every object is, of course, an improper part of itself.
Every group has itself ( the improper subgroup ) and the trivial subgroup as two of its fully characteristic subgroups.

Every and rotation
Every rotation maps an orthonormal basis of R < sup > 3 </ sup > to another orthonormal basis.
Every proper rotation is the composition of two reflections, a special case of the Cartan – Dieudonné theorem.
Every nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional linear subspace of R < sup > 3 </ sup > which is called the axis of rotation ( this is Euler's rotation theorem ).
Every rotation Rot ( φ ) has an inverse Rot (− φ ).
Every rotation in three dimensions is defined by its axis — a direction that is left fixed by the rotation — and its angle — the amount of rotation about that axis ( Euler rotation theorem ).
Previously a daily segment, Underbelly didn't appear as often in the rotation ( hence Maddow's inclination to add " Every day ... or so " to her introduction of the segment ).

Every and three-dimensional
Every point in three-dimensional Euclidean space is determined by three coordinates.
Every non-empty intersection of a 3-sphere with a three-dimensional hyperplane is a 2-sphere ( unless the hyperplane is tangent to the 3-sphere, in which case the intersection is a single point ).

Every and Euclidean
Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.
Every circle in Euclidean space is a great circle of exactly one sphere.
* Every triangle group T is a discrete subgroup of the isometry group of the sphere ( when T is finite ), the Euclidean plane ( when T has a Z + Z subgroup of finite index ), or the hyperbolic plane.
Every tame knot in three dimensional Euclidean space has a ' fundamental quandle '.
Every dilation of a Euclidean space that is not a congruence has a unique fixed point that is called the center of dilation.
Every plane B that is completely orthogonalTwo flat subspaces S < sub > 1 </ sub > and S < sub > 2 </ sub > of dimensions M and N of a Euclidean space S of at least M + N dimensions are called completely orthogonal if every line in S1 is orthogonal to every line in S2.

Every and space
** Every vector space has a basis.
** Every infinite game in which is a Borel subset of Baire space is determined.
** Every Tychonoff space has a Stone – Čech compactification.
* Theorem Every reflexive normed space is a Banach space.
Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.
* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.
* Every compact metric space is separable.
* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.
* Pseudocompact: Every real-valued continuous function on the space is bounded.
Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.
Every compact metric space is complete, though complete spaces need not be compact.
Every node on the Freenet network contributes storage space to hold files, and bandwidth that it uses to route requests from its peers.
Every space filling curve hits some points multiple times, and does not have a continuous inverse.
* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )
Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.
Every normed vector space V sits as a dense subspace inside a Banach space ; this Banach space is essentially uniquely defined by V and is called the completion of V.

Every and is
Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.
Every single problem touched on thus far is related to good marketing planning.
Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.
Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.
Every man in every one of these houses is a Night Rider.
Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).
Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.
Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.
Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

1.200 seconds.