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Page "Euclidean geometry" ¶ 26
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For and example
For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.
For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??
For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;
For example, No. 56 printed the patent giving the Electoral Prince the title of Duke of Cambridge.
For example, he captured some persons from York County, who with teams were taking to Philadelphia the furniture of a man who had just been released from prison through the efforts of his wife, and who apparently was helpless to prevent the theft of his household goods.
For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;
For example, in the third chapter of Matthew, verses 13-16, describing the baptism of Jesus, the 1611 version reads:
For example: 1.
For example, it probably will be necessary for the Corps to have authority to pay medical expenses of volunteers.
For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.
For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.
For example, out of the social evils of the English industrial revolution came the novels of Charles Dickens ; ;
For example, a 12-to-one engine would power a supersonic VTOL fighter.
For example: Af.
For example: Af.
For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.
For example: Af.
For example, let's consider a standard 283 cubic inch Chevy Aj.
For an example let's dream up an engine that has a final combustion chamber volume of 5 cubic inches and a cylinder volume of 45 cubic inches.
For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.
For example, the Chamber of Commerce of Gatlinburg, Tennessee, sponsors special camera tours into the Great Smoky Mountains to get pictures of the profusion of wild flowers flourishing in these wooded regions.
For example, the Friday after Thanksgiving can be substituted for Washington's birthday.
For example, the officials of Poughkeepsie town ( township ) where the project is located think highly of it because it simplifies their snow clearing problem.
For example, don't pay in a truck policy for medical coverage that you may be paying for in a health and accident policy.
For example: If your bodily injury claims start payment after the first $250, a 25% premium saving is often made.

For and Euclidean
For nearby astronomical objects ( such as stars in our galaxy ) luminosity distance D < sub > L </ sub > is almost identical to the real distance to the object, because spacetime within our galaxy is almost Euclidean.
For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account when calculating the luminosity distance of an object.
For example, in three-dimensional complex Euclidean space,
For any subset A of Euclidean space R < sup > n </ sup >, the following are equivalent:
For a set P of points in the ( d-dimensional ) Euclidean space, a Delaunay triangulation is a triangulation DT ( P ) such that no point in P is inside the circum-hypersphere of any simplex in DT ( P ).
For over two thousand years, the adjective " Euclidean " was unnecessary because no other sort of geometry had been conceived.
For example, a smooth manifold is a Hausdorff topological space that is locally diffeomorphic to Euclidean space.
For illustration, the Euclidean algorithm can be used to find the greatest common divisor of a = 1071 and b = 462.
( For example, the scientific progress of general relativity demonstrates that philosophers be wrong to pronounce a priori that space should have a Euclidean nature.
For any natural number n, an " n-sphere ," often written as S < sup > n </ sup >, is the set of points in ()- dimensional Euclidean space which are at a fixed distance r from a central point of that space, where r is, as before, a positive real number.
For example, in Z < sup > n </ sup > with Euclidean metric, a sphere of radius r is nonempty only if r < sup > 2 </ sup > can be written as sum of n squares of integers.
For example, the real line is Tychonoff under the standard Euclidean topology.
For example, the minimum spanning tree of the graph associated with an instance of the Euclidean TSP is a Euclidean minimum spanning tree, and so can be computed in expected O ( n log n ) time for n points ( considerably less than the number of edges ).
For any natural number n, an n-sphere of radius r is defined as the set of points in ( n + 1 )- dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real number.
For any natural number n, an n-sphere of radius r is defined as the set of points in ( n + 1 )- dimensional Euclidean space that are at distance r from some fixed point c, where r may be any positive real number and where c may be any point in ( n + 1 )- dimensional space.
For S a subset of a Euclidean space, x is a point of closure of S if every open ball centered at x contains a point of S ( this point may be x itself ).
For instance, the general linear group GL ( n, R ) of all invertible n-by-n matrices with real entries can be viewed as a topological group with the topology defined by viewing GL ( n, R ) as a subset of Euclidean space R < sup > n × n </ sup >.
For example, in the " game " of Euclidean geometry ( which is seen as consisting of some strings called " axioms ", and some " rules of inference " to generate new strings from given ones ), one can prove that the Pythagorean theorem holds ( that is, you can generate the string corresponding to the Pythagorean theorem ).
For instance, bending without stretching or tearing a page of paper gives an isometric embedding of the page into Euclidean space because curves drawn on the page retain the same arclength however the page is bent.
For example, it follows that any closed oriented Riemannian surface can be C < sup > 1 </ sup > isometrically embedded into an arbitrarily small ε-ball in Euclidean 3-space ( there is no such C < sup > 2 </ sup >- embedding since from the formula for the Gauss curvature an extremal point of such an embedding would have curvature ≥ ε < sup >- 2 </ sup >).
For example, Euclidean geometry without the parallel postulate is incomplete ; it is not possible to prove or disprove the parallel postulate from the remaining axioms.
For a subset S of Euclidean space R < sup > n </ sup >, the following two statements are equivalent:
For example, Euclidean space is an example of a flat space, and Minkowski space is an example of a flat space-time.

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