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If two triangles do not meet the Delaunay condition, switching the common edge BD for the common edge AC produces two triangles that do meet the Delaunay condition:
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If and two
If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.
If I now risk some comparisons with Sons And Lovers let it be clear that I am not comparing the two works or judging their merits ; ;
If nothing else, at least two good songs came out of the project, `` Out Of This World '' and `` June Comes Around Every Year ''.
If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.
Somebody, got to be somebody If I don't put my two cents in soon, somebody else will I know they're waitin only for one thing: for the bastards what done it to be nailed.
If we cluster together, the redcoats can make an advantage out of it, but there's not a blessed thing they can do with two or three of us except chase us, and we can outrun them ''.
If you've travelled in Europe a time or two, it is quite certain that you've had that wanting-to-be-alone feeling or that you will get it on your next visit across the Atlantic.
If A is the major axis of an ellipsoid and B and C are the other two axes, the radius of curvature in the ab plane at the end of the axis Af, and the difference in pressure along the A and B axes is Af.
If we try to study T using characteristic values, we are confronted with two problems.
If the distribution of the 71 items were wholly concordant in the two families, the distance would of course be 0.
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 a child loses a molar at the age of two, the adjoining teeth may shift toward the empty space, thus narrowing the place intended for the permanent ones and producing a jumble.
If you are not well acquainted with the area in which you wish to locate, or if you are not sure that you and your family will like and make a success of farming, usually you would do better to rent a place for a year or two before you buy.
If the change, at first sight, seems minor, we may recall that it took the Italian painters about two hundred years to make an analogous change, and the Italian painters, by universal consent, were the most brilliant group of geniuses any art has seen.
If we add to these contacts with friendly members the `` contacts with an organization of the church '' ( 11.2 per cent of the cases ), then a substantial two thirds of all recruitment is through friendly contact.
If the Orioles are to break their losing streak within the next two days, it will have to be at the expense of the American League champion New York Yankees, who come in here tomorrow for a night game and a single test Sunday afternoon.
If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.
If we look about the world today, we can see clearly that there are two especially significant factors shaping the future of our civilization: science and religion.
** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.
* If two small categories are weakly equivalent, then they are equivalent.
If the demands of these two sovereigns upon his duty of allegiance come into conflict, those of the United States have the paramount authority in American law ; likewise, those of the foreign land have paramount authority in their legal system.
If there is a mixture of only two types of atoms, not counting impurities, such as a copper-nickel alloy, then it is called a binary alloy.
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )
If a tile is placed between two hotel chains of the same size, the individual player who places the tile decides which hotel chain remains on the board and which is acquired.
If two players tie for majority, they will share both shareholder bonuses.
If and triangles
If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.
* SAS ( Side-Angle-Side ): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
* SSS ( Side-Side-Side ): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
* ASA ( Angle-Side-Angle ): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.
* AAS ( Angle-Angle-Side ): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent.
* RHS ( Right-angle-Hypotenuse-Side ): If two right-angled triangles have their hypotenuses equal in length, and a pair of shorter sides are equal in length, then the triangles are congruent.
If two triangles satisfy the SSA condition and the length of the side opposite the angle is greater than or equal to the length of the adjacent side, then the two triangles are congruent.
If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side opposite the angle is equal to the length of the adjacent side multiplied by the sine of the angle, then the two triangles are congruent.
If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side opposite the angle is greater than the length of the adjacent side multiplied by the sine of the angle ( but less than the length of the adjacent side ), then the two triangles cannot be shown to be congruent.
If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar.
If an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other.
If this meant triangles or more complicated geometric figures, well then, one accepted that too ".
If they are not the same, i. e. some are narrow triangles, while others maybe wide trapizoids or shouldered triangles, then the mass or area of the output function must be known or calculated.
If an instantaneous centripetal force ( red arrow ) is considered on the planet during its orbit, the area of the triangles defined by the path of the planet will be the same.
If and do
If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;
If I even hint at it do you think it will matter that you are his nephew -- and not even a blood nephew ''??
If one dancer slaps another, the victim may do a pirouette, sit down, or offer his assailant a fork and spoon.
If these people were denied a voice ( do they have a moral right to a voice??
If the detective insists upon retaining his personal standards, he must now do so in conscious defiance of his society.
If Mrs. Wright doesn't accept the terms in the morning, I'll go either to Tokyo or to Holland, to do what I can.
If Robinson was a liar and a slanderer, he was also a very canny gentleman, for nothing that Pike could do would pry so much as a single word out of him.
If man is actually the product of his environment and if science can discover the laws of human nature and the ways in which environment determines what people do, then someone -- a someone probably standing outside traditional systems of values -- can turn around and develop completely efficient means for controlling people.
If they do as well as they did in 1960 there can be no complaint.
If he snatches a toy, she says, `` Caroline wants her own truck just as you do ''.
If they do meet and recognize one another, slap backs and embrace, the moment soon is done.
If they also defeat the school bill, the GOP task force won't have much research to do.
If one follows the reports of the Congress, one finds that there still seems considerable uncertainty in the minds of the leaders themselves about what exactly to do in this matter.
If we want to preserve our sovereignty, this is the way to do it ; ;
If I hafta do this to stay alive by God I'll do it.
If only Simms Purdew could do that, whatever the thing he remembered and told.
If and when Hino decided to tell him about his experiences, he would do so unasked.
If there is anything which we can do in the executive branch of the Government to speed up the processes by which we come to decisions on matters on which we must act promptly, that in itself would be a major contribution to the conduct of our affairs.
If you elect to use the Standard Deduction or the Tax Table, and later find you should have itemized your deductions, you may do so by filing an amended return within the time prescribed for filing a claim for refund.
If you do use a cold frame be sure that its ventilation is adequate.
If the superintendents do not receive more cooperation from Handlers, it has been suggested that licensed Judges also be qualified to judge this Class.
If the house you plan to buy or build won't have big overhangs, you can still do a fair job of keeping the sun off walls and windows with properly designed trellises, fences and awnings.
If, in a certain part of the range, it starts life 1 foot longer than do any of the other ( relatively large ) giants, and reaches maturity at, let us guess, 18 inches longer than the others, a quadrupling of the maturity length would result in a maximum of ( nearly ) 40 feet.
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