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If the circles are represented in trilinear coordinates in the usual way, then their radical center is conveniently given as a certain determinant.
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If and circles
If the dominant country's influence is felt in social and cultural circles, such as " foreign " music being popular with young people, it may be described as cultural imperialism.
If the parameter " dopefish " is added to the executable, a sample of burping is heard and Scott's Mystical Head is seen spinning in circles on the screen.
If you measure the circumferences of circles of steadily larger diameters and divide the former by the latter, all three geometries give the value π for small enough diameters but the ratio departs from π for larger diameters unless Ω = 1:
* If four arbitrary points A, B, C, D are given that do not form an orthocentric system, then the nine-point circles of ABC, BCD, CDA and DAB concur at a point.
* If four points A, B, C, D are given that form a cyclic quadrilateral, then the nine-point circles of ABC, BCD, CDA and DAB concur at the anticenter of the cyclic quadrilateral.
( If they are not orientable the natural fibration by circles is not necessarily a Seifert fibration: the problem is that some fibers may " reverse orientation "; in other words their neighborhoods look like fibered solid Klein bottles rather than solid tori .< ref > Ronald Fintushel, Local S < sup > 1 </ sup > actions on 3-manifolds, Pacific J. o. M. 66 No1 ( 1976 ) 111-118, http :// projecteuclid. org /...) The classification of such ( oriented ) manifolds is given in the article on Seifert fiber spaces.
* If a circle q passes through two distinct points A and A ', inverses with respect to a circle k, then the circles k and q are orthogonal.
* If the circles k and q are orthogonal, then a straight line passing through the center O of k and intersecting q, does so at inverse points with respect to k.
If the radical center lies outside of all three circles, then it is the center of the unique circle ( the radical circle ) that intersects the three given circles orthogonally ; the construction of this orthogonal circle corresponds to Monge's problem.
If C and C are tangent Ford circles, then the half-circle joining ( p / q, 0 ) and ( r / s, 0 ) that is perpendicular to the x-axis is a hyperbolic line that also passes through the point where the two circles are tangent to one another.
If M consists of a circle, and N of two circles, M and N together make up the boundary of a pair of pants W ( see the figure at right ).
If you watch the animation above you will see two circles ( one about half way between the edge and center, and the other on the edge itself ) and a straight line bisecting the disk, where the displacement is close to zero.
If a straight line is considered a degenerate circle with zero curvature ( and thus infinite radius ), Descartes ' theorem also applies to a line and two circles that are all three mutually tangent, giving the radius of a third circle tangent to the other two circles and the line.
If four circles are tangent to each other at six distinct points, and the circles have curvatures k < sub > i </ sub > ( for i = 1, ..., 4 ), Descartes ' theorem says:
If one of the three circles is replaced by a straight line, then one k < sub > i </ sub >, say k < sub > 3 </ sub >, is zero and drops out of equation ( 1 ).
If two circles are replaced by lines, the tangency between the two replaced circles becomes a parallelism between their two replacement lines.
If the cloth is first folded then bound, the resulting circles will be in a pattern depending on the fold used.
If and are
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 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 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.
Defoe then commented, `` If they Could Draw that young Gentleman into Their Measures They would show themselves quickly, for they are not asham'd to Say They want only a head to Make a beginning ''.
If Jews are identified as a religious body in a controversy that comes before a national or international tribunal, it is obviously compatible with the goal of human dignity to protect freedom of worship.
Without preliminaries, Esther asked him, `` If you are a world citizen, will you take Garry Davis' place in his tent while he goes to the hospital ''??
If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.
If the would-be joiner asks these questions he is not likely to be duped by extremists who are seeking to capitalize on the confusions and the patriotic apprehensions of Americans in a troubled time.
If the record buyer's tastes are somewhat eclectic or even the slightest bit esoteric, he will find them satisfied on educational records.
If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.
If they are to be commended for foresight in their planning, what then is the judgment of a town council that compounds this problem during the planning stage??
If the Communists are sincere in wanting a united, neutral and disarmed Germany, it might well be advantageous for the German people in this nuclear age.
If only this could be done more often -- with such heartening results -- many of the earth's `` big problems '' would shrink to the insignificances they really are.
If any are left, presently, we may expect to see signs specifically prohibiting the feeding of them too.
If the raw population figures are crucially relevant, then it is idle to think of liberation, as idle as to suppose that Poland might liberate Russia.
If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.