Fixed point sentence example

fixed point
  • 1 3p6xcv-ros, shortest, and Xpovos, time), a term invented by John Bernoulli in 1694 to denote the curve along which a body passes from one fixed point to another in the shortest time.
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  • Taking any number n to be represented by a point on a line at distance nL from a fixed point 0, where L is a unit of length, we start with a series of points representing the integers I, 2, 3,.
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  • If a point be in motion in any orbit and with any velocity, and if, at each instant, a line be drawn from a fixed point parallel and equal to the velocity of the moving point at that instant, the extremities of these lines will lie on a curve called the hodograph.
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  • The C.P. of water lines passing through a fixed point lies on a straight line, the antipolar of the point; and thus the core of a triangle is a similar triangle of one quarter the size, and the core of a parallelogram is another parallelogram, the diagonals of which are the middle third of the median lines.
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  • - In the uniplanar motion of a homogeneous liquid the equation of continuity reduces to du dv dx' dy-O' u= -d,y/dy, v = d i t/dx, (2) surface containing so that we can put _ (6) (9) we have (I) (2) (5) (I) where 4 is a function of x, y, called the streamor current-function; interpreted physically, 4-4c, the difference of the value of 4, at a fixed point A and a variable point P is the flow, in ft.
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  • There can be no exact computation of time or placing of events without a fixed point or epoch from which the reckoning takes its start.
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  • In the history of Babylonia, the fixed point from which time was reckoned was the era of Nabonassar, 747 B.C. Among the Greeks the reckoning was by Olympiads, the point of departure being the year in which Coroebus was victor in the Olympic Games, 776 B.C. The Roman chronology started from the foundation of the city, the year of which, however, was variously given by different authors.
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  • the distance of its foot from a certain fixed point or origin 0 on the base (or the base produced), will be denoted by x, so that u is some function of x.
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  • of travel, and let x be the distance of any point M from a fixed point O.
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  • 9) be a point fixed in space in the disturbed region, B a fixed point where the medium is not yet disturbed, the medium A FIG.
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  • Every point is equidistant from a fixed point within the surface; this point is the "centre," the constant distance the "radius," and any line through the centre and intersecting the sphere is a "diameter."
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  • Here we are dependent (i.) on general 1 This date appears to be satisfactorily established by Ramsay, " A Second Fixed Point in the Pauline Chronology," Expositor, August 1900.
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  • 44-64, we should have a fixed point from.
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  • It is generated by the extremities of a rod which is constrained to move so that its middle point traces out a circle, the rod always passing through a fixed point on the circumference.
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  • word is KipKcos, generally used in the form rcpi?cos), a plane curve definable as the locus of a point which moves so that its distance from a fixed point is constant.
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  • The fixed point in the preceding definition is termed the " centre " (C in fig.
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  • the north and south poles occupy permanent geographical positions, yet the axis is not directed towards a fixed point in the heavens; variation of latitude, however, is associated with the shifting of the axis within the earth, i.e.
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  • It may be defined as a section of a right circular cone by a plane parallel to a tangent plane to the cone, or as the locus of a point which moves .so that its distances from a fixed point and a fixed line are equal.
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  • 1, where P is a point on the curve equidistant from the fixed line AB, known as the directrix, and the fixed point F known as the focus.
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  • In any continuous motion of a solid about a fixed point 0, the limiting position of the axis of the rotation by which the body can be brought from any one of its positions to a consecutive one is called the instantaneous axis.
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  • The quadratic moment,s with respect to different planes through a fixed point 0 are related to one another as follows.
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  • We take next the case of a particle attracted towards a fixed point 0 in the line of motion with a force varying as the distance from that point.
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  • The vertical oscifiations of a weight which hangs from a fixed point by a spiral spring come under this case.
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  • 63, where the ~(0 A pendulum virtually oscil lates about C as a fixed point of suspension.
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  • Another important example is that of a particle subject to an acceleration which is directed always towards a fixed point 0 and is proportional to the distance from 0.
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  • Hodograph.The motion of a particle subject to a force which passes always through a fixed point 0 is necessarily in a plane orbit.
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  • We note further that if a body be free to turn about a fixed point 0, there are three mutually perpendicular lines through this point about which it can rotate steadily, without further constraint.
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  • This is the same as the motion about a fixed point under the action of extraneous forces which have zero moment about that point.
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  • The components of angular momentum about the axis of the flywheel and about the vertical will be Cn and A ~ respectively, where A is the moment of inertia about any axis through the masscentre (or through the fixed point 0) perpendicular to that of symmetry.
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  • We can hence deduce the condition of steady precessional motion in a top. A solid of revolution is supposed to be free to turn about a fixed point 0 on its axis of symmetry, its masscentre G being in this axis at a distance h from 0.
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  • If we now apply them to the case of a rigid body moving about a fixed point 0, and make Ox, Oy, Oz coincide with the principal axes of inertia at 0, we have X, u, v=Ap, Bq, Cr, whence A (B C) qr = L,
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  • It will be suftlcient to take the case of motion about a fixed point 0; the angular co-ordinates 0, ~, i,l of Euler may then be used for the purpose.
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  • A mass M hangs from a fixed point by a string of length a, and a second mass m hangs from M by a string of length b.
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  • If in (21) we imagine that x, y, I denote infinitesimal rotations of a solid free to turn about a fixed point in a given field of force, it appears that the three normal modes consist each of a rotation about one of the three diameters aforesaid, and that the values of in are proportional to the ratios of the lengths of corresponding diameters of the two quadrics.
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  • The figure of the path of con tact is that traced on a fixed plane by the tracing-point, when the rolling curve is rotated in such a manner as always to touch a fixed straight line EIE (or EIE, as the case may be) at a fixed point I (or I).
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  • p~ sinO p, cose 210s If a screw rotates, the number of threads which pass a fixed point in one revolution is the number of threads in the screw.
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  • Sylvester discovered that this property of the parallelogram is not confined to points lying in one line with the fixed point.
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  • The crisis of his mental conflict had just been passed in Tirol, and he was now beginning to let his creed grow again from the one fixed point which nothing had availed to shift: "The one great certainty to which, in the midst of the darkest doubt, I never ceased to cling - the entire symmetry and loveliness and the unequalled nobleness of the humanity of the Son of Man."
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  • In June 1696 Bernoulli addressed a letter to the mathematicians of Europe challenging them to solve two problems - (1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P 1, P 2, then AP 1 m +AP 2 m will be constant.
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  • The Greek geometers invented other curves; in particular, the conchoid, which is the locus of a point such that its distance from a given line, measured along the line drawn through it to a fixed point, is constant; and the cissoid, which is the locus of a point such that its distance from a fixed point is always equal to the intercept (on the line through the fixed point) between a circle passing through the fixed point and the tangent to the circle at the point opposite to the fixed point.
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  • If we take a fixed point (x',y',z') and a curve u = o of order m, and suppose the axes of reference altered, so that x', y', z' are linearly transformed in the same way as the current x, y, z, the curves (x' - 'x' + y z' 2 u = o, (r = I, 2, ...
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  • Take a rod LMN bent at right angles at M, such that MN= AB; let the leg LM always pass through a fixed point 0 on AB produced such that OA = CA, where C is the middle point of AB, and cause N to travel along the line perpendicular to AB at C; then the midpoint of MN traces the cissoid.
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  • To investigate the form of the curve use may be made of the definition: the ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point (the focus) to its distance from a straight line (the directrix) is constant and is less than unity.
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  • One definition, which is of especial value in the geometrical treatment of the conic sections (ellipse, parabola and hyperbola) in piano, is that a conic is the locus of a point whose distances from a fixed point (termed the focus) and a fixed line (the directrix) are in constant ratio.
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  • cardo, a hinge; the fixed point on which anything turns), a phrase used for the principal virtues on which conduct in general depends.
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  • The latitude of a celestial object is the angle which the line drawn from some fixed point of reference to the object makes with the plane of the ecliptic.
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  • When you rappel down, you loop the rope over your anchor, your fixed point up top, so in effect, it's secured in the middle of the line.
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  • circular motion about a fixed axis Rotation about a fixed point.
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  • What we can suggest is that any analysis of such matters must include this epigram as a fixed point in its hermeneutical line.
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  • We choose a fixed point on the celestial equator, called the vernal equinox, or the First Point of Aries.
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  • fixed-point overflow exception.
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  • fixed-point data format, the result cannot be guaranteed.
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  • fixed-point overflow mask is enabled in the PSW, an interrupt occurs.
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  • fixed-point numbers; you can use these for accurate monetary calculations, for example.
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  • fixed-point theorem is stated, explained and proved by entirely elementary techniques.
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  • The fixed point sets will then lie on totally geodesic sub manifolds, of even codimension.
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  • The only fixed point is the Crask Inn itself, which gradually recedes into the distance behind you.
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  • All points in a rigid body move in a circular motion about a fixed axis rotation about a fixed point.
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  • Setting up a fixed point on Leck Fell using laser theodolite.
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  • In this case, the fixed point and shift vector are transformed using the current normalization transformation.
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  • See also: V3D_f, polygon3d, fixed point trig.
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  • When passing through its position of equilibrium, since gravity can do no more work upon it without changing its fixed point of support, all the energy of oscillation is kinetic. At intermediate positions the energy is partly kinetic and partly potential.
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  • Let PP1P2 be the path of the moving point, and let OT, OT 1, OT2, be drawn from the fixed point 0 parallel and equal to the velocities at P, P 1, respectively, then the locus of T is the hodograph of the orbits described by P (see figure).
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  • Suppose now an observer to be looking from a fixed point at the bead through the hole in the phonic wheel, he will see the bead as 8 bright points flashing out in each beat, and in succession at intervals of k second.
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  • In acoustics we meet with the case where a body is urged towards a fixed point by a force varying as the distance, and is also acted upon by an extraneous or disturbing force which is a given function of the time.
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  • See also: V3D_f, polygon3d, Fixed point trig.
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