Polygon sentence example

polygon
  • The polygon of forces is then made up of segments of a vertical line.
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  • This polygon is the partial polygon of resistance.
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  • This is the proposition known as the polygon of forces.
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  • By considering the circle as the limit of a polygon, it follows that the formulae (iii) and (v) of § 26 hold for a right circular cylinder and a right circular cone; i.e.
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  • The planned building is a regular polygon of nine sides.
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  • The sides of the polygon may be arranged in any order, provided care is taken so to draw them that in passing round the polygon in C D _E FIG.
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  • This polygon falls under the definition of a reciprocal figure given by Clerk Maxwell, if we consider the frame as a point in equilibrium under the external forces.
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  • In all cases the magnitude and direction, and joining the vertices of the polygon thus formed to an arbitrary pole 0.
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  • It is evident that a system of jointed bars having the shape of the funicular polygon would be in equilibrium under the action of the given forces, supposed applied to the joints; moreover any bar in which the stress is of the nature of a tension (as distinguished from a thrust) might be replaced by a string.
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  • To every line in either of the original figures corresponds of course a parallel line in the other; moreover, it is seen that concurrent lines in either figure correspond to lines forming a closed polygon in the other.
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  • Thus ii AB, BC, CD represent the given loads, in the force-diagram, we construct the sides corresponding to OA, OB, OC, OD in the funicular; we then draw the closing line of the funicular polygon, and a parallel OE to it in the force diagram.
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  • Hence if a system of vertical forces be in equilibrium, so that the funicular polygon ii closed, the length which this polygon intercepts on the vertical through any point P gives the sum of the moments about P of all the forces on one side of this vertical.
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  • Let all the resultants acting at the several centres of resistance be produced until they cut one another in a series of points so as to form an unclosed polygon.
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  • A curve tangential to all the sides of the polygon is the line of pressures.
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  • The conditions (c) may thus be expressed: first, that the sum of the vectors Wr must form a closed polygon, and, second, that the sum of the vectors War must form a closed polygon.
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  • Then, transferring the product Wr correspondinf with this balance weight to the reference plane, proceed to draw the force polygon.
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  • The type was fixed on a large cylinder, and instead of the printing surface presenting a complete circle, the different columns were each arranged so as to form a polygon.
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  • The plinth is a polygon of twenty sides.
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  • For the next step you want to draw the polygon on the right side.
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  • Next, you can fill the polygon by choosing a fill color.
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  • The fortress has the shape of an irregular polygon.
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  • The various polygon shapes were rendered in bright primary colors.
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  • The convex hull is the minimum area convex polygon which will entirely contain the set.
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  • How would you set about deciding whether they defined a convex polygon?
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  • You can draw a closed polygon by finishing at the point you started.
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  • He will tell us more about GLUT windows management and more about polygon rendering.
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  • The yellow area was covered simply by using a rectangular shape rather than with a fiddly polygon.
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  • It is convenient to introduce the function =log =log (Q / q) + 01 (4) so that the polygon representing 12 conformally has a boundary given by straight lines parallel to the coordinate axes; and then to determine S2 and w as functions of a variable u (not to be confused with the velocity component of q), such that in the conformal representation the boundary of the and w polygon is made to coincide with the real axis of u.
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  • The external forces on a frame or bridge in equilibrium under those forces may, by a well-known proposition in statics, be represented by a closed polygon, each side of which is parallel to one force, and represents the force in magnitude as well as in direction.
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  • We then have the polygon of forces Exaf, the reciprocal figure of the lines meeting at that point in the frame, and representing the forces at the point Exaf; the direction of the forces on EH and XA being known determines the direction of the forces due to the elastic reaction of the members AF and EF,, showing AF to push as a strut, while EF is a tie.
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  • A single known force in a polygon determines the direction of all the others, as these must all correspond with arrows pointing the same way round the polygon.
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  • Taking the circumference as intermediate between the perimeters of the inscribed and the circumscribed regular n-gons, he showed that, the radius of the circle being given and the perimeter of some particular circumscribed regular polygon obtainable, the perimeter of the circumscribed regular polygon of double the number of sides could be calculated; that the like was true of the inscribed polygons; and that consequently a means was thus afforded of approximating to the circumference of the circle.
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  • Looking only at a polygon view of the silicate tetrahedra, we can see each is isolated from the other.
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  • If you want to draw an unclosed polygon, you can use the new drawPolyline method instead.
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  • The other problem comes when a hatch line passes through a vertex of the polygon.
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  • Drawing polygons Use the polygon tool to click points representing the vertices of the required polygon.
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  • The graphics chip tops at 166 megahertz and uses 2 MB of RAM, which gives it the ability to process complex polygon movement and 3D textures.
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  • Eventually, despite its reported "64-bit" prowess, the Atari Jaguar just could not keep up with the polygon pushing power of the Sony PlayStation.
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  • Yes folks, another pack of modders is at it again, enriching our video game world with more of what everybody wants: topless polygon women.
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  • The first 3D Final Fantasy game features polygon baddies and a cinematic camera that swirls around the battlefield as you attack and cast spells.
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  • Maybe you are just curious about how games are made like, "how does polygon collision work?" or "how do you work with artificial intelligence?"
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  • The fourth installment, Mortal Kombat 4, replaced the digitized characters with 3D polygon models, a first for the series.
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  • Lara Croft may look more like a real person, but the original polygon model may be a little more, er... effective, if you know what I mean.
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  • Sure there were polygon babes riding BMX bikes, but the clips are what caused the controversy and the eventual AO rating.
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  • Now there's a polygon gal you can wrap your heart around.
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  • Enhanced math, polygon and CPU performance make previously impossible gaming into reality.
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  • It essentially runs 7 processors (but only six are used by the system, the other is used by the operation system) for pure polygon and processing power.
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  • If you want to be sneaky, arrange your ships near each other, but in some sort of polygon.
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  • For longer bridges the funicular polygon affords a method of determining maximum bending moments which is perhaps more convenient.
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  • In shape Milan is a fairly regular polygon, and its focus is the splendid Piazza del Duomo, from which a number of broad modern streets radiate in all directions.
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  • It is a regular polygon with five bastions, founded by Frederick III.
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  • This diagram consists of a polygon whose successive sides represent /\p9
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  • Further, at any one of the centres of load let PL represent the magnitude and direction of the gross load, and Pa, Pb the two resistances by which the piece to which that load is applied is supported; then wifl those three lines be respectively the diagonal and sides of a parallelogram; or, what is the same thing, they will be equal to the three sides of a triangleS and they must be in the same plane, although the sides of the polygon of resistances may be in different planes.
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  • When the load on one of the pieces is parallel to the resistances which balance it, the polygon of resistances ceases to be closed, two of the sides becoming parallel to each other and to the load in question, and extending indefinitely.
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  • Line of PressuresCentres and Line of Resistance.The line of pressures is a line to which the directions of all the resistances in one polygon are tangents.
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  • This paper is principally based on the following general theorem, which is a remarkable extension of Pascal's hexagram: "If a polygon move so that each of its sides passes through a fixed point, and if all its summits except one describe curves of the degrees m, n, p, &c., respectively, then the free summit moves on a curve of the degree 2mnp. ..
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  • Aligarh Fort, situated on the Grand Trunk road, consists of a regular polygon, surrounded by a very broad and deep ditch.
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  • This result is easily extended to the case of a polygon of any number of sides; it has an important application in hydrostatics.
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  • A system of forces represented completely by the sides of I plane polygon taken in order is equivalent to a couple whosc moment is represented by twice the area of the polygon; this is proved by taking moments about any point.
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  • The funicular or link polygon has its vertices on the lines of action of the given forces, and its sides respectively parallel to the lines drawn from 0 in the force-diagram; in particular, the two sides meeting in any vertex are respectively parallel to the lines drawn from 0 to the ends of that side of the force-polygon which represents the corresponding force.
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  • Then from the proportionality and parallelism sides of a triangle, there results the following of the load and the two resistances applied to each piece of the structure to the three theorem (originally due to Rankine): If from the angles of the polygon of loads there be drawn lines (Ri, R2, &c.), each of which is parallel to the resistance (as Pi F2, &c.) exerted FIG.
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  • This may be called a partial polygon of resistances.
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  • If the polygon intersects itself, care must be taken to attribute to the different parts of the area their proper signs.
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  • Partial Polygons of Resistance.In a structure in which there are pieces supported at more than two joints, let a polygon be con-.
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  • In considering its properties, the load at each centre of load is to be held to include the resistances of those joints which are not comprehended in the partial polygon of resistances, to which the theorem of 7 will then apply in every respect.
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  • For figures of more than four sides this method is not usually convenient, except for such special cases as that of a regular polygon, which can be divided into triangles C by radii drawn from its centre.
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  • This polygon of forces may, by a slight extension of the above definition, be called the reciprocal figure of the external forces, if the sides are arranged in the same order as that of the joints on which they act, so that if the joints and forces be numbered I, 2, 3, 4, &c., passing round the outside of the frame in one direction, and returning at last to joint 1, then in the polygon the side representing the force 2 will be next the side representing the force I, and will be followed by the side representing the force 3, and so forth.
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  • If there are no redundant members in the frame there will be only two members abutting at the point of support, for these two members will be sufficient to balance the reaction, whatever its direction may be; we can therefore draw two triangles, each having as one side the reaction YX, and having the two other sides parallel to these two members; each of these triangles will represent a polygon of forces in equilibrium at the point of support.
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  • The latter, as we know, calculated the perimeters of successive polygons, passing from one polygon to another of double the number of sides; in a similar manner Gregory calculated the areas.
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  • When all the forces are vertical, as will be the case in girders, the polygon of external forces will be reduced to two straight lines, fig.
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  • The case of the funicular polygon will be of use to us later.
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  • Internally it is a polygon of sixteen unequal sides, and the cupola is supported by sixteen ribs, springing from the same number of columns.
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