# How to use *Polygon* in a sentence

The

**polygon**of forces is then made up of segments of a vertical line.This

**polygon**is the partial**polygon**of resistance.The fortress has the shape of an irregular

**polygon**.The various

**polygon**shapes were rendered in bright primary colors.This is the proposition known as the

**polygon**of forces.AdvertisementYou can draw a closed

**polygon**by finishing at the point you started.Aligarh Fort, situated on the Grand Trunk road, consists of a regular

**polygon**, surrounded by a very broad and deep ditch.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.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.In all cases the magnitude and direction, and joining the vertices of the

**polygon**thus formed to an arbitrary pole 0.AdvertisementIt 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.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.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.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.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.AdvertisementLet 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**.A curve tangential to all the sides of the

**polygon**is the line of pressures.Then, transferring the product Wr correspondinf with this balance weight to the reference plane, proceed to draw the force

**polygon**.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**.For the next step you want to draw the

**polygon**on the right side.AdvertisementNext, you can fill the

**polygon**by choosing a fill color.How would you set about deciding whether they defined a convex

**polygon**?He will tell us more about GLUT windows management and more about

**polygon**rendering.The yellow area was covered simply by using a rectangular shape rather than with a fiddly

**polygon**.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.AdvertisementThe 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.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.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**.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.Looking only at a

**polygon**view of the silicate tetrahedra, we can see each is isolated from the other.If you want to draw an unclosed

**polygon**, you can use the new drawPolyline method instead.The other problem comes when a hatch line passes through a vertex of the

**polygon**.Drawing polygons Use the

**polygon**tool to click points representing the vertices of the required**polygon**.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.Eventually, despite its reported "64-bit" prowess, the Atari Jaguar just could not keep up with the

**polygon**pushing power of the Sony PlayStation.The first 3D Final Fantasy game features

**polygon**baddies and a cinematic camera that swirls around the battlefield as you attack and cast spells.Maybe you are just curious about how games are made like, "how does

**polygon**collision work?" or "how do you work with artificial intelligence?"The fourth installment, Mortal Kombat 4, replaced the digitized characters with 3D

**polygon**models, a first for the series.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.Sure there were

**polygon**babes riding BMX bikes, but the clips are what caused the controversy and the eventual AO rating.Now there's a

**polygon**gal you can wrap your heart around.Enhanced math,

**polygon**and CPU performance make previously impossible gaming into reality.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.If you want to be sneaky, arrange your ships near each other, but in some sort of

**polygon**.For longer bridges the funicular

**polygon**affords a method of determining maximum bending moments which is perhaps more convenient.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.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.It is a regular

**polygon**with five bastions, founded by Frederick III.This diagram consists of a

**polygon**whose successive sides represent /\p9When 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.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.The planned building is a regular

**polygon**of nine sides.The convex hull is the minimum area convex

**polygon**which will entirely contain the set.This result is easily extended to the case of a

**polygon**of any number of sides; it has an important application in hydrostatics.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.This may be called a partial

**polygon**of resistances.The plinth is a

**polygon**of twenty sides.If the

**polygon**intersects itself, care must be taken to attribute to the different parts of the area their proper signs.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.Partial Polygons of Resistance.In a structure in which there are pieces supported at more than two joints, let a

**polygon**be con-.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.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.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.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.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.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.The case of the funicular

**polygon**will be of use to us later.Internally it is a

**polygon**of sixteen unequal sides, and the cupola is supported by sixteen ribs, springing from the same number of columns.