A system of forces represented completely by the sides of a plane polygon taken in order is equivalent to a couple whose moment is represented by twice the area of the polygon; this is proved by taking moments about any point.
In a structure in which there are pieces supported at more than two joints, let a polygon be constructed of lines connecting the centres of load of any continuous series of pieces.
This result is easily extended to the case of a polygon of any number of sides; it has an important application in hydrostatics.
Of polygons of n sides with a given perimeter the regular polygon encloses the greatest area.
This diagram consists of a polygon whose successive sides represent the given forces P1, P2, P3 .
The polygon of forces is then made up of segments of a vertical line.
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.
The Germans advancing in the evening from Becelaere were sharply repulsed by the centre infantry brigade of the 7th Division east of Polygon Wood.
The Germans do not appear to have penetrated into the Polygon Wood at any point.
Warwicks of the 7th Division, and in the afternoon an advance was made north of Polygon Wood by the 6th Infantry Brigade in co-operation with the French IX Corps on the left.
Further north again, in Polygon Wood and to the east of it, the 2nd Division, though repeatedly attacked, more than held its own.
In the course of the morning of 24th October the Reserve Division attacked the line of the 21st Infantry Brigade in overwhelming strength, and broke through north of Reutel, penetrating into Polygon Wood.
Polygon Wood, and of the 1st Northamptonshires, who had come up to Glencorse Wood, south-west of the Nonne Bosch, and with other units of the 2nd and 3rd Infantry Brigades had filled the gap which extended thence to the Menin road.
Thus, in Figure 71 a, the circle is inscribed within the polygon, while in Figure 72 the polygon is circumscribed by the circle; the first is therefore a circumscribed and the second an inscribed polygon.
In both of these examples we have assumed that the diameter across corners of the polygon was given, but suppose the diameter across the flats were given, and the construction is a little more complicated.
When the dimension of the polygonacross its corners is given, the circle drawn to that dimension circumscribes the polygon, because the circle is without or outside of the polygon and touches it at its corners only.
The term polygon is applied to figures having flat sides equidistant from a common centre.
A regular polygonis one the sides of which are all of an equal length.
This scale lacks, however, one element, in that the diameter across the flats of a regular polygonbeing given, it will not give the diameter across the corners.
From the point O to the numerals denoting the radius of the polygon is the radius across the flats, while from point O to the horizontal line drawn from those numerals is the radius across corners of the polygon.
A figure orpolygon having nine sides and nine angles.
A polygon or plane figure with nine sides and nine angles; a nonagon.
A figure or polygon bounded by twelve sides and containing twelve angles.
You will find that if the radius of the circle be one, the side of the polygon is .
It is in the form of a letter to Mr. Smith: "You may do this: calculate the side of a polygon of 24 sides inscribed in a circle.
The method of the equilibrium polygon is a safe, sane, and sound way to calculate an arch.
Healthy intellectual life is the perfectly balanced outcome of the complex polygon of forces which has its seat within the brain.
But the suppression of certain lines in this polygon does not suppress life, nor does it necessarily destroy consciousness.
On the centre of the side a b of the polygon he erected the perpendicular, e f, having a length equal to one-sixth of a b.
XEFA; beginning with the upward thrust EX, continuing down XA, and drawing AF parallel to AF in the frame we complete the polygon by drawing EF parallel to EF in the frame.
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.
IJKY, in the frame is represented by a polygon of the same name in the reciprocal figure.
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.
For longer bridges the funicular polygon affords a method of determining maximum bending moments which is perhaps more convenient.
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.
A general improvement in nutrition and other home circumstances might tend to 'steepen' the polygon of variation, i.
If we treat the general aptitude (or 'cleverness') of the children as differing only by more or less, the problem becomes one of fitting the types of school to a fairly exactly ascertainable polygon of intellectual variation.
In the centre the leading waves of the 169th, after some resistance in Glencorse Wood which they overcame, succeeded in penetrating Polygon Wood, where they probably gained their objective.
The French judged rightly in abandoning a fort, the front of whose polygon is only 150 feet, and which our shells would have destroyed in three days.
The regularity of the polygon and circular forms, and the small works intended to cover the doors of the building, are, above all, remarkable.
Euclid contents himself with saying that the circle is greater than any polygon that can be inscribed in it, and less than any polygon that can be described about it.
The second episode befell during our brief rest after the Polygon Wood, when I had ridden down the line one afternoon to see a friend in the Heavy Artillery.
We were shoved in at the Polygon Wood on the 26th, and after four days got so badly mauled that we were brought out to refit.
Except for the days of the Polygon Wood it was neither very severe nor very distinguished, and you will find it in the history books.
In the above-mentioned survey Cambridge Street is Sovereign Street, and the oval piece with Southwick Crescent at one end is Polygon Crescent, a name now only retained in Polygon Mews.
And the more sides a polygon to be inscribed in a circle successively has, so much the greater will the perimeter of the polygon be than the perimeter of the circle.
The sixteen rooms of the polygon are roofed with glass, to let in the flood of light, and a few feet below the glass is another roofing, or awning, to soften its intensity and to mitigate the heat of the direct rays of the sun.
But if four-seventeenths of a revolution had been taken for the angle of the creases, the ultimatepolygon would have had thirty-four sides.
It represents the radial line of a polygon the same as the radius represents half the diameter of a circle.
The figure shows an irregular polygon (that is, many-sided figure) and is a re-entering polygon.
Its form was an oblong quadrangle, the exterior polygon being several hundred yards in circumference.
The original form of Fort Chartres was an irregular quadrangle, with four bastions; the sides of the exterior polygon being about five hundred feet in extent.
He did not return to The Polygon on Saturday night; Mary fretted all Sunday.
This,' he says of Mrs. Clairmont and her coming to The Polygon (vide pp.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "polygon" in a variety of sentences. We hope that you will now be able to make sentences using this word. Other words: enclosure; figure; triangle
