The cross section resembles that of jute, but the corners of the polygons are rounded off.
Cross section: polygons strongly coherent and regular, much like those of hemp, but the central opening is larger; coloured yellow, darker at the rim.
By a judicious use of this Law of Nature, the Polygons and Circles are almost always able to stifle sedition in its very cradle, taking advantage of the irrepressible and boundless hopefulness of the human mind.
If they are not polygons, I think it absurd to use polygons in their stead.
Relations between Polygons of Loads and of Resistances.
In drawing these polygons the magnitude of the vector of the type Wr is the product Wr, and the direction of the vector is from the shaft outwards towards the weight W, parallel to the radius r.
A, B in one figure will then correspond to the side common to the two polygons A, B in the other.
Of polygons of n sides with a given perimeter the regular polygon encloses the greatest area.
Of two regular polygons of the same perimeter, that with the greater number of sides encloses the greater area.
The angles of regular polygons are designated by their degrees of angle, "at the centre" and "at the circumference.
The proof of the construction is shown in the figure, the hexagon and other polygons being marked simply for clearness of illustration.
They were near lakes among polygons some of which had low centers whereas others had high centers.
On July 9, we visited polygons having raised centers and young called continually but we could not locate them.
This longspur nest, among polygons of low hummocks, was bordered by mosses and grasses nine inches high.
They were frequently on polygons having raised centers.
The red phalarope on July 7 was the fifth most common bird in the area, making up two per cent of the avian population and was commonly seen on polygons having high centers.
On windy, cold days the ptarmigan were mainly on south exposures among grasses and sedges along lakes and on windless days were on flat tundra of polygons but near dwarf shrubs.
They were numerous on polygons having low centers and on high windswept knolls in association with black-bellied plovers, ruddy turnstones and pectoral sandpipers.
X Onions and Orchids "The perimeters of similar polygonsare as their homologous sides.
She obligingly furnished a sample: "The perimeters of similar polygons are as their homologous sides.
The proof of the construction is shown in the figure, the hexagon and other polygons being marked for clearness of illustration.
They were taking turns tossing some small polygons, and evidently the objective of whatever they were doing lay in the way the polygons fell.
He concentrated it, he focused it, and one of the polygons rose slowly from the ground and drifted into the air above the Martians' heads.
The third is the somewhat interesting but mathematically unimportant application of the regular polygons to geometric design.
For example, the classification of polygons or of quadrilaterals, once so popular in textbook making, has generally been abandoned as tending to create or perpetuate unnecessary terms.
The perimeters of similar regular polygons are proportional to their radii, and their areas to the squares of the radii.
It is easily seen that this is true only with the limitation set forth in most textbooks, that the spherical polygons considered are convex.
Here it will be seen that the equilateral triangle and the regular hexagon are the basal figures, and a few of the properties of these polygons might be derived from the study of such a design.
From the square, regular polygons of 2^n sides; From the regular pentagon, regular polygons of 2^n .
After they are proved it is assumed that the circle is the limit of the regular inscribed and circumscribed polygonsas the number of sides increases indefinitely.
The areas of two similar polygons are to each other as the squares on any two corresponding sides.
There is, however, a much more worthy interest than the mere mensuration of the circle, namely, the construction of such polygons as can readily be formed by the use of compasses and straightedge alone.
Congruent polygons are therefore necessarily equivalent, but equivalent polygons are not in general congruent.
Congruent polygonshave mutually equal sides and mutually equal angles, while equivalent polygons have no equality save that of area.
While in elementary geometry the only regular polygons studied are convex, it is interesting to a class to see that there are also regular cross polygons.
In connection with the study of the regular polygons some interest attaches to the reference to various forms of decorative design.
Of these regular polygons two are of special interest, and these will now be considered.
This review of the names of the polygons offers an opportunity to impress their etymology again on the mind.
It is because there are properties appertaining to polygons of any number of sides and that may be immediately applied to any particular polygon.
The two first books are almost strictly, as Kepler styles them, geometrical, relating in great measure to the inscription of regular polygons in a circle.
Whilst it is always possible to draw a circle which is inscribed in or circumscribed about a given triangle, this is not the case with quadrilaterals or polygons of more sides.
Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have; and the polygons are to one another in the duplicate ratio of their homologous sides.
Bryson of Heraclea took an important step when he circumscribed, in addition to inscribing, polygons to a circle, but he committed an error in treating the circle as the mean of the two polygons.
Three regular polygons of six or more sides cannot form a solid angle.
The fourth book contains only problems, all relating to the construction of triangles and polygons inscribed in and circumscribed about circles, and of circles inscribed in or circumscribed about triangles and polygons.
Euclid does not use the word regular, but he describes the polygons in question as equiangular and equilateral.
These have many properties which are quite analogous to those of triangles and polygons in a plane.
Till the beginning of the 19th century nothing was added to the knowledge of regular polygons as given by Euclid.
We conclude with a few theorems about regular polygons which are not given by Euclid.
We also represent every stress twice over, for it appears as a side of both the polygons corresponding to the two joints between which it acts.
We might in this way form a series of polygons of forces, one for each joint of the frame.
The right lines similarly situated in the two polygons are proportional to the homologous sides of the polygons.
The perimeters of two similar polygons are to each other as the homologous sides of these polygons.
The areas of similar polygons are to each other as the squares of the homologous sides of the polygons.
Of polygons inscribed and circumscribed to the circle.
Regular polygons of the same number of sides are similar, and their perimeters are to each other as the radii of the circles to which they are inscribed or circumscribed.
Of the area of polygons and of that of the circle.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "polygons" in a variety of sentences. We hope that you will now be able to make sentences using this word.
