Fig. 205.
[ CXIV]
The Hexagon
The hexagon is a six-sided figure which, if inscribed in a circle, will have each of its sides equal to the radius of that circle (Fig. 206). If inscribed in a rectangle ABCD, that rectangle will be equal in length to two sides of the hexagon or two radii of the circle, as EF, and its width will be twice the height of an equilateral triangle mon.
| Fig. 206. | Fig. 207. |
To put the hexagon into perspective, draw base of quadrilateral AD, divide it into four equal parts, and from each division draw lines to point of sight. From h drop perpendicular ho, and form equilateral triangle mno. Take the height ho and measure it twice along the base from A to 2. From 2 draw line
to point of distance, or from 1 to ½ distance, and so find length of side AB equal to A2. Draw BC, and EF through centre o·, and thus we have the six points through which to draw the hexagon.
[ CXV]
A Pavement Composed of Hexagonal Tiles
In drawing pavements, except in the cases of square tiles, it is necessary to make a plan of the required design, as in this figure composed of hexagons. First set out the hexagon as at A, then draw parallels 1 1, 2 2, &c., to mark the horizontal ends of the tiles and the intermediate lines oo. Divide the base into the required number of parts, each equal to one side of the hexagon, as 1, 2, 3, 4, &c.; from these draw perpendiculars as shown in the figure, and also the diagonals passing through their intersections. Then mark with a strong line the outlines of the hexagonals, shading some of them; but the figure explains itself.