|
Drawing 3. Figure 3.2. From the
center of this circle, mark off 5 radii, OK, OP, OJ, OR, and
OM, spaced at every 72°. (For convenience, clarity, and symmetry,
place the radius, OJ, pointing up vertically to the "12
o'clock" position. The drawing is now bilaterally symmetrical).
Inscribe the sides of the pentagon within the circle where the
radii intersect the circle, at K, P, J, R, and M. This circle
is the circumcircle or excircle. A radius of this circle, OM
for example, is labeled r1. Inscribe a circle with the radius,
r 2, inside the pentagon and tangent to each of the five mid-sides.
This inscribed circle is the incircle. Note well the small length
of line, a, the difference between the two radii, r1 and r2.
These two radii are in a ratio of 2 : f.
This length is extremely difficult to measure precisely with
an inch rule or meter stick, so use compasses or dividers as
this small line segment "a" is the key to the entire
construction, and its measurement must be as precise as possible.
Without it, we will not be able to draw the circle for the equilateral
triangle or the circle for the heptagon.  |