id: 02323802
dt: j
an: 1998e.03531
au: Hilton, Peter; Pedersen, Jean
ti: How to construct regular 7-sided polygons - and much else besides. Pt. 1.
The basic construction.
so: Parabola 34, No. 1, 2-12 (1998).
py: 1998
pu: AMT Publishing, Australian Mathematics Trust, University of Canberra,
Canberra; School of Mathematics \& Statistics, University of New South
Wales, Sydney
la: EN
cc: G40
ut:
ci:
li:
ab: In this article (and its sequel) the authors show you that, slightly
redefining the problem formulated by the Greeks, you will be able, in
principle, to construct, for any given value of $N$, a polygon that
will be an arbitrarily good approximation to a regular $N$-gon.
Furthermore, all this can done by a systematic and explicit
paper-folding procedure that is described in detail, which depends only
on the precise value of $N$. The authors argue that in practice the
approximations we obtain by folding paper are quite as accurate as the
real world constructions obtained with a straight edge and compass ‒
for the latter are only perfect in the mind. In both cases the real
world result is a function of human skill, but the authors’
procedure, unlike the Euclidean procedure, is very forgiving, in that
it tends to reduce the effects of human error ‒ and, for most people,
it is far easier to bisect an angle by folding paper than even when
geometric figures are obtained from the best of modern-day computers
their accuracy depends on the precision of the computer calculation and
the resolution of the printer. (from the introduction)
rv: