MATHEMATICS AND ORIGAMI

Mathematics and Origami

If the length of the strip is great, the process is facilitated; the remaining paper (fig.5)

can be hidden within the polygon itself. This way we produce fig. 6 that is shown in its obverse

and reverse sides.

10.3 HEPTAGON
10.3.1 H. HUZITA ́S SOLUTION

Let the regular heptagon of fig. 1 with radius one unit and central angle ω (ω 1 = ω; ω 2 =

2 ω; ω 3 = 3ω).

Being a close polygonal line, the sum of the abscissas of its seven vertices will add up to

zero:

1 + 2cos ω + 2cos 2ω + 2cos 3ω = 0 (1)

Reminding that:

ω ω ω

ω ω ω ω

cos 3 4 cos 3 cos

cos 2 cos sen 2 cos 1

3

2 2 2

= −

= − = −

1

2 3

(^45)
6
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