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Topic: Consturction of 17-sided regular polygon
Replies: 4   Last Post: Feb 8, 1999 2:23 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: Consturction of 17-sided regular polygon
Posted: Jan 31, 1999 9:05 AM
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On Sun, 31 Jan 1999, Peter Hung wrote:

> I have trying to find out the procedure for constructing a regular 17-sided
> polygon.


The neatest construction I know is due to Richmond - I call it the
"quadruple quadrisection constriction":

1) quadrisect the perimeter of the circle, by points N,S,E,W;

2) quadrisect the radius ON by the point A;

3) quadrisect the angle OAE by the line AB;

4) quadrisect the straight angle BAC by the line AD:

N
I |
| J
C |
F
A
|
W---------G-D-O-B-----H-----E
|
|
|
|
|
|
S

5) draw the semicircle DFE, cutting ON in F;

6) draw the semicircle GFH, centred at B;

7) cut the semicircle WNE by the perpendiculars GI and HJ to WE.

Then I and J are points of the regular heptakaidecagon on the
circle ENWS that has one vertex at E.

John Conway





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