A regular polygon with 17 sides (regular heptadecagon) can be constructed with a ruler and a
compass (unlike a regular polygon with 7 sides). Such a construction is provided by a free to
download program "Ruler and Compass".
Step 1.
Choose a horizontal line AB. Draw a perpendicular line to AB passing through A.
Draw a circle C with a center at A and radius AB.
In this picture point A is denoted by P and point B by Q. This picture was drawn by a program
"Ruler and Compass" mentioned above. Differences in names are because program itself chooses
names. Points A and B are defined by this program by lines
A=point(250,250)
P1=point(250,350)
Horizontal straight line L is defined by
L=line(A,P1)
and line perpendicular (vertical) LL by
LL=Perp(L,A)
Procedure Perp(...) is provided by a library unit of
a program "Ruler and Compass". It draws perpendicular lines
using ruler and compass.
Take an intersection point of a circle C and a vertical straight line LL
E=IntersCircLin(C,LL,1)
In the picture it is denoted by computer by P1.
Take a center F of the segment EA (on the picture - center of the segment with ends P and
P1) and G - center of the segment AF.
F=SegmentCenter(E,A)
G=SegmentCenter(F,A)
Procedure SegmentCenter(...) is provided by a library unit of the program "Ruler and Compass".
Point G is denoted by R2 in the picture.
Take a quarter of the angle from A to G and from G to P1. To do this we construct bisect lines
twice.
Step 2.
Draw a line passing through G, having an angle 45 degrees with a straight line GJ.
(In the picture G is R2, J is a point S).
Program of "Ruler and Compass" does this by finding a perpendicular straight line first and
then by finding a bisect line.
Point M is an intersection point of a constructed straight line and the line L. Point M
is denoted by B6 in the picture.
Step 3.
Draw a circle C1 with the diameter from M to P1. (points B6 and Q of the picture). This circle cuts
the straight line LL at the point N (point T6 of the picture).
Corresponding lines of the program are
Draw a circle C2 with center at J (point S of the picture) and radius JN (N is a point T6 of the picture).
C2=circle(J,N)
R=IntersCircLin(C2,L,1)
R is the intersection point of C2 with L (point W6 of the picture).
Construct a straight line perpendicular to L and passing throug W6. Denote by P4 an intersection point of
this straight line with the circle C2.
L5=Perp(L,R)
P4=IntersCircLin(C,L5,2)
Points P1 and P4 (points Q and P7 of the picture) vertices of the regular heptadecagon inscribed into C.
(There are 2 vertices of this polygon between Q and P7).
Step 4.
Having 2 vertices of a regular pentagon it is easy to find other vertices
because all of them belong to the circle C in equal distances.
This is the first round of constructing of vertices of regular heptagon.
Procedure RegPoint(...) is used for this construction. This procedure finds a point on a circle (which is
the first
variable of procedure), in the same distance to a point (second variable of procedure) as the
distance of 2 points (second and third variable of procedure).
Procedure is provided by a program, it is in a library. It uses ruler and compass only.
Step 5.
Construct all remaining vertices with 2 next rounds.
Software that you really need.