TITLE:
Construction of Regular Heptagon by Rhombic Bicompasses and Ruler
AUTHORS:
A. Wünsche
KEYWORDS:
Plane Geometry, Algebra, Geometric Constructions, Heptagon, Cyclotomic Equations, Neusis
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.15,
August
19,
2014
ABSTRACT: We discuss a new
possible construction of the regular heptagon by rhombic bicompasses explained
in the text as a new geometric mean of constructions in the spirit of classical
constructions in connection with an unmarked ruler (straightedge). It avoids
the disadvantages of the neusis construction which requires the trisection of
an angle and which is not possible in classical way by compasses and ruler. The
rhombic bicompasses allow to draw at once two circles around two fixed points
in such correlated way that the position of one of the rotating points (arms)
on one circle determines the position of the points on the other circle. This
means that the positions of all points (arms) on both circles are determined in
unique way.