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Journal for Geometry and Graphics 20 (2016), No. 1, 075--083
Copyright Heldermann Verlag 2016

Geometrical Shapes Allowing the Construction of the Midpoint of a Segment Using a Straightedge Only

Victor Oxman
Western Galilee College, P.O.Box 2125, Acre 24121, Israel

Moshe Stupel
Shaanan College, P.O.Box 906, Haifa 26109, Israel

Avi Sigler
Technical College for Aviation Professions, Haifa, Israel

Finding the middle point of a segment is one of the basic constructions for the case when there are restrictions requiring the use of an unmarked ruler (a straightedge) only. When a segment is given with its midpoint, this considerably expands the set of possible constructions using a straightedge only. It is well known that the middle point of a segment cannot be found by using a straightedge only; however, when certain geometrical shapes are given in the plane it is possible to carry out this construction. The paper gives 10 examples of shapes allowing elegant constructions of the midpoint of a certain segment using a straightedge only.

Keywords: geometric constructions, constructions using a straightedge only, midpoint of a segment.

MSC: 51M15

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