Geodesic
Geometrical Shapes Allowing the Construction of the Midpoint of a Segment Using a Straightedge Only
Journal for geometry and graphics, Tome 20 (2016) no. 1, pp. 75-83 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51M15
Mots-clés : geometric constructions, constructions using a straightedge only, midpoint of a segment 
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     title = {Geometrical {Shapes} {Allowing} the {Construction} of the {Midpoint} of a {Segment} {Using} a {Straightedge} {Only}},
     journal = {Journal for geometry and graphics},
     pages = {75--83},
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V. Oxman; M. Stupel; A. Sigler . Geometrical Shapes Allowing the Construction of the Midpoint of a Segment Using a Straightedge Only. Journal for geometry and graphics, Tome 20 (2016) no. 1, pp. 75-83. http://geodesic.mathdoc.fr/item/JGG_2016_20_1_JGG_2016_20_1_a6/