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# Beyond the compass: Exploring geometric constructions via a circle arc template and a straightedge

Academic Editor: Suzieleez Syrene Abdul Rahim

• For thousands of years, the compass-and-straightedge tools have dominated the learning and teaching of geometry. As such, these inherited, long-standing instruments have gained a lustre of naturalized pedagogical value. However, mounting evidence suggests that many learners and teachers struggle to efficiently, effectively and safely use compasses when constructing geometric figures. Compasses are difficult for learners to use, can lead to inaccurate drawings, and can be dangerous. Thus, there is value in reconsidering the role of the compass in the learning and teaching of geometric constructions and to offer better tools as alternatives. The purpose of this work is to address the aforementioned need by proposing an alternative tool to the compass that is safer, more efficient and more effective. We will argue that a circle arc template forms such an alternative tool, and we will illustrate how learners and teachers can add value to their classrooms by using it, in conjunction with a straightedge, to establish the well-known constructions seen in geometry curricula around the world.

 Citation: • • Figure 1.  Compass constructions made easy 

Figure 2.  Circle arc template

Figure 3.  A given line segment $\overline {AB}$

Figure 4.  Circle arc template with centre at $A$

Figure 5.  Circle arc template with centre at $A$

Figure 6.  A first arc

Figure 7.  Circle arc template with centre at $B$

Figure 8.  Second arc with intersection points labelled

Figure 9.  Intersection points, $D$ and $E$

Figure 10.  Straightedge aligned with points $D$ and $E$

Figure 11.  Line segment $\overline {DE}$ constructed

Figure 12.  Finished construction. $\overline {DE}$ is the perpendicular bisector of $\overline {AB}$

Figure 13.  Line segment $\overline {AB}$

Figure 14.  Circle arc template with centre at $A$

Figure 15.  Marking point of intersection made with $\overline {AB}$

Figure 16.  Point of intersection labelled $P$

Figure 17.  Circle arc template with centre at $B$

Figure 18.  Marking point of intersection made with $\overline {AB}$

Figure 19.  Point of intersection labelled $S$

Figure 20.  Circle arc template with centre at $P$

Figure 21.  Marking point of intersection made with $\overline {AB}$

Figure 22.  Point of intersection labelled $Q$

Figure 23.  Circle arc template with centre at $S$

Figure 24.  Marking point of intersection made with $\overline {AB}$

Figure 25.  New point of intersection labelled $R$

Figure 26.  Circle arc template with centre at $Q$

Figure 27.  Arc with centre at point $Q$

Figure 28.  Circle arc template with centre at $R$

Figure 29.  Arc with centre at point $R$ and intersection points labelled

Figure 30.  Intersection points $D$ and $E$

Figure 31.  Straightedge aligned with points $D$ and $E$

Figure 32.  Straightedge aligned with points $D$ and $E$

Figure 33.  Finished construction. $\overline {DE}$ is the perpendicular bisector of $\overline {AB}$

Figure 34.  $\angle AOB$

Figure 35.  Circle arc template with centre at $O$

Figure 36.  Marking point of intersection, $P$

Figure 37.  Marking point of intersection, $Q$

Figure 38.  $\angle AOB$ with points $P$ and $Q$

Figure 39.  Circle arc template with centre at $P$

Figure 40.  'Small' section of arc traced, with centre at $P$

Figure 41.  Circle arc template with centre at $Q$

Figure 42.  Arc with centre at $Q$ intersecting previous arc to form point $C$

Figure 43.  Line segment $\overline {OC}$ is constructed using straightedge

Figure 44.  Finished construction. $\overline {OC}$ is the bisector of $\angle AOB$

Figure 45.  Line Segment $\overline {AB}$ and point $P$

Figure 46.  Circle arc template with centre at $P$

Figure 47.  Points $Q$ and $R$ constructed

Figure 48.  Drawing arc with centre at point $Q$

Figure 49.  Drawing arc with centre at point $R$

Figure 50.  New point of intersection labelled $S$

Figure 51.  Line segment $\overline {PS}$ is constructed using straightedge

Figure 52.  Finished construction. $\overline {PS}$ is perpendicular to $\overline {AB}$

•  Open Access Under a Creative Commons license

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