Posing and Solving Mathematical Problems by Patricio Felmer Erkki Pehkonen & Jeremy Kilpatrick

Author:Patricio Felmer, Erkki Pehkonen & Jeremy Kilpatrick
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Locus and the Concept of Central Symmetry

Figure 14 shows another example that illustrates how the availability of digital affordances can redirect or open a new path for exploration. Point D is inside of angle BAC. How to draw a segment from side AC to side AB such that the chosen point D is the midpoint of the segment?

Fig. 14H solves the problem

We choose any point P on side AC and reflect it with respect to D to obtain P′. The locus of P′ when point P moves along AC is a parallel line to AC. H is the intersection point of the locus and side AB and H′ is the reflected point of H with respect to D. Segment HH′ is the solution. Let us insist that the availability of a flexible transformation as the central symmetry molds the solution we find for this problem. Our way of thinking is transformed by the presence of the mediating artifact .

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