Abstract
<p>In this paper an attempt is made to design a mathematical machine based on the Pythagorean theory of fitting an equivalent parallelogram (given angle and side) with another parallelogram. An equivalent square or rhombus is constructed given a rectangle or a parallelogram respectively. It is then proved that this mechanism can simultaneously draw a parabolic arc. The parameters of this mathematical machine are checked. In each case, an attempt is made to find the focus and the directrix of the corresponding parabola. The important help of the GeoGebra software for the initial mechanical design of the machine is highlighted, but also the important differences of this simulation from the physical construction.</p><p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/soc/0713/a.php" alt="Hit counter" /></p>
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