In 1672 Georg Mohr proved that you can draw any common geometric figure using just the collapsible compass (the straight edge can be used at the end for aesthetic reasons to more easily visualise what the construction accomplishes, but it never plays an active role in its creation). However, using both of these tools is in fact excessive. it cannot be used to translate distances, but rather to simply draw circles once we fix the radius, and reverting to its original form after the circle is drawn. Here we assume that the compass is a “collapsible” one, i.e. In fact, there is a theorem which states that any common geometric figure in a plane (we call such representations Euclidean) can be drawn using only these two simple tools. Therefore, it became very important to be able to construct geometric representations using only a compass and a straightedge (a ruler without a measure of distance). One of the issues they faced back then was that units of measure were unreliable, and like the perfectionists that they were, the wise of old would not be satisfied with crooked lines or anything but exact measures of angles. However, the Ancient Greek mathematicians were more geometers than arithmeticians, obsessed with the outer world and the symmetries and rules that govern it. If you ask a random person when and where do they believe mathematics as we know it today first originated from, most would probably answer the same: Ancient Greece.
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