I am curious why it is necessary for people to learn how to use compasses and straightedges in geometry, and not just rely on a drawing program.
I have a couple ideas, but I might be missing something or have a gap, so any opinions supported by facts or credible sources is great!
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I come from an Olympiad math background and thus have spent countless hours wielding my compass and straightedge to solve Olympiad geometry problems. I have also used softwares like GeoGebra when training, and in my experience there are advantages and disadvantages to both systems.
Put simply, I believe GeoGebra is great for quickly drawing diagrams and verifying conjectures. It is also an invaluable tool for problem writing because you can change the setup of the configuration and watch all the other dependent points/lines/circles/etc. change in real-time. This allows one to empirically verify theorems that can then be mathematically proven. On the other hand, I believe manually drawing these diagrams on paper with a compass and straightedge has contributed much more to my geometric intuition. I'm not quite sure how to put this into words but here's a little example that may shed some light. Suppose the task was to draw a triangle and identify its incenter. If I was on a drawing software, it's as simple as picking three points, connecting them, and finding an incenter button. (Maybe I would have to do the extra step of making two auto-generated angle bisectors and intersecting them, but the point still stands.) If I was in an Olympiad setting and needed to draw an accurate diagram, I would start instead by drawing the circumcircle of the triangle, then drawing in the triangle itself, then drawing perpendiculars from the circumcenter to identify the midpoints of two of the three formed arcs, then connecting those points to the opposite vertices to make two angle bisectors, then drawing the incenter as the intersection of the angle bisectors. The latter approach draws upon and reinforces my understanding of the deep connections between the circumcircle and the incircle, which is often useful for solving more complex problems.
TL;DR: GeoGebra is fast and efficient, compass and straightedge gives you more time to internalize as you draw and reinforces intuition/relationships.
It is also worth noting that my opinion may be slightly biased as over 95% of all the geometry I have ever done was via hand-drawn diagrams.
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I think that constructions with compass and straightedge are important in math education because are linked to the definition of a special subset of the real numbers: the constructible numbers.
They form a subfield of $\mathbb{R}$ that is a ''tower'' of quadratic extensions of $\mathbb {Q}$ and this fact has some interest in the study of reducible polynomials.
But, I see that maybe all this is not so interesting for beginner , if the teacher does not motivate the study.
As with any technological aid, I think the real question is not about whether the technology is used but rather about how it is used. I can imagine drawing programs being used in ways that greatly enhance the student's learning of geometry. I can also imagine them being used in ways that actually inhibit such learning. The focus should always be on ideas, rather than techniques. The technology should be used to stimulate thought, rather than as a substitute for thought. Provided that this is done, I see no reason why compasses and straightedge should be necessary.