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You are watching: Pros and cons of using a compass and straightedge
I am curious why it is vital for people to learn just how to use compasses and straightedges in geomeattempt, and also not just rely on a drawing program.
I have actually a couple ideas, however I can be missing somepoint or have a gap, so any opinions sustained by facts or credible resources is great!
Similar to any type of technological help, I think the real question is not around whether the modern technology is supplied however fairly around exactly how it is offered. I deserve to imagine drawing programs being supplied in methods that substantially improve the student"s discovering of geometry. I can likewise imagine them being offered in means that actually inhilittle such finding out. The focus must always be on principles, fairly than techniques. The modern technology have to be offered to stimulate believed, quite than as a substitute for thought. Provided that this is done, I view no reason why compasses and also straightedge need to be vital.
I think that constructions with compass and straightedge are essential in couchsurfingcook.com education and learning bereason are attached to the interpretation of a one-of-a-kind subset of the real numbers: the constructible numbers.
They develop a subfield of $couchsurfingcook.combbR$ that is a ""tower"" of quadratic extensions of $couchsurfingcook.combb Q$ and this reality has some interemainder in the examine of reducible polynomials.
But, I watch that probably all this is not so exciting for beginner , if the teacher does not motivate the study.
I come from an Olympiad couchsurfingcook.com background and for this reason have invested many hours wielding my compass and also straightedge to fix Olympiad geometry problems. I have likewise used softwares prefer GeoGebra once training, and in my experience there are benefits and disadvantages to both units.
Put sindicate, I believe GeoGebra is great for easily illustration diagrams and verifying conjectures. It is additionally an inhelpful tool for trouble writing bereason you can adjust the setup of the configuration and also watch all the other dependent points/lines/circles/etc. readjust in real-time. This allows one to empirically verify theorems that deserve to then be couchsurfingcook.comematically prstove. On the various other hand also, I think manually illustration these diagrams on paper via a compass and straightedge has actually added much more to my geometric intuition. I"m not quite certain how to put this into words however here"s a little example that may shed some light. Suppose the task wregarding attract a triangle and identify its infacility. If I was on a drawing software, it"s as simple as picking 3 points, connecting them, and also finding an incenter switch. (Maybe I would need to carry out the added step of making two auto-produced angle bisectors and also intersecting them, yet the allude still stands.) If I was in an Olympiad establishing and essential to draw a precise diagram, I would start rather by illustration the circumcircle of the triangle, then drawing in the triangle itself, then drawing perpendiculars from the circumfacility to identify the midpoints of two of the 3 developed arcs, then connecting those points to the oppowebsite vertices to make two angle bisectors, then drawing the infacility as the intersection of the angle bisectors. The latter technique draws upon and also reinpressures my expertise of the deep relations between the circumcircle and also the incircle, which is often useful for resolving even more facility troubles.
TL;DR: GeoGebra is rapid and also reliable, compass and straightedge gives you even more time to internalize as you attract and reinpressures intuition/relationships.
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It is also worth noting that my opinion may be slightly biased as over 95% of all the geomeattempt I have actually ever before done was through hand-drawn diagrams.