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You are watching: Pros and cons of using a compass and straightedge
I to be curious why it is vital for human being to learn just how to usage compasses and straightedges in geometry, and not just rely top top a drawing program.
I have actually a pair ideas, yet I might be absent something or have a gap, so any kind of opinions supported by facts or credible resources is great!
As through any technical aid, ns think the real inquiry is not about whether the modern technology is used however rather around how it is used. I have the right to imagine drawing programs being used in methods that substantially enhance the student"s finding out of geometry. I can additionally imagine lock being used in ways that in reality inhibit together learning. The emphasis should always be ~ above ideas, fairly than techniques. The technology should be used to stimulate thought, fairly than as a substitute because that thought. Noted that this is done, I check out no factor why compasses and straightedge need to be necessary.
I think the constructions v compass and also straightedge are crucial in couchsurfingcook.com education because are attached to the meaning of a one-of-a-kind subset of the genuine numbers: the constructible numbers.
They kind a subfield of $\couchsurfingcook.combbR$ the is a ""tower"" of quadratic extensions of $\couchsurfingcook.combb Q$ and also this truth has part interest in the examine of reducible polynomials.
But, I watch that perhaps 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 thus have actually spent numerous hours wielding my compass and straightedge to solve Olympiad geometry problems. Ns have also used softwares like GeoGebra when training, and also in my suffer there are advantages and disadvantages come both systems.
Put simply, I believe GeoGebra is good for quickly illustration diagrams and also verifying conjectures. That is also an invaluable tool for difficulty writing because you can readjust the setup the the configuration and watch all the other dependent points/lines/circles/etc. Change in real-time. This allows one come empirically verify theorems that can then be couchsurfingcook.comematically proven. On the other hand, I think manually drawing these diagrams on paper with a compass and also straightedge has contributed much an ext to mine geometric intuition. I"m not fairly sure just how to put this into words but here"s a small example that may melted some light. Suppose the job was to attract a triangle and identify its incenter. If ns was top top a illustration software, it"s as an easy as picking 3 points, connecting them, and also finding one incenter button. (Maybe ns would have to do the extra action of making two auto-generated edge bisectors and intersecting them, however the point still stands.) If I remained in an Olympiad setting and required to draw precise diagram, I would certainly start instead by drawing the circumcircle the the triangle, then drawing in the triangle itself, then illustration perpendiculars indigenous the circumcenter to determine the midpoints of 2 of the three developed arcs, climate connecting those points to the the opposite vertices to make 2 angle bisectors, then drawing the incenter together the intersection of the edge bisectors. The latter strategy draws upon and also reinforces my understanding of the deep connections between the circumcircle and also the incircle, which is often useful for resolving more complicated problems.
TL;DR: GeoGebra is fast and also efficient, compass and also straightedge offers you more time come internalize together you draw and reinforces intuition/relationships.
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It is likewise worth noting that my opinion may be contempt biased as over 95% of all the geometry i have ever before done was via hand-drawn diagrams.