Closed 4 years ago.
You are watching: Advantages of using a compass and straightedge
I am curious why it is vital for world to learn just how to use compasses and straightedges in geometry, and not just rely top top a illustration program.
I have actually a pair ideas, however I can be lacking something or have actually a gap, so any type of opinions supported by truth or credible sources is great!
As through any technological aid, i think the real concern is not about whether the an innovation is used but rather about how that is used. I can imagine drawing programs being used in means that significantly enhance the student"s finding out of geometry. I can additionally imagine them being provided in ways that in reality inhibit together learning. The emphasis should always be ~ above ideas, quite than techniques. The technology should be provided to wake up thought, rather than as a substitute for thought. Listed that this is done, I check out no factor why compasses and straightedge have to be necessary.
I think the constructions v compass and also straightedge are important in starrkingschool.net education due to the fact that are linked to the an interpretation of a special subset of the real numbers: the constructible numbers.
They kind a subfield that $\starrkingschool.netbbR$ that is a ""tower"" the quadratic expansions of $\starrkingschool.netbb Q$ and also this fact has part interest in the research of reducible polynomials.
But, I see that probably all this is no so interesting for starting person , if the teacher does no motivate the study.
I come native an Olympiad starrkingschool.net background and also thus have spent numerous hours wielding my compass and also straightedge to solve Olympiad geometry problems. I have also used softwares like GeoGebra as soon as training, and in my suffer there are benefits and disadvantages come both systems.
Put simply, I believe GeoGebra is great for quickly drawing diagrams and also verifying conjectures. It is also an invaluable tool for difficulty writing due to the fact that you can adjust the setup that the configuration and also watch every the various other dependent points/lines/circles/etc. Readjust in real-time. This permits one to empirically verify theorems that deserve to then be starrkingschool.netematically proven. ~ above the other hand, I believe manually drawing these diagrams on document with a compass and straightedge has contributed much much more to mine geometric intuition. I"m not rather sure just how to put this into words yet here"s a little example the may burned some light. Expect the task was to draw a triangle and also identify its incenter. If ns was top top a illustration software, it"s as straightforward 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 angle bisectors and also intersecting them, however the suggest still stands.) If I was in an Olympiad setting and necessary to draw an accurate diagram, I would start rather by illustration the circumcircle that the triangle, then drawing in the triangle itself, then drawing perpendiculars native the circumcenter to recognize the midpoints of 2 of the three developed arcs, then connecting those points come the the contrary vertices come make two angle bisectors, then drawing the incenter together the intersection that the angle bisectors. The latter strategy draws upon and also reinforces my expertise of the deep connections between the circumcircle and the incircle, which is often beneficial for solving more complex problems.
TL;DR: GeoGebra is fast and also efficient, compass and also straightedge provides you an ext time come internalize together you draw and reinforces intuition/relationships.
See more: How Many Cups In 60 Oz Of Water? How Many Cups In 60 Ounces
It is likewise worth noting the my opinion might be slightly biased as over 95% of all the geometry ns have ever before done was via hand-drawn diagrams.