4 ms·
I think the point is less to provide a completely proper proof of Thales Theorem, and more to demonstrate the fundamental principle of what a proof is (an argum
by tech_ken 2y ago
I think the point is less to provide a completely proper proof of Thales Theorem, and more to demonstrate the fundamental principle of what a proof is (an argument to back-up a seemingly intractable statement), and how one might construct one (use concepts which we already understand, ex. rectangles, to create some plausible reasoning). Yes it involves some bad habits (relying primarily on visual intuition), but you've got to start somewhere. Moreover, the deficiencies of the example become the motivators for the next example ("so in the last example we did X, but that has problem A, so now we try Y").
- t_mann 2y agook, but if it's for pedagogical purposes, then it's even more important to point out that you're not done here (which the article misses). also, but this is purely personal preference, I don't think geometrical constructions are a good way to introduce someone to proofs. it's easy to fall into traps of circular reasoning (as in this example) or outright wrong arguments, it's not clear when you've done enough work, and it doesn't generalize well to other problems (what is the general strategy here - "draw more stuff and hope you see something"?). personally, I'd much rather have an introduction to proofs eg through something like Induction - it's very clear when you're 'done', there's no debate about whether it's a 'real' proof, much less risk of falling into traps, it's closer to university-level math and, most importantly, it's a versatile general tool that is easy to apply to new problems (and easy to see where it can be applied)
- lupire 2y agoGeometrical constructions are valid if you use axioms. You can misuse induction (all horses are the same color, heap of sand cannot exist) and algebra (1 = 2 via division by zero)