Timeline for An example of a beautiful proof that would be accessible at the high school level?
Current License: CC BY-SA 3.0
7 events
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| Dec 8, 2011 at 16:29 | comment | added | roy smith | Having taught the first 4 or 5 books of Euclid to bright 8-10 year olds, I agree with mbsq, but it doesn't sound as if darj is to be easily convinced. And I also agree that one of the interesting things about proofs in math is clarifying just why one thinks something is obvious, and sometimes finding out that one has been missing a lot of subtlety. When showing that a parallelogram can be transformed into a rectangle of same area, how many of us have been guilty of always drawing the parallelogram with one upper vertex lying directly over the base? Euclid is more thorough. | |
| Sep 9, 2011 at 21:07 | comment | added | darij grinberg | ... ways doesn't help. In reality, mathematics is maybe 1% about proving things that are intuitively obvious (even topology), and 99% about proving things that are either surprising or seem to be useful in proving surprising things. Skepticism is a good life lesson, but it is better taught by providing examples of false intuitively obvious assertions with counterexamples than by providing examples of correct intuitively obvious assertions with their seemingly redundant proofs. | |
| Sep 9, 2011 at 21:04 | comment | added | darij grinberg | I disagree. In school, mathematical proofs are like castles built on sand - not only do most students never realize what they are for, but they often tend to be sloppy right up to flawed (not "flawed" in the sense of "informal", but flawed in the sense of arguments that wouldn't be accepted as a correct proof even in a published paper), and the idea that proofs can be interesting is totally missing (at best they are considered a necessary evil by students and teachers alike). Adding to this a "revelation" that mathematicians prove trivial things in complicated (for students, at least) ... | |
| Sep 9, 2011 at 19:00 | comment | added | Monroe Eskew | The arguments are not so painful. #4 merely involves some observations relating the center of a circle, isoceles triangles, and the fact that two distinct lines intersect at most once. In any case I disagree with the sentiment. Part of the mathematical way of thinking is resisting the urge to accept things just because they seem obvious at first, and always demand that your knowledge but put on a firmer footing. I believe this is the essential "life lesson" students should take from mathematics. Sadly it is not being imparted in today's secondary schools much. | |
| Sep 9, 2011 at 11:50 | comment | added | darij grinberg | What I absolutely dislike about 4) is how it cements the common misconception that mathematics is about giving painstakingly difficult proofs to intuitively obvious statements. Part 3) is only slightly better in this aspect. The rest are pretty good. | |
| Sep 9, 2011 at 4:23 | history | edited | Monroe Eskew | CC BY-SA 3.0 |
added 72 characters in body
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| Sep 9, 2011 at 4:17 | history | answered | Monroe Eskew | CC BY-SA 3.0 |