Originally posted by PalynkaNo, you mentioned the "vertex of the middle-left square", which I interpreted as "top right corner of the left hand square in the middle row".
I don't even mention the "top right corner of the left hand square in the middle row", so I doubt you're even trying to understand.
My post is still there, if you care to read it.
Since you have troubles explaining yourself and get huffy when asked to do so, I won't waste any more time with you or your posts.
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Originally posted by Fat LadyIf you read the sentence to the end you'd see that after "vertex of the middle-left square" came "is in the midpoint of the top side of the lower left square."
No, you mentioned the "vertex of the middle-left square", which I interpreted as "top right corner of the left hand square in the middle row".
Since you have troubles explaining yourself and get huffy when asked to do so, I won't waste any more time with you or your posts.
Now answer this: How many vertices of that square can be also the midpoint of the top side of the lower left square?
Originally posted by PBE6Oh yes, I certainly agree that the shapes are congruent (thank you for reminding me of the correct word!) and that it fairly obvious that they are (if the diagram is drawn accurately), but to get to that stage you have to imagine the two whole squares removed.
I think you would agree that each half of the object is congruent to the other. Although they aren't "mirror symmetrical" to each other, they are "rotationally symmetrical". However I solved this problem the same way you did, with an area formula.
I'm not sure if this is the proper name for this type of solution, but to me it seemed "constructive" (i.e. bu ...[text shortened]... discovered a "secret", resulting in that AHA!! moment we all relish so much. 🙂
What if you initially guessed wrong and tried to do this with the line going from A to the point 1/3 of the way down BC? Then you would spend time deciding that the two resulting shapes were not congruent and reject this solution.
The good thing about solving it methodically is that you end up with the solution after a certain amount of time. I love clever solutions, but only if they result in getting to the answer much quicker or if there isn't an obvious way to do it methodically at all.
Originally posted by PBE6Maybe you've missed that the point of this thread was Fat Lady trying to show off and failing miserably.
I think you would agree that each half of the object is congruent to the other. Although they aren't "mirror symmetrical" to each other, they are "rotationally symmetrical". However I solved this problem the same way you did, with an area formula.
I'm not sure if this is the proper name for this type of solution, but to me it seemed "constructive" (i.e. bu ...[text shortened]... discovered a "secret", resulting in that AHA!! moment we all relish so much. 🙂
Originally posted by PBE6Have you been reading "The Mathematical Experience"?
I think you would agree that each half of the object is congruent to the other. Although they aren't "mirror symmetrical" to each other, they are "rotationally symmetrical". However I solved this problem the same way you did, with an area formula.
I'm not sure if this is the proper name for this type of solution, but to me it seemed "constructive" (i.e. bu ...[text shortened]... discovered a "secret", resulting in that AHA!! moment we all relish so much. 🙂
Originally posted by PalynkaThat's quite harsh. Not being able to understand a single concept does not mean you are not intelligent. For instance, many bright mathematicians struggle with Analysis but that does not mean they won't make good Group theorists.
Maybe you've missed that the point of this thread was Fat Lady trying to show off and failing miserably.
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Originally posted by SwlabrI definitely agree, but I never said he wasn't intelligent. Just that the opening post and his insistence that HIS answer was the best, made me think this was more about ego than intelligence or mathematics.
Not being able to understand a single concept does not mean you are not intelligent. For instance, many bright mathematicians struggle with Analysis but that does not mean they won't make good Group theorists.
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Originally posted by PBE6🙂
Nope, just thinking about thinking, but I just Googled this book and it sounds pretty interesting! I'll have to take a look next time I'm at the book store.
Thinking about thinking is one of the most important things. In this context it is called meta-mathematics.
If you have the time do read that book because it is very good in mathematical awakenings. I just found out http://www.amazon.com/What-Mathematics-Really-Reuben-Hersh/dp/0195113683 and I think I'll devour that book. It seems to be pretty interesting and polarizing too.
Edit: One review
http://www.maa.org/reviews/whatis.html
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Originally posted by PalynkaPerhaps. I'm always wary about how people come across on forums-too many innocent posts have been taken in ways that they were not meant!
I definitely agree, but I never said he wasn't intelligent. Just that the opening post and his insistence that HIS answer was the best, made me think this was more about ego than intelligence or mathematics.
It must be pointed out, however, that Fabian didn't really explain himself too well in his first post. He just said "consider symmetry", which in itself is not rigorous, thus Fat Lady replied with a rigorous. proof.
Anyway, I'n not going to let myself be dragged into any arguments or anything. Both methods are correct, but the rotational symmerty one is more beautiful. 🙂
Originally posted by adam warlockInteresting. I tend to have a very formalist view of mathematics, so it would be good to read something that challenges it.
🙂
Thinking about thinking is one of the most important things. In this context it is called meta-mathematics.
If you have the time do read that book because it is very good in mathematical awakenings. I just found out http://www.amazon.com/What-Mathematics-Really-Reuben-Hersh/dp/0195113683 and I think I'll devour that book. It seems to be pretty interesting and polarizing too.
Edit: One review
http://www.maa.org/reviews/whatis.html
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Originally posted by PalynkaThe previous book "The Mathematical Experience" also disagrees the three main views of mathematics (besides doing a lot of other things) but seems to be much more milder than this one.
Interesting. I tend to have a very formalist view of mathematics, so it would be good to read something that challenges it.
I am platonist/realist and so I look forward reading this new book and foaming out of my mouth at most of it.
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
http://www.dartmouth.edu/~matc/MathDrama/reading/Hamming.html
http://plato.stanford.edu/archives/fall2004/entries/mathphil-indis/