posted
I have five weeks to prove that, if the area of a parallelogram is half the square of the shorter diagonal, and the sides and area are of rational measure, the parallelogram MUST be a square. My actuary dad and I have been at it for a week, and we can prove a few inequalities, but nothing conclusive. Since the instructions say we can get help from ANY SOURCE except Lipscomb faculty, so long as we eventually present it in person without notes, I figured it couldn't hurt to post it here. Any hints or advice (or a full blown proof) would be wonderful.
-------------------- "This is why you people think I'm so unknowable. You don't listen!" - God, "God, the Devil and Bob"
Registered: Mar 1999
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posted
Are you sure you're saying this right? Is it half the square or half the square root? And when you say diagonal, are you referring to the line between two opposite corners?
posted
A parallelogram is simply a rectangle that was built by the lowest bidder. Probably the same construction outfit that rebuilt the major road leading to my subdivision.
-------------------- The philosopher's stone. Those who possess it are no longer bound by the laws of equivalent exchange in alchemy. They gain without sacrifice and create without equal exchange. We searched for it, and we found it.
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-------------------- Yes, you're despicable, and... and picable... and... and you're definitely, definitely despicable. How a person can get so despicable in one lifetime is beyond me. It isn't as though I haven't met a lot of people. Goodness knows it isn't that. It isn't just that... it isn't... it's... it's despicable.
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posted
Ok, this may be a retarded question, but how can a square have a shorter diagonal?
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Cartman
just made by the Presbyterian Church
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posted
A square with sides s has two diagonals d of equal length. A parallelogram with base and height s has two diagonals dl and ds of unequal length, one of which is always longer and the other of which is always shorter than d. You are seeing now?
-------------------- ".mirrorS arE morE fuN thaN televisioN" - TEH PNIK FLAMIGNO
Registered: Nov 1999
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posted
I hated proofs too - infact I was talking about proofs with a friend at uni the otherday who did his first degree in mathematics!! Hah!
I guess I sorta understand now, but during higher maths as school in year 11 and 12 - I was always frustrated and annoyed that the bloody teacher could never 'explain' where he or HOW he STARTED the proof. It was as if he just pulled some formula or "If such and such is this, then that is that" out of his arse!
I'm guessing you have to use equations that are 'part of the "area"' of the equation or problem you are trying to proove? Doesn't that mean that you need a fair understanding of a specialise area of that mathematics branch you are working on at that time? How long does a proof have to be?
So you use "knowns" to "prove" an "unknown"? Sorta like doing experiments, only your tools are equations?
Anyway goodluck.
-------------------- "Bears. Beets. Battlestar Galactica." - Jim Halpert. (The Office)
posted
Oh, an actual help Omega - have you tried some of the sci.* newsgroups - I'm sure there is a maths one there. Try looking and posting through Google Groups - I personally like Forte Free Agent to peruse my newsgroup messages (although I haven't in a while - I used to post there WAY more than I do here now - It was a little excessive!)
-------------------- "Bears. Beets. Battlestar Galactica." - Jim Halpert. (The Office)
Cartman
just made by the Presbyterian Church
Member # 256
posted
So you use "knowns" to "prove" an "unknown"?
Erh, a real mathematician would probably cringe at this explanation, but you use something that you know and is proven (that the diagonals of a square are equal in length) to deduce something else that you also know but isn't proven (that, if half of the square of the shortest diagonal of a parallelogram is equal to its surface area, the parallelogram is in fact a square). Or... something.
Registered: Nov 1999
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Re geometrical proofs: they were my favorite thing, actually, in high school or junior high, prior to that point in school where I just sort of gave up on things (Algebra II).
Re nerds: I'm totally reading David Foster Wallace's Everything and More right now. (It is about Cantor and infinity and, I don't know, ordinals or something. Math is hard. I like shopping!)
Registered: Mar 1999
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posted
Why else do you think he's so popular here? His sparkling personality? I laugh heartily.
-------------------- Yes, you're despicable, and... and picable... and... and you're definitely, definitely despicable. How a person can get so despicable in one lifetime is beyond me. It isn't as though I haven't met a lot of people. Goodness knows it isn't that. It isn't just that... it isn't... it's... it's despicable.
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