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Grex > Tutoring > #14: Algebra, Geometry, Calculus, Trig, all that good stuff |  |
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toking
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Algebra, Geometry, Calculus, Trig, all that good stuff
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Jun 30 14:50 UTC 1997 |
This is it, the place to come and praise or discuss those shiney black
and magnificent numbers.
Their curves, their angels, the sheer magnificence of them all.
Everything from using calculators to obscure refrences to that PBS
sensation "Math Net".
Reverse Polish notation? No problem
Advanced calculus? No problem
Geometric proofs? No problem
Get your fork and dig in.
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| 132 responses total. |
toking
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response 1 of 132:
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Jun 30 14:52 UTC 1997 |
By the way, while I respect math and all its glory, I am positivley
incompetent when it comes to its application.
I won't contribute any answers in this item, but I probably will ask
some question <maybe>.
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danr
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response 2 of 132:
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Jun 30 15:10 UTC 1997 |
I'm a real engineer when it comes to mathematics. Unless someone can show me a
practical application, I'm not that interested in it.
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mary
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response 3 of 132:
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Jun 30 15:33 UTC 1997 |
I don't tend to embrace a lot of "wish I would have" type
thinking but I do wish I'd consistently used algebra
so that it would be there now when I need it.
An example - just last Saturday, while waiting at the airport,
I was trying to figure out the time difference between Ann Arbor
and London, England, as well as the flight time simply by using
the known departure and arrival times both ways. The plane
left DTW at 7:25 p.m., local time, arriving Heathrow at 7:30 a.m.,
London time. Returning, it left London at 10:50 a.m., London time,
arriving Ann Arbor, 1:50 p.m., local time. Now, I would have
had to think this out long-hand, if you will. Whereas John
took pen to paper and had the answer in moments. There was
a bit of rounding that had to take place in consideration
of the jet stream but algebra worked in a very practical
application.
I wish I hadn't let my mathematics skills get so rusty.
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toking
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response 4 of 132:
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Jun 30 18:39 UTC 1997 |
When I cxan remember what to do, I kinda like algebra, my problem is
that I am usually just plain confused by it.
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remmers
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response 5 of 132:
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Jun 30 20:44 UTC 1997 |
Re #3: It was a simple problem of two linear equations in two
unknowns. I've taught that stuff often enough that I can do it
in my sleep, almost.
This one had the slight extra complication that it was a
Diophantine equation in one of the variables (i.e. the solution
had to be a whole number), since you don't have fractional
differences in time zones (except maybe in places like Nova
Scotia).
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i
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response 6 of 132:
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Jul 1 01:08 UTC 1997 |
i*pi
e + 1 = 0
(I want to attribute to Euler, but I keep getting the feeling that that's
off. Do you recall, John?)
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valerie
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response 7 of 132:
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Jul 1 05:31 UTC 1997 |
This response has been erased.
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remmers
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response 8 of 132:
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Jul 1 13:28 UTC 1997 |
Re #6: I believe it's called Euler's identity, but I could be
misremembering. The equation is interesting in that it connects
five fundamental mathematical constants: 0, 1, e, pi, i.
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nt
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response 9 of 132:
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Jul 1 15:25 UTC 1997 |
Anyone ever tried placing 8 queens(ministers or whatever you call) on a chess
board without their powers clashing each other? I guess its an Artificial
Intelligenc(AI) question.
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remmers
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response 10 of 132:
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Jul 1 15:36 UTC 1997 |
Not really AI. I (and many other people as well) have written
programs to generate and display all such configurations. It
turns out that there are 12 essentially distinct solutions.
(Where by "essentially distinct" I mean that one is not simply
a rotation or reflection of another.)
See Edsger Dijkstra's essay in the book _Structured Programming_
by Dijkstra, Hoare, and Dahl for an excellent discussion of this
problem and its algorithmic solution.
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i
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response 11 of 132:
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Jul 2 01:50 UTC 1997 |
Re: #8
Alas, no. Rudin (_Real & Complex_, 3rd ed., p. 2) uses the title "Euler's
it
identity" for the equation e = cos t + i sin t. (Meanwhile, Ahlfors
calls that formula "Euler's formula" in _Complex Analysis_, 3rd ed., p. 42.)
The source I first saw it in (I want to say Rudin, but can't find it in
either _Principles_ or _Real & Complex_) noted the property you did and
attributed the formula to one of the old masters.
But I now think you're right that it's Euler.
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mary
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response 12 of 132:
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Jul 2 12:36 UTC 1997 |
Re: #7 Carlos is taking a summer term at Cambridge.
Yep, it takes 7 hours to fly to London and 8 hours to
fly back, against the jet stream.
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remmers
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response 13 of 132:
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Jul 2 16:08 UTC 1997 |
Re #11: Gad, people are still reading Ahlfors' _Complex
Analysis_. That was the textbook when I took complex analysis
in college (the class was taught by Ahlfors as well).
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i
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response 14 of 132:
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Jul 2 17:09 UTC 1997 |
Re: #13
This was Ahlfors *3rd ed.* - (c)1979 - I took it in '86. You probably used
the original - (c)1953. (But the 2nd ed. was (c)1966, so you may have been
a guinea pig for an early draft of it or some such...)
Looking in the Columbia Encyclopedia (5th ed.) under Euler, I found the
formula directly attributed to him with the 5-big-numbers property noted.
But I don't think that's where I originally saw it. <sigh> Perhaps my
memory hails from some untracable & nearly forgotten lecture of math
classes past...
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