In article .com,
wrote:
why would "equations for getting the maximum use of a given width and
length of corrugated cardboard (roll) sheeting..." need to involve "i"?

Well, one is subtracting from a given area, and the numbers subtracted
are therefore 'negative'. As the numbers are _areas_, then we have a
negative number that often needs to have its square root taken.
Mathematically, this does not work. as -1 x -1 = 1. So. " i " is
introduced to make the calculations work.

Interesting application. Areas and lengths have different dimensions
(dimensional analysis), so you aren't talking about dimensionless values.
The width and length are also, presumably, orthogonal. I'm also not clear
what would involve you in such a calculation of an area of -1 x -1 that was
on the physical sheet...

Is there an advantage over just essentially representing the 'area' as a
vector result perpendicular to the surface and giving it a size of width x
length? (in effect, using a cross-product vector approach.)

Slainte,

Jim

--
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Audio Misc http://www.st-and.demon.co.uk/AudioMisc/index.html
Armstrong Audio http://www.st-and.demon.co.uk/Audio/armstrong.html
Barbirolli Soc. http://www.st-and.demon.co.uk/JBSoc/JBSoc.html

In article , Stewart Pinkerton
wrote:
On 10 Mar 2006 07:54:43 -0800, " wrote:

http://mathforum.org/library/drmath/view/58251.html

Wrong side of the pond thing, you Brits? Or is it that you need to be
ahead of us Colonials... and go all the way to j?

Nope, it depends on whether you're a mathematician or an EE.

Just to make things more confusing, you can also end up using 'j' for
current density as well as 'i' for current... :-)

The problem is that we don't have enough letters...

Slainte,

Jim

--
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Audio Misc http://www.st-and.demon.co.uk/AudioMisc/index.html
Armstrong Audio http://www.st-and.demon.co.uk/Audio/armstrong.html
Barbirolli Soc. http://www.st-and.demon.co.uk/JBSoc/JBSoc.html

"flipper" wrote in message
...
Which, btw, is exactly the same situation as those who don't think i
exists.

It doesn't. But then, "numbers" don't exist in any meaningful sense. You can
have, say, five apples, but you can't just have five. It's just an idea.

"flipper" wrote in message
...
On Mon, 13 Mar 2006 00:12:55 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
. ..
Which, btw, is exactly the same situation as those who don't think i
exists.

It doesn't. But then, "numbers" don't exist in any meaningful sense.

If you go back and look at the context that's been removed you'll see
that I said it's as 'real' as the 'real' numbers are. The point is
it's 'reality' is conceptually no different regardless of what common
conceptualization, or lack thereof, you now wish to obscure the
matter with.

I wasn't disputing your argument! Yes, i is as real as any other number.

You can
have, say, five apples, but you can't just have five. It's just an idea.

Ideas 'exist'. They must since you apparently have one

I have an idea of, say, a machine that turns lard into banknotes. That
doesn't mean it exists. Equally, I have an idea of the number "five". The
idea exists, the number doesn't necessarily exist.

in article , Rich Wilson at
wrote on 3/12/06 9:14 PM:


"flipper" wrote in message
...
On Mon, 13 Mar 2006 00:12:55 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
...
Which, btw, is exactly the same situation as those who don't think i
exists.

It doesn't. But then, "numbers" don't exist in any meaningful sense.

If you go back and look at the context that's been removed you'll see
that I said it's as 'real' as the 'real' numbers are. The point is
it's 'reality' is conceptually no different regardless of what common
conceptualization, or lack thereof, you now wish to obscure the
matter with.

I wasn't disputing your argument! Yes, i is as real as any other number.

You can
have, say, five apples, but you can't just have five. It's just an idea.

Ideas 'exist'. They must since you apparently have one

I have an idea of, say, a machine that turns lard into banknotes. That
doesn't mean it exists. Equally, I have an idea of the number "five". The
idea exists, the number doesn't necessarily exist.


Yes, but the idea of numbers is a priori; the lard converter is not.

Jon

"Eiron" wrote in message
...
wrote:

OK... how would you come up with the square root of -4? Practical
application, you are starting with so many square feet of feedstock,
you are making 22 boxes each requiring two 4 square foot faces, two
feet on a side and other sides may vary within certain parameters, and
12 boxes each requiring two 1 square foot faces. But the dimensions of
the first box must be calculated to have the correct volume as a
function of dimensions and not preclude the similar values for the
second box. So, you are SUBTRACTING dimensions as square roots of total
areas required for square cuts. As sq.rt. -4 does not calculate, but
sq.rt. 4 x i does... that is how it comes in. Keep in mind that one
*could* reverse the signs in one's head the reality is that all the
areas calculated are *real*, but as there are many sign-changes in the
calculation apart from negative number roots, the chance of error
increases greatly. The elegant part of all this is that the " i " drops
out at the end of the calculations, but it allows the rule of 8 (8
basic axioms of 'real' numbers) to apply during.

Sorry, still don't get it. Perhaps a simple example might help.

is it because i is black?

"Jon Yaeger" wrote in message
...
in article , Rich Wilson at
wrote on 3/12/06 9:14 PM:


"flipper" wrote in message
...
On Mon, 13 Mar 2006 00:12:55 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
...
Which, btw, is exactly the same situation as those who don't think i
exists.

It doesn't. But then, "numbers" don't exist in any meaningful sense.

If you go back and look at the context that's been removed you'll see
that I said it's as 'real' as the 'real' numbers are. The point is
it's 'reality' is conceptually no different regardless of what common
conceptualization, or lack thereof, you now wish to obscure the
matter with.

I wasn't disputing your argument! Yes, i is as real as any other number.

You can
have, say, five apples, but you can't just have five. It's just an
idea.

Ideas 'exist'. They must since you apparently have one

I have an idea of, say, a machine that turns lard into banknotes. That
doesn't mean it exists. Equally, I have an idea of the number "five". The
idea exists, the number doesn't necessarily exist.


Yes, but the idea of numbers is a priori; the lard converter is not.

I'm not familiar with the latin phrase and the Wikipedia definition ain't
helping... care to explain your argument in English?

in article , Rich Wilson at
wrote on 3/12/06 9:23 PM:


"Jon Yaeger" wrote in message
...
in article , Rich Wilson at
wrote on 3/12/06 9:14 PM:


"flipper" wrote in message
...
On Mon, 13 Mar 2006 00:12:55 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
...
Which, btw, is exactly the same situation as those who don't think i
exists.

It doesn't. But then, "numbers" don't exist in any meaningful sense.

If you go back and look at the context that's been removed you'll see
that I said it's as 'real' as the 'real' numbers are. The point is
it's 'reality' is conceptually no different regardless of what common
conceptualization, or lack thereof, you now wish to obscure the
matter with.

I wasn't disputing your argument! Yes, i is as real as any other number.

You can
have, say, five apples, but you can't just have five. It's just an
idea.

Ideas 'exist'. They must since you apparently have one

I have an idea of, say, a machine that turns lard into banknotes. That
doesn't mean it exists. Equally, I have an idea of the number "five". The
idea exists, the number doesn't necessarily exist.


Yes, but the idea of numbers is a priori; the lard converter is not.

I'm not familiar with the latin phrase and the Wikipedia definition ain't
helping... care to explain your argument in English?

This link should do it:

http://www.importanceofphilosophy.co...l_APriori.html

Jon

"Jon Yaeger" wrote in message
...
in article , Rich Wilson at
wrote on 3/12/06 9:23 PM:


"Jon Yaeger" wrote in message
...
in article , Rich Wilson at
wrote on 3/12/06 9:14 PM:


"flipper" wrote in message
...
On Mon, 13 Mar 2006 00:12:55 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
...
Which, btw, is exactly the same situation as those who don't think i
exists.

It doesn't. But then, "numbers" don't exist in any meaningful sense.

If you go back and look at the context that's been removed you'll see
that I said it's as 'real' as the 'real' numbers are. The point is
it's 'reality' is conceptually no different regardless of what common
conceptualization, or lack thereof, you now wish to obscure the
matter with.

I wasn't disputing your argument! Yes, i is as real as any other
number.

You can
have, say, five apples, but you can't just have five. It's just an
idea.

Ideas 'exist'. They must since you apparently have one

I have an idea of, say, a machine that turns lard into banknotes. That
doesn't mean it exists. Equally, I have an idea of the number "five".
The
idea exists, the number doesn't necessarily exist.


Yes, but the idea of numbers is a priori; the lard converter is not.

I'm not familiar with the latin phrase and the Wikipedia definition ain't
helping... care to explain your argument in English?

This link should do it:

http://www.importanceofphilosophy.co...l_APriori.html

OK... so "a priori" knowledge is knowledge that has no reference to
reality... i.e. knowledge about things that don't exist.

in article , Rich Wilson at
wrote on 3/12/06 9:50 PM:


"Jon Yaeger" wrote in message
...
in article , Rich Wilson at
wrote on 3/12/06 9:23 PM:


"Jon Yaeger" wrote in message
...
in article , Rich Wilson at
wrote on 3/12/06 9:14 PM:


"flipper" wrote in message
...
On Mon, 13 Mar 2006 00:12:55 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
...
Which, btw, is exactly the same situation as those who don't think i
exists.

It doesn't. But then, "numbers" don't exist in any meaningful sense.

If you go back and look at the context that's been removed you'll see
that I said it's as 'real' as the 'real' numbers are. The point is
it's 'reality' is conceptually no different regardless of what common
conceptualization, or lack thereof, you now wish to obscure the
matter with.

I wasn't disputing your argument! Yes, i is as real as any other
number.

You can
have, say, five apples, but you can't just have five. It's just an
idea.

Ideas 'exist'. They must since you apparently have one

I have an idea of, say, a machine that turns lard into banknotes. That
doesn't mean it exists. Equally, I have an idea of the number "five".
The
idea exists, the number doesn't necessarily exist.


Yes, but the idea of numbers is a priori; the lard converter is not.

I'm not familiar with the latin phrase and the Wikipedia definition ain't
helping... care to explain your argument in English?

This link should do it:

http://www.importanceofphilosophy.co...l_APriori.html

OK... so "a priori" knowledge is knowledge that has no reference to
reality... i.e. knowledge about things that don't exist.

My understanding of a priori as it applies to math is that we have a concept
of numbers that seem to be beyond argument, but on closer inspection, is
actually based upon faith. We can't really "prove" the number 5, for
example, but we operate on the assumption that "5" is true. As an article
of faith, perhaps it is "more empirical" (if such a non-sequitur can be used
to describe something that is based upon "faith") than, say, the imaginary
concept of a lard converter. We don't really depend upon concept of a lard
converter for understanding other concepts as we do numbers.

It is a bit of an abstract and subtle distinction.

Perhaps a philosopher or professional parser such as Mr. Byrnes can correct
me or shed more light on the distinction, if indeed there is one?

;-)

Jon