Super discussion about negative numbers on the BBC
 

On Fri, 10 Mar 2006 16:01:05 -0000, "Glenn Booth"
wrote:

Hi,

"Don Pearce" wrote in message
...
On 10 Mar 2006 07:23:35 -0800, " wrote:

What is this "i" thing? I know all about "j".

My exam board (way back when there were 'O' levels)
had some problems with this - people who took 'A'
levels in both maths (where it was 'i') and physics (where
it was 'j') often got them mixed up, and lost marks. There
was a minor rebellion, and in the end the mathematicians
lost. The square root of -1 was termed "j" from then on.

It's probably a moot point now - the last Physics A level
paper I looked at required no knowledge of either. a.c.
electricity is now the domain of Universities, it would seem.

Regards,

Glenn.



Addition an subtraction are for A level. Multiplication and division
are now optional post grad modules.

d

Pearce Consulting
http://www.pearce.uk.com

Super discussion about negative numbers on the BBC
 

Hi,

wrote in message
oups.com...
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?

No, but it is considered sensible to differentiate between electrical
current and the square root of -1. It's safer. People such as NASA
might really screw up if the units are not well defined. ;-)

Incidentally, the 6th Edition of the ASACOS Guidelines for preparation
of ANSI standards suggests the use of "j" is preferable to the use of
"i" to
represent sqrt(-1).

Regards,

Glenn.

Super discussion about negative numbers on the BBC
 

Hi,

"Don Pearce" wrote in message
...

Addition an subtraction are for A level. Multiplication and division
are now optional post grad modules.

With a calculator, naturally.

Regards,

Glenn.

Super discussion about negative numbers on the BBC
 

On Fri, 10 Mar 2006 16:37:41 -0000, "Glenn Booth"
wrote:

Hi,

"Don Pearce" wrote in message
...

Addition an subtraction are for A level. Multiplication and division
are now optional post grad modules.

With a calculator, naturally.


No other way is currently known - post doc research is underway.

d

Pearce Consulting
http://www.pearce.uk.com

Super discussion about negative numbers on the BBC
 

In article . com,
" wrote:

When it gets into " i ", things get really interesting.

I was once greatly surprised running into a lecture on i once, from
none-other than a purchasing agent for a box-maker... pre-computer. He
showed me his equations for getting the maximum use of a given width
and length of corrugated cardboard (roll) sheeting... each one included
i. This guy was a high-school drop-out, but he used 'imaginary numbers'
every day.

That seems far fetched, why would "equations for getting the maximum use
of a given width and length of corrugated cardboard (roll) sheeting..."
need to involve "i"?


Regards,

John Byrns


Surf my web pages at, http://users.rcn.com/jbyrns/

Super discussion about negative numbers on the BBC
 

In article .com,
" 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?

Math people and accountants call the square root of -1 "i", engineers and
other such riff raff call it "j".


Regards,

John Byrns


Surf my web pages at, http://users.rcn.com/jbyrns/

Super discussion about negative numbers on the BBC
 

"Don Pearce" wrote in message
...
On Fri, 10 Mar 2006 16:37:41 -0000, "Glenn Booth"
wrote:

Hi,

"Don Pearce" wrote in message
...

Addition an subtraction are for A level. Multiplication and division
are now optional post grad modules.

With a calculator, naturally.


No other way is currently known - post doc research is underway.

Meanwhile, the term "mental arithmetic", having fallen into disuse,
has been stolen by the medical industry and refers to a head count
in a psychiatric hospital.

What would today's 18 year olds make of a slide rule?

Glenn.

Super discussion about negative numbers on the BBC
 

Hi,

"John Byrns" wrote in message
...
In article .com,
" 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?

Math people and accountants call the square root of -1 "i", engineers
and
other such riff raff call it "j".

Accountants have no concept of "i" or "j" whatever. The have an entirely
different definition of "imaginary numbers". They put them on your bill,
labelled "hourly rate".

Regards,

Glenn.

Super discussion about negative numbers on the BBC
 

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.

This was a lecture mind... so here is the issue: feedstock is
expensive, and there are thousands of sizes of boxes. These were
corrugate boxes, with varying dimensions. This plant did not 'stock',
but made to order, to size. The knives were capable of cutting in
either horizontally or vertically and as finenly placed as necessary,
as well as partial cuts. Set-up and roll changing were the costliest
operations (as both involved machine shut-down), waste being the third
largest cost. Several sizes of boxes could be run at once. He
calculated how to run the orders to avoid waste and slivering, and to
minimize the number of different widths of feedstock required. He chose
to use the 'imaginary number i' in his process. It seemed to work as
their scrap-pile was rather tiny to his great pride and joy.

I pointed to Drexel U, as that is where I took my engineering courses.
In the process of those courses, we were given some practical field
applications of otherwise very dry concepts. This was one of them.

Peter Wieck
Wyncote, PA

Super discussion about negative numbers on the BBC
 

John Byrns wrote:
In article .com,
" 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?

Math people and accountants call the square root of -1 "i", engineers and
other such riff raff call it "j".

Regards,

John Byrns

Surf my web pages at, http://users.rcn.com/jbyrns/

I prefer to think of engineers as useful fellows; I know many both in
electronics and automobiles who are the salt of the earth and have
elegant minds besides. It's their inferiors, the "engineers" (and their
hangers-on) who are clearly trailer park trash, know it, resent it
loudly, and take out their frustration for being talentless on us.

There is a useful American engineering use of "j" in the higher math of
tubes to define all the relationships of phase shift. See for instance
the work of Julian L Bernstein, the last associate dean of the RCA
Institutes; he appears to have been in charge of the Day Schools, which
probably beside the US Navy gave the finest tube education ever
available. I have a complete mathematical transfer model in an Excel
spreadsheet, based on Mr Bernstein's work, that I will discuss when the
boards are calmer.

Such use of "j" as at right angles (plus or minus something in our
case) is particularly in line with the history of thought experiments
of the square root of minus one (and other imaginary numbers) being at
right angles to the continuum negative-positive.

I recommend this super radio discussion about the history of negative
numbers for the larger perspective; be quick though as it the BBC only
keeps it up for a week:
http://www.bbc.co.uk/radio/aod/netwo...l?radio4/inour...


I would have liked to have heard more about how modern electronics is
impossible without the square root of minus one, but I suppose in an
introductory programme all one is entitled to is a glancing reference.
Leaving the listener hungry for more is what defines a really good
programme!

Andre Jute