wrote


i remember that a very good book that helped me understand was


Pocket Ref by Thomas Glover. Lots of useful info in there if you know how
to digest it.

Steve

On Jun 15, 7:21 am, wrote:
how do you imagine imaginary
numbers - positive and negative phasors and vectors - +j -j - I KNOW
they mean something, but its just chicken tracks to me.

Andrew VK3BFA.

And if I have stuffed up the cutting and quoting bit above and got the
names wrong - sorry, no offense meant.


Don't worry about it. Just accept it.

Don't let the name imaginary bother you. Use the term complex
instead.

With DC in the steady state, the power is Voltage times Current.

With AC the power is the Voltage times the Current that is in phase
with the voltage. P = E I cos theta. If theta is 45 degrees then Cos
theta is 1/ 2^.5

Now if you think of a 45, 45, 90 triangle , then the current that is
in phase can be represented by one of the legs of the triangle. The
total current is represented by the hypotenuse. So what is the other
leg of the triangle? It is the current that is 90 degrees out of
phase with the voltage. It is orthogonal to the in phase current.
That is you can change the value without affecting the other leg
( you do affect the total current, but not the in phase current )

Now if you can see that, then all that stuff about complex numbers is
just a way to do the calculations instead of drawing triangles. Got
two vectors you want to add. Just draw one and then draw the second
with the beginning of it at the end of the first.
Or you can break both vectors into two parts that are orthogonal and
add the " real " parts and then add the "imaginary" parts.And you end
up with the same total length and direction, but you did not have to
draw the two vectors.

I hope that is clear to you. It is to me.

Dan
AD7PI

wrote in message
...
On Jun 15, 7:21 am, wrote:
how do you imagine imaginary
numbers - positive and negative phasors and vectors - +j -j - I KNOW
they mean something, but its just chicken tracks to me.

Andrew VK3BFA.

And if I have stuffed up the cutting and quoting bit above and got the
names wrong - sorry, no offense meant.


Don't worry about it. Just accept it.

Don't let the name imaginary bother you. Use the term complex
instead.

With DC in the steady state, the power is Voltage times Current.

With AC the power is the Voltage times the Current that is in phase
with the voltage. P = E I cos theta. If theta is 45 degrees then Cos
theta is 1/ 2^.5

Now if you think of a 45, 45, 90 triangle , then the current that is
in phase can be represented by one of the legs of the triangle. The
total current is represented by the hypotenuse. So what is the other
leg of the triangle? It is the current that is 90 degrees out of
phase with the voltage. It is orthogonal to the in phase current.
That is you can change the value without affecting the other leg
( you do affect the total current, but not the in phase current )

Now if you can see that, then all that stuff about complex numbers is
just a way to do the calculations instead of drawing triangles. Got
two vectors you want to add. Just draw one and then draw the second
with the beginning of it at the end of the first.
Or you can break both vectors into two parts that are orthogonal and
add the " real " parts and then add the "imaginary" parts.And you end
up with the same total length and direction, but you did not have to
draw the two vectors.

I hope that is clear to you. It is to me.

Dan
AD7PI


Thanks for proving my original point far better than I ever could. What is
clear to you is completely incomprehensible to most of the rest of us. That
is the way it works. Six foot eight inch basketball players have no trouble
dunking either. They wouldn't be able to understand why you can't except
that you are lacking something they have. That's the way it is with math.
Those who can comprehend it have something the rest of us don't have. But I
learned long ago that the math guys were often very, very bad at all kinds
of other things and different ways of thinking. Only a very few lucky people
can comprehend higher math and do everything else well too. You don't want
to compete with those guys unless you happen to be one of them. It's like
the time I was watching a lecture on cable TV and it was an advanced
computer science class. I'm no dummy but I couldn't understand a thing the
teacher was saying. It was so far over my head it was a joke. But for the
people that can comprehend it that were in the class it made perfect sense.
It's a case of one having to know one's limitations, I guess.


Hawke

"Ignoramus20633" wrote in message
...
On 2008-06-14, cavelamb himself wrote:
Steve Austin wrote:
Bob La Londe wrote:

"Ignoramus27711" wrote in
message ...

Do you remember

A^2 + B^2 = C^2

Pick any two and calculate the third. I used to use it all the time
in my dad's hardware store to calculate how much guy wire somebody
needed to support an antenna tower. Same principle, different
application.




That's not algebra. That's geometry.


A^2 +B^2 -C^2 = 0

looks like algebra


I thought it was Greek.

Hawke

"Hawke" wrote in message
news:NWm5k.1360$_n.847@fe95...

wrote in message
...
On Jun 15, 7:21 am, wrote:
how do you imagine imaginary
numbers - positive and negative phasors and vectors - +j -j - I KNOW
they mean something, but its just chicken tracks to me.

Andrew VK3BFA.

And if I have stuffed up the cutting and quoting bit above and got the
names wrong - sorry, no offense meant.


Don't worry about it. Just accept it.

Don't let the name imaginary bother you. Use the term complex
instead.

With DC in the steady state, the power is Voltage times Current.

With AC the power is the Voltage times the Current that is in phase
with the voltage. P = E I cos theta. If theta is 45 degrees then Cos
theta is 1/ 2^.5

Now if you think of a 45, 45, 90 triangle , then the current that is
in phase can be represented by one of the legs of the triangle. The
total current is represented by the hypotenuse. So what is the other
leg of the triangle? It is the current that is 90 degrees out of
phase with the voltage. It is orthogonal to the in phase current.
That is you can change the value without affecting the other leg
( you do affect the total current, but not the in phase current )

Now if you can see that, then all that stuff about complex numbers is
just a way to do the calculations instead of drawing triangles. Got
two vectors you want to add. Just draw one and then draw the second
with the beginning of it at the end of the first.
Or you can break both vectors into two parts that are orthogonal and
add the " real " parts and then add the "imaginary" parts.And you end
up with the same total length and direction, but you did not have to
draw the two vectors.

I hope that is clear to you. It is to me.

Dan
AD7PI


Thanks for proving my original point far better than I ever could. What is
clear to you is completely incomprehensible to most of the rest of us.
That
is the way it works. Six foot eight inch basketball players have no
trouble
dunking either. They wouldn't be able to understand why you can't except
that you are lacking something they have. That's the way it is with math.
Those who can comprehend it have something the rest of us don't have.

What most of them had was better teachers. My Russian neighbors are math
whizzes. They had great teachers.

But I
learned long ago that the math guys were often very, very bad at all kinds
of other things and different ways of thinking. Only a very few lucky
people
can comprehend higher math and do everything else well too. You don't want
to compete with those guys unless you happen to be one of them. It's like
the time I was watching a lecture on cable TV and it was an advanced
computer science class. I'm no dummy but I couldn't understand a thing the
teacher was saying. It was so far over my head it was a joke. But for the
people that can comprehend it that were in the class it made perfect
sense.
It's a case of one having to know one's limitations, I guess.

I'd give it 90% teachers, 10% personal limitations. And 50% individual
interest. g

--
Ed Huntress

On Sun, 15 Jun 2008 22:35:39 -0700, "Hawke"
wrote:


"Ignoramus20633" wrote in message
m...
On 2008-06-14, cavelamb himself wrote:
Steve Austin wrote:
Bob La Londe wrote:

"Ignoramus27711" wrote in
message ...

Do you remember

A^2 + B^2 = C^2

Pick any two and calculate the third. I used to use it all the time
in my dad's hardware store to calculate how much guy wire somebody
needed to support an antenna tower. Same principle, different
application.




That's not algebra. That's geometry.


A^2 +B^2 -C^2 = 0

looks like algebra


I thought it was Greek.

Hawke


A-rab. From al-jabr.

Best regards,
Spehro Pefhany
--
"it's the network..." "The Journey is the reward"
Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog Info for designers: http://www.speff.com

On Jun 16, 3:21*pm, Spehro Pefhany
wrote:
I thought it was Greek.
Hawke
A-rab. From al-jabr.
Spehro Pefhany

The name is from Persia, the concepts are Greek + Babylonian + Indian
+ Chinese.

On Jun 15, 10:34 pm, "Hawke" wrote:

That's the way it is with math.
Those who can comprehend it have something the rest of us don't have. But I
learned long ago that the math guys were often very, very bad at all kinds
of other things and different ways of thinking. Only a very few lucky people
can comprehend higher math and do everything else well too. You don't want
to compete with those guys unless you happen to be one of them. It's like
the time I was watching a lecture on cable TV and it was an advanced
computer science class. I'm no dummy but I couldn't understand a thing the
teacher was saying. It was so far over my head it was a joke. But for the
people that can comprehend it that were in the class it made perfect sense.
It's a case of one having to know one's limitations, I guess.

Hawke

There are obviously differences in how quickly people learn, but I
don''t think that only a few can comprehend higher math. I think the
problem is that most people do not go back and refresh their
comprehension of the math that they took a few years back. If you do
not have a solid understanding of the more basic stuff, you don't
have a chance to understand the next level.

I know a fair number of people that took calculus, passed the course,
and promptly started to forget it. Not too many that go back a couple
of years later and refresh their knowledge.

Dan

On Mon, 16 Jun 2008 16:32:50 -0700 (PDT), the renowned Jim Wilkins
wrote:

On Jun 16, 3:21*pm, Spehro Pefhany
wrote:
I thought it was Greek.
Hawke
A-rab. From al-jabr.
Spehro Pefhany

The name is from Persia, the concepts are Greek + Babylonian + Indian
+ Chinese.

The English name is from Arabic, not Farsi, via Latin:

http://www.bartleby.com/61/52/A0195200.html "..from Arabic"

http://www.merriam-webster.com/dictionary/algebra "from Arabic
al-jabr, literally, the reduction"

http://dictionary.reference.com/browse/algebra " Ar"

OED also agrees.

Is it this that you're referring to?
http://en.wikipedia.org/wiki/Muhamma...4%81rizm%C4%AB



Best regards,
Spehro Pefhany
--
"it's the network..." "The Journey is the reward"
Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog Info for designers: http://www.speff.com

On Jun 17, 1:21 am, " wrote:
...
I know a fair number of people that took calculus, passed the course,
and promptly started to forget it. Not too many that go back a couple
of years later and refresh their knowledge.

Dan

I did, first time in the 60's, second in the 90's. The second time I
understood it MUCH better and maintained a 4.0, probably because it
was taught as a practical tool instead of an art form, and I wasn't so
distracted.

The main distraction was a sweet young lady whose father taught
Physics. He had quit Chemistry because he couldn't visualize the
structures of molecules, which was easy for me, but I got lost when
math became non-intuitive.

Talking to another physics professor I found he couldn't tell which
elements of a simple triangular sign support were in tension or
compression without solving for the signs of the vectors.

To tie this back into recreational metalworking, the two old textbooks
that help me the most with beam and column calculations are Harry
Parker's "Simplified Design of Structural Steel" and "Simplified
Design of Structural Timber". The "AISC Manual of Steel Construction"
is good but doesn't include small sizes. Parker shows how to calculate
centroids, sectional modulus, radius of gyration etc for rectangular
shapes using only simple algebra and says to use tables for the
complicated shapes.

Parker's practical approach: "Minute accuracy in computing the
deflection of beams is seldom necessary. The designer only wishes to
know whether the deflection is excessive."

"E, the modulus of elasticity of structural steel, is 29,000,000 psi.
Frequently, however, designers use 30,000,000 psi to simplify the
computations."

Me too. My quickie mental Metric conversions are
1 Meter = 1 yard + 10%
1 Kilogram = 2 pounds + 10%
1 Newton = 1/4 pound - 10%
1 Liter = 1 quart + 5%, figured as 10% / 2
1 mm = 0.040"
2.5 Microns = one tick on an indicator that reads to 0.0001"

Jim Wilkins

On Jun 17, 7:52*am, Spehro Pefhany
wrote:
On Mon, 16 Jun 2008 16:32:50 -0700 (PDT), the renowned Jim Wilkins scrove
...
The name is from Persia, the concepts are Greek + Babylonian + Indian
+ Chinese.

The English name is from Arabic, not Farsi, via Latin:

Is it this that you're referring to?http://en.wikipedia.org/wiki/Muhamma...1_al-Khw%C4%81...

Spehro Pefhany

Yep, from Persia but he apparently wrote the original in Arabic, just
as the West usually wrote in Latin at that time.

Like so much of ancient knowledge it was a synthesis of contributions
from all over the civilized world that ran from the Mediterranean to
China and was connected by coastal trade and the Silk Route.

It's not lost on me that my Northern European ancestors dressed in
animal skins and lived in mud huts until the Romans dragged us into
that civilization, about the time of Christ.

Jim Wilkins

wrote:

There are obviously differences in how quickly people learn, but I
don''t think that only a few can comprehend higher math. I think the
problem is that most people do not go back and refresh their
comprehension of the math that they took a few years back. If you do
not have a solid understanding of the more basic stuff, you don't
have a chance to understand the next level.

I know a fair number of people that took calculus, passed the course,
and promptly started to forget it. Not too many that go back a couple
of years later and refresh their knowledge.

Dan


I will agree with that. I can probably do the very basic differential
and simple integrals but the more complex ones, I'd have to look up.
I took those courses 54 55 and never had a lot of use for either after
the first several years. But the trig I've used continuously so it's
right there.
...lew...