Pole mounted transformers appear to take a single phase tap from the
three phase transmission system and produce two phase power for
120/240 residential service.  Just wondering if this is true and if so
how it converts from one phase to two phase.  Thanks!

Hello Rob, I started to answer your question from personal knowledge.
I am glad that I didn't because I would have not found this
information. This starts at the generation source and continues to the
residential service. It does a much better job of explaining than I
could do and has many pictures of equipment you will see in your
neighborhood. Should you have any further questions after reading this
info I will be glad to try and answer. Here is the link:

http://science.howstuffworks.com/power.htm

Enjoy reading, Redhoss

Thanks redhoss.  That site does a good job of explaining the
transmission system from end to end.  This will be a good starting
point from which I can learn more about transformers and how they can
be configured convert from one phase to two phase (somehow offsetting
one phase by 180 degrees) apparently without any moving parts.  Other
solutions to this one phase to n phase problem I've seen involve
mechanical parts (motor/generator).  Thanks again.

I would like to try to describe how the transformer works if I may.

First, lets describe a 180 degree, 2-phase circuit.  It is one where
at every moment, the voltage on one leg is exactly the opposite sign
and value of the other leg.

Now to the transformer.  For your basic transformer, you connect one
winding to a powering voltage, and another winding to the output
voltage.  The two windings are connected by the varying magnetic field
caused by the alternating current.  It really makes no difference what
the input or output voltages are, and in fact ANY basic transformer
can accept the driving power from either side.

(This effect is why it is so important that if you have a home
generator, when you are using it during power outages you MUST not
have a connection to the power lines.  You could power the utility?s
lines and harm someone trying to fix the system).

But back to your question???

In the typical US power supply, the power company supplies power at
voltages from 1200 to 12,000 volts to the transformer.  Now it becomes
a little tricky.  The output across the full transformer is 240 volts!

If this is the case, how do you get 120 volts in your house?

The transformer has a THIRD connection, right in the middle.  This is
the wire that they attach to the ground.  The voltage from this tap to
EITHER END is 120 volts.  And, for the voltage to add up to 240 volts,
the voltage at one end is exactly the opposite sign of the other end. 
So you have two phases, 180 degrees apart.

Another way to think of this would be to consider a DC (battery)
circuit with two batteries connected together.  If we have two 1.5
volt batteries connected together, we get 3.0 volts out.  But if we
bring a wire from the middle and attach it to either end, the voltage
is 1.5 volts.  Clearly one of the ends will be positive and the other
negative.  In the case of AC current, the transformer substitutes for
the battery.

Factoid:  This distribution system, which is unique to the US, is left
over from the old Edison distribution system, where they in fact did
send DC to the houses (Neutral, +110 V, and -110 V).  When Tesla
convinced old man Westinghouse to develop AC current, they had to
supply the same voltages because light bulbs and the like were already
there.

I just looked more closely at your initial question about 3-phase
lines.  I would like to clarify that 3-phase circuits use THREE
transformers, typically one between each leg.

In residential service, you will typically have a three-phase main
running down a corridor.  Splitting off of this main circuit are the
lines that serve the residences.  Each branch leg consists of one of
the phases, so along that branch is only single phase service.  It is
at the stepdown transformers that you get the 120/240 voltages.

liner,
Many thanks for all the information you passed in in your comments.
Very helpful and interesting. Rob.

Just to add onto liner-ga's excellent comment, the third connection in
the middle is known as a Center-tap. This method can also be used to
split voltage in different ways, and more than one center tap can be
used to obtain more than one voltage.