When the teacher (had) arrived, they stopped talking.

New2grammar

It's weird that the first pair is not acceptable whereas the second pair is fine.

my other book = ?the other book of mine

my other books  = other books of mine

The first is definite; the second indefinite.  Ant has the basic idea.  See his post.

Let me repeat what I wrote.  Note that your second equality is not something I claimed as an equality. 

my other book =  *my the other book = ?the other book of mine >>> Singluar Definite.

*my another book = *my an other book = another book of mine >>> Singular Indefinite.

my other books = *my the other books = ?the other books of mine  >>> Plural Definite.

*my some other books = some other books of mine = other books of mine >>> Plural Indefinite.

So the typical forms are:

Definite -- Singular / Plural:  my other book; my other books  (The reference is to a particular book or set of books.)

Indefinite -- Singular / Plural:  another book of mine; other books of mine (The reference is to an unspecified book or set of books.) 

 CJ 

It can _also_ be indefinite. Here's a bad yet working example:

"These are my books. The books on the shelf are my other books" -- it is equal to "the books on the shelf are mine _too_". "Being mine" is a _descriptive_ property, and so is "my other books".

New2grammar

The concept of definite and indefinite is killing me. I'm really lost.

Then how come you use articles correctly most of the time? ;)

"The concept of definite/indefinite" is sure definite because it has been identified by specifying the topic.

"New2Grammar has proposed _a_ revolutionary concept of definite/indefinie". Here the "concept" is indefinite, as in "I have bought _a_ new car" or "I have invented _a_ new type of steam engine". Only a description of the concept is specified, which in no way makes it definite because there may exist other concepts of definite/indefinite, as well as other types of steam engines. Hence the term "descriptive".

"The concept of the steam engine is killing me" — here is implied the general principle of the operation of the steam engine. Of course, the principle is unique and therefore the concept of it is definite. By adding "of the steam engine" we uniquely identify what we speak of... We have "restricted" a multitude of concepts to only one element (the concept of the steam engine), whence the term "restrictive".

Anton

P.S.: Sorry is this only increased your confusion...

New2grammar

My problem with definite and indefinite articles is less than with definite/indefinite pronouns. I think I'm starting to see other and another as indefinite articles, my as definite article and mine as indefinite article.

There's no such corellation, except for "another", which is in fact "an" + "other", so dont' need to think of these words as capable of rendering a noun definite or indefinite on their own.

"Take by my hand" — how can it be definite when we don't no which hand is in question?

"Your English is better than mine" — how can it be indefinite when it's a comparison of the English skills of two people?

... And so on.

New2grammar

I have to say referring to other, another, my, mine as definite/indefinite is something new to me.

We didn't refer to this words alone. It were noun phrases buit therewith that we called definite or indefinite. And since nouns can be (in)definte, that's all right.

"Is this the reason you call it indefinite?"
Yes.

"Does the person I speak to know which books I'm talking about? No. Do I know? Yes."

I don't think this is the question you have to ask. My shelter is a castle. Do I know whereof I speak? Yes. Do I use the indefite article? Yes!

To decide whether a thing is definite I suggest that you ask a question like: do I describe or specify this thing? In the first case you'll have to use the indefinte article, and the definite one in the second case.

"Anton, By the way what's all those underscores? They make your posts difficult to read, IMO."

I just wanted to emphasize words that way... and it didn't work. I would use a bold font if this new forum's editor was't so slow and funny and unstable in Opera...

EDIT: Sorry for the typo above: the example should have been: "Take me by my hand" (as is sung in Diamonds' "The Stroll"...