Hi again everybody. Now this will sound like a trivial question but I'd like some views on it please. We all hear about diagonal centre DC and DW and any diagrams in books or web-sites show the classic 8 directions along and backing LOD (which is unambiguous ) to wall, to centre, and backing these. Then we have directions which are 45 degrees (2/8 of a turn)to these - DW, DC, and backing these.
Now I've (a senior pre-champ international standard dancer) heard some teachers say things like "take that DW step towards the corner" .I understand that the 45 degrees are not meant to be at protractor precision, and of course in an actual competition, some compromise might be unavoidable. My difficulty with the "aim for the corner" concept is 3-fold:
1) that on a long, narrow floor, this could become almost LOD and the figures (e.g. outside change to PP) would dance differently. And I daren't ask how DC might be interpreted from halfway down the long side of the floor.
2) all technique books talk about "3/8 turn" between steps 1and 2 (for example) which strongly implies from backing LOD to 45 degrees DW (as an example).
3) why not just call it "TC" (to corner)?
Sorry to seem a little pedantic, but it's bothering me and causing some partnership problems (and thus important to clarify). You may have guessed that my background is in science. But please don't be upset by that - somebody has to do it.

Tech. books are essentially a guide, and also to standardise universal teaching methods.
One does not need a slide rule, to meet that minute precision you seem to need .

Adjustments whilst dancing, often require imprecise amounts of turn etc.

IF you were dancing for a medal test exam, or, being examined as a prof. then unwise to deviate from the " book"

I also have a science/engineering background so I may be biased, but I believe it is important to teach beginners the correct alignment of figures. It is part of the basic groundwork they need to be able to properly progress around the floor without impeding other dancers. Being pedantic, alignment refers to where you are facing and direction refers to where you are moving which is not always the same thing.

I spend quite a bit of time with my beginners working on alignments in the hope that a steady drip, drip, drip will evenually make its way into their memories. I always make the point that Centre does NOT mean the centre of the room, especially approaching a corner. It takes a while before they grasp the concept that, at a corner, DC is the same as DW on new LOD, but once they get it, it sticks. I also get them to consider the alignments as they apply to a non rectangular room as we have a few odd shaped village halls around here.

I can see that a teacher may suggest a pupil takes a step towards a corner, but only when close to the corner, not from halfway along the hall.

My real bugbear is when pupils come from other teachers who a) don't tell them the names of the figures, and b) teach them to "turn to face the piano"! I must stress that the local pukka dances schools do not teach their potential medallists/competitors that way.

You've lost me here On the bit were you say in paragraph two, " at a corner ".
Look at the top left where it says Re " Diagonal " . Stand in Reply and step towards the D. of " Diagonal " with the R.F. Now step across to the top of the D. with the L.F.and bring the feet together having now made 3/8's of a Turn. You are now facing strait down the floor against the L.O.D. It doe not matter if you are on side one or side two thats how you should complete the first three steps of a Natural Turn. Now turn the whole thing a 1/4 of a turn to the left The words Re Diagonal would be at the bottom left corner you are now on side two. And proceed with you Natural Turn. Which of course would be at the top starting side two
In the first Medal I took which was Bronze . In the Quickstep half way down side one we had to do a complete Natural Spin Turn to finish backing Diagonal to the Center with the L.O.D and continue down the floor to the corner with a Progressive Chasses and a Lock Steps .Still on side One.

Guest, kudos to your teacher for making you dance a full spin turn along the side of the room. Many take the easy option of putting the spin turn in a corner as less turn is required. The problem is that this goes into muscle memory as the default action for a spin turn which then tends to be underturned everywhere and it becomes awkward to make the full amount of turn when needed, let alone an overturned version.

I'm afraid your explanation confused me as I was not sure where the corner was, so let me elaborate on my earlier comment.
Consider a typical beginner routine of repeated natural turn, change step, reverse turn, change step (different teachers will have a favourite starting point in this cycle). When danced near the beginning of a long room, the natural turn (6 steps) will end facing DC which may also approximate to facing the physical centre of the room which is why we need to be clear about what we mean by DC. There is now plenty of room to continue the routine with change step and reverse etc.

Eventually we get close to the corner. The full natural turn still ends DC although we are now long past the physical centre but there is now no room to continue with the change step and reverse. The usual approach is to turn the corner by underturning the natural to end DC on the new LOD. This can lead to the pupil turning the corner too early, potentially impeding the couple behind them. We can minimise the early turn by ensuring the first step of the natural turn is taken into the physical corner rather than DW which is possibly what provoked Phil's original question.

Another approach is to recognise that the full natural turn to end DC (side 1) is also now facing DW on the new LOD (side 2), so we can continue straight into another natural turn having effectively turned the corner.

I refer to side 1 & 2 above only for clarity as I try to wean my beginners off routines as soon as I can and encourage them to decide for themselves which figures to dance next, based on where they are in the room, which way they are facing and which foot is free to move.

Why some people have a problem with which direction they should be facing is a lack of understanding of how to move from the end of side 1 ( the long side ) to the beginning of side 2. ( the short side ). Lets suppose that the Stage takes up the whole of side 2. At the end of side 1 after the first three steps of a Natural Turn we have our back square to the Stage. On our next three step we do not have the 3/8 of a turn because we need to finish facing diagonal to the center on step 6 of the Natural Turn .We do Not have our back square to the stage we should be facing diagonal to the center on side 2 ready for our Change Step which has no turn. and continue into our Reverse Turn.
There was a Lecture I attended . The Lecturer asked all the ladies only to take to the floor.She said I want you all to dance a Basic Waltz including a whisk and Chasse into a Natural Spin Turn to music. These ladies were competition dancers. It was a total mess. Without a partner they were lost. She proved her point that the ladies must know their steps better than they know the back of their hand. On came the men. No problem. She even had us doing the same steps with our eyes closed.