Dressage; working on some lengthening and geometry

Today we kept working on how to communicate with each other about basic dressage movements.  John started us with some trot, and we went from 20 meter circles to 10 meter circles, moving around the arena.  In the second half of the lesson, I missed the geometry of the circle, and when I got it back (John had to say "turn further in" - I tried like 3 times and missed each time), the circle suddenly fixed itself.  John said it as it was easier for Duke to bend around my leg if we had the shape right, but I think I would describe it more as the circle flowed better.  My first circle, John said he wasn't sure what shape I was making, and it was something like an ice cream cone - it started as a half circle, but became some weird pointy thing on the other side.
In the circles, we worked on the same instructions from a few lessons ago, where John would tell me the appropriate aids (outside leg, inside leg at girth, bend to the inside, both legs, etc.) and then after a few corrections like that, I could feel Duke shift.  John called it - I think - that he had some bounce; I felt it like his shoulders balanced and he kind of lifted up into the shoulders instead of plowing down into them.
Those are good exercises because I feel it when it is correct, and I can compare the feeling of being correct to the "normal" feeling, but the hard part of this exercise is the sequence of aids to get to that correct feeling is pretty far beyond my grasp, and I need John's help so that I can just focus on giving the aids, instead of thinking about what aids he needs, and then feel how the correctness comes.
From there we did some canter work, on 10 meter circles, 12 meter circles, and 20 meter circles.  Duke felt fast, but decently balanced.
Then we did some lengthening, at both the trot and canter.  To set these up, John would have us work haunches in, then bend to the inside, then soften and let him straighten, then use both legs to ask him to go forward.
There were a few good lessons in here.  One is that I ask him to come back with upper thigh only - John said that is a dressage thing, but not so good for jumping, so to think about using my whole leg (and whole leg first) and THEN use my half halt if he doesn't listen to the leg.  (This was a bit of a theme, also especially with the 10 meter circles which was to ride with the outside hand, not the inside hand, but even more important, off my leg, not my hand.  This is SO hard and I'm pretty sure the same thing as the right turn from the jump lesson Thursday that was so hard to do (mentally).)
Also, in this exercise, John asked me where he felt, and I said "he's riding around with his haunches pointed towards you" (on the right lead canter) so John said "point him more towards me" so I did - which felt wild and crazy, like we were half passing around John on the circle, and then John had me bend Duke to the inside then look back, and at that point, he was basically in the correct arc around the circle.  What felt like wild and crazy in the middle of the circle like a clock hand wasn't even on the correct bend yet.  So John said to test that at home - don't just ride and feel that it's right, but move him a little to the inside or a little to the outside with his haunches, and then see how that feels, so I can learn to adjust my feel for what the proper bend is.
The other really good lesson in this was the geometry of the line across the diagonal.  I asked John to show me on the ground afterwards - the corner of the arena makes a triangle - you have to cut the triangle in half, so you angle from the long edge to half way on the first short edge, bend around the corner, touch again at half way on the second short edge, then leave the triangle just before the letter so that you are moving straight by the first quarter line.  John said the movement should be at its best from quarter line to quarter line.  Then, you do the same thing in reverse when you're touching on the other side, but this way is a little easier because you leg yield just a bit to the outside (to hit the rail before the letter), bend around the inside, and use the far wall to line up the next turn.  It is a few steps that are straighter than I would have described it, both before and after the turn onto the diagonal.  This was one of those John explanations that was a bit of a eureka moment (kind of like not riding with only my thighs) which I wouldn't necessarily think to ask about, but he has such a great explanation of the why and how that I feel like I can apply it when I get home.
Our final exercise was working on the stretchy trot circle.  I was throwing away the reins, and John said instead to keep the contact.  We had to try this several times because I would revert to throwing them away as soon as Duke made any movement towards stretching his neck down.
Similarly, he said that a horse with a good topline creates less wear and tear on his own legs, and that a horse can run a few shows on adrenalin, but then he needs his own muscle to keep from breaking down.  He said that's why it's important to work them regularly - not just 2-3 days a week - and why to avoid getting in a rut and thinking things are going ok, but to keep striving to make him work better.
Duke was soft, sweet, and willing, and it was a fun lesson.  Mom was here watching.  I think it is our last day of "summer" without rain.