The carpenter's ruler doesn't really match because the spacing is fixed or only artificially varied.

As a dancer, the amount of leg division we can safely use depends on how fast your body is moving. The faster it is moving, the more we can safely travel, but also the more we must rise to absorb our arrival without stumbling past the foot.

Suomynon. Forget the carpenters ruler then. It is very hard to find a model without drawing. Try this. Two CD cases open end to end. A pencil under the right side a match box under the left. The right side is as 3 and. The left side as much on the toes as is possible. That is roughly the type of curve which I believe I see on the tapes I am looking at. I wonder , have you ever seen officially the curve as a drawing from an instruction book. I never have. But to get back to the story. Lay the CD cases flat . Raise the two ends as suggested. The model is still the same length. but has a lift instead of just length. To get from one end to the other is still the same distance travelled, just part of it is down and then up and not straight across

Guys
forget these analogies, which are very difficult to perfect because human anatomy and body dynamics are so complicated. Just watch an intermediate, and then watch Andrew Sinkinson. The difference is clear, and it's obvious which is better

Yes, I understand that if you incline a segment of fixed length to put the higher end at two different rise heights, the distance over the floor will be reduced... pythogoras and all.

But that's not what we have in dancing. The distance of comfortable, workable leg division is not constant at all. It depends on the speed the body is moving at - if you are moving fast, it's easy to divide your legs far without getting stuck in a split. If you aren't moving much at the bottom of the swing, you can't divide your legs much without getting into an awkward position.

Similary, the height of rise you can achive depends more on your speed than on your foot strength. If you are going fast at the bottom of the swing (travelling far), you will have to rise high in order to absorb that energy - fail to do so and you will stumble past the foot closure or overturn your body to a distorted position. If you get higher than your foot strength can support, your fall will be abrupt rather than a smooth transition back into travel across the floor, but that's a problem for the next half, not the first half.