Elbeinlaw

Thank you all for your input. You've answered my question, given me more jargon to foist on unsuspecting persons, and made some interesting points about ... stuff. In pondering this--can't ride today, so have to think--I'm fascinated by how 45% became 100%. On the one hand, it's obvious: if you're looking at Euclidian geometry, then a rise/run where rise=run just naturally seems like it would be x/x, or 1, or 100%.

But if you're doing anything practical in the real (nonEuclidian) world, it doesn't make any sense. If you're roofing, a 45 degree/100% slope isn't the highest a roof can effectively be: that's going to be something like 60 degrees (thinking of those snow roofs in Switzerland). And how would you describe those roofs, even outside of the problem of Hochdeutsch? They'd have to be something like 140%, which makes no sense, because they're steep but not outside the bounds of reality. In an alternate universe, it would seem to me like if you started with practical reality, where percentages were representations of the proportion of a "whole," whatever that is, you'd say that a 100% slope would be 90 degrees--it's the highest a slope can go before it's no longer a slope at all. (And that would make sense in roofing, because a 60% slope would then be something like (just guessing here) 75 degrees.) And a 0% slope would be 0 degrees. That seems to me to be imminently more intuitively sensible.

But for some reason, our forebears decided that practicalities weren't the focus of this datum, it was the arithmatic fraction substituting for the rise/run formulation.

So I wonder why our intellectually giant forebears choose this formulation/