Re:World's steepest funicular railway opens in Switzerland
by danbruc on Saturday December 16, 2017 @10:40AM
(#15939971)
If you used the difference in height over the actual distance traveled instead of the horizontal distance, then 100 % would indeed be vertical. I.e. instead of using sin(a)/cos(a) you could just use sin(a) and for small angles the values are close but the later one approaches 1 while the former one diverges as you approach 90°. I would probably have picked the later one but the former one is probably somewhat easier to work with in practice, e.g. for construction work.
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Re:World's steepest funicular railway opens in Switzerland
by Sharlin on Saturday December 16, 2017 @03:59PM
(#15942064)
> sin(a)/cos(a)
Also called tan(a) ;)
Re:World's steepest funicular railway opens in Switzerland
by danbruc on Saturday December 16, 2017 @05:38PM
(#15942627)
The other variant was actually meant to read sin(a)/1 to highlight the ratio in both cases but I abandoned that halfway through because I thought it makes the hypotenuse look special while it really is not in the sin(a)/cos(a) variant where the more natural description would be tan(a)/1 but that kind of ruins the simple association with the side lengths of a right triangle. I had another idea how to formulate it that would not favor one of the variants but as far as I can tell the necessary distinction between the two catheti that exists in German does not exist in English and so I left it as it is.