What is the true angle of a cheese slope? What is the true angle of a cheese slope?



Bricklink lists it as "Slope 30 1 x 1 x 2/3" while LDraw and Peeron list it as "Slope Brick 31 1 x 1 x 2/3". Why do these sources disagree, and what is the real angle?
I guess I could send the question to math.se, but I think we can figure that one out ourselves; it's just a bit of trigonometry after all, right?

Let's see:
- The large side is 20 ldu (standard brick width).
- The small side is 16 ldu (2 plates) - 4 ldu (half a plate), that is 12 ldu (half the height of a brick).

So the angle is tan-1(12/20), which is approximately 30,96°. So it's closer to 31, but gives 30 if truncated down.

As for why the sources differ, I couldn't find documentation on the naming process they both use, but I can easily imagine that someone measuring the angle with a simple protractor could be mistaken by a degree. Another possible explanation would be that the people behind the BrickLink naming chose to round the angle down to simplify things, as a 30° angle feels more natural than a 31° one; while LDraw people may be more used to precise measurements and felt that 31° was closer to the truth. Again, this is all pure speculation, I didn't find naming conventions or guidelines for either.