Before ever starting to analyze your numbers and their implications, some things should be, I think, stated in a clearer way; describing thoroughly as possible what each thing represents is a basic prior step before attempting to reach any conclusion.
I assume the first circle in which A,B and C are is the \"first level\" ground.
Question is, what is the circumference which contains D, E and F representing?
At first, I thought you were representing, with the first, the \"outern\" circumference, and with the last the \"inner\" circumference, but I discarded that since, in that case, both circumferences should be on the same plane.
Then, I searched for an alternative explanation of why that other circumference may represent. So I asked myself, perhaps he\'s trying to represent the second level? (that is the one below the first, where Hydlaa and Oja are, and hasn\'t still been implemented in game) I thought that was more accordingly to the painting given as help.
Then I went to check the book.
The diameter of first level is, it says, 50km. That then confirms that the circle containing ABC is indeed the first level since AB=r=25km
Then I said, ok, let\'s try to confirm that second circle represents the second level.
The distance between 1st and 2nd levels, as the book says is 5km. That would mean that BE=H3 should be 5km. On your notes is 4,14km. Well, perhaps that circle indeed represented the second level...
The book also claims the second level to have a diameter of 40km. That means that section DE should be, then, 20km. According to your notes, section DE=r2 has 16,23km. An error too big as to consider that indeed, that was the second level.
So then, I came back to my first hypothesis. That second circle you drew must represent then, the inner circumference (although I maintain that it _has_ to be on the same plane as the outern one) so I went to check the book again. Inner circumference with a perimeter of 102 km. Ah! Amazingly that leads to a radius of 16,23km exactly r2.
So that then leads to a conclusion that helps me to finally see what you meant: The surface were the things are placed in the first level (and then the other levels too) isn\'t flat, but all of it following a curve (banking I think is the word) like the ones you can see at Indianapolis circuit.
Then again, I\'ll have to differ with that vision, since, as you also state at your conclusion, you got an angle of 25?, that means a pendant of about 50% (considering that 90? would be infinitum pendant and 45? would be 100% pendant, just trying to make a rude aprox.) and indeed that\'s absolutely insane. Not only for the effort that would represent for travelling, but also because things should be rolling towards the inner circumference pretty easily, forming a nice cascade of rocks, fruits and other delicious things that would be the new neighbours (at least for some seconds) for the rests of the levels.
Without entering to evaluate the exactity of your numbers and formulas (I don\'t doubt you\'ve thought about them) I prefer to focus in those aspects, rather than trying to dig too whole, if there\'s really nothing to get from there.
Where I think your error is?
In taking the numbers with a too narrowed view.
The book isn\'t exact.
We don\'t know about the methods that were used to make those calculations, and even more, we don\'t know about the number Pi; more concretedly, the accuracy that Yliakeans have with that number.
Concentrating on the first floor the book says:
First level: Diameter 50km, floor 10 km wide.
Thanks to your drawing I understood what the book meant with that \"wide\" and that leads to two different radius. One for the outern circumference and the other for the inner. So outern radius=25km, while inner radius= 15km.
The next thing the book talks about is perimeters. Inner circumference 102km, and outern 157km.
That leads again to two radius. Inner one=16,23 outern one= 24,99km.
As you can see the outern perimeter is perfectly calculated and that can lead to think that, indeed Yliakeans know about number Pi (and with accuracy)
So, now, what we do with that difference in the inner radius stimation? You searched your reason, ended with the \"indianapolis curves\" and also to an alpha that almost seems impossible.
I prefer to take another position: we don\'t know how those measures where made, there\'s a 10% of difference between those two different values for r2 that I prefer to assign to different measuring methods. While I\'m too amazed about the exact of the outern, I fail to see what may have happened to the cartographer to fail with the inner.
Anyway, for sure the poor guy had a big deal popping all those measures, just keep in mind that the \"whole\" on the first level has a diameter of 30km, and hey, that\'s a big whole.
I\'ll too await to see what people thinks about the issue, anyway Nikodemus, thanks a lot for the effort you put in it, at least to me, your post has let me finally understand what you were referring to when talking about \"not flat ground\" you simply meant heavily inclined ground.
See you around.
EDIT1: How is it that this thread has 5 stars? oO
EDIT2: Also observe that H should be too, almost the total height of the stalagmite (if we substract from it the distance from the first floor to the ceiling) and the book just says that the distance between levels is 5km, and there are 8 levels :S
