Editing Talk:Suzumiya Haruhi:Volume5 Snow Mountain Syndrome (section)

== Discrete Mathematics ==

There are some errors in the text:
# ''This principle holds for all polyhedron'': It holds for all convex polyhedra, but there are some non-convex polyhedra with Euler characteristic not equal to 2. See [http://en.wikipedia.org/wiki/Euler_characteristic#Examples_of_non-convex_polyhedra].
# ''The answer of taking the amount of vertices minus the number of sides must be 2'': Should be ''The answer of taking the number of vertices plus the number of sides minus the number of edges must be 2''.
# ''The seven bridges problem is rooted from this principle'': The two problems are different and only loosely related.
# The line SUZU-KY is not explained in the text.

The generalization for other dimensions (x - y + z = D - 1) is also incorrect. In a planar graph, the outer (not bounded) region represents a side and should be added, i.e., the formula remains 'points + sides - edges = 2'.

:I agree that the text was not correct, however it is not clear if this error is a problem with the translation or with the original writing. If it's a translation error then by all means let it be fixed... if the author of the original work screwed it up perhaps it deserves consideration first. More importantly, does changing the math have any impact on the "solution" given in the story? [[User:Smidge204|Smidge204]] 10:31, 27 November 2006 (PST)

::I've only corrected the second error, since Koizumi knows the correct formula. The first point is a general mistake and depends on the definition of polyhedron (the statement is true if a polyhedron is convex by definition), i.e. no change is needed.
::Koizumi only considers the cases D=2 or D=3 in x - y + z = D - 1. In these cases the formula is correct since he doesn't count the outer region in the planar case, but it is not correct for higher dimensions D. I think that an end note is sufficient for this point. -- [[User:89.58.149.4|89.58.149.4]] 13:00, 27 November 2006 (PST)

::: To the generalization for other dimensions, please note that the equation only stands for the bound of D = 2 or D = 3, as said above by 89.58.149.4
::: To the description on 2, notice that the shapes in question within the chapter are all convex polyhedra.  Non-convex polyhedra are not discussed within the scope of this chapter. 
::: On the bridge question, it is as the author has written. 
::: To comment no.4, thank you for pointing out the omission.  It has been rectified. --[[User:Shiratoriryuuko|shiratoriryuuko]] 12:34, 28 November 2006 (PST)