Talk:Minkowski's theorem

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I wander whether "Minkowski’s theorem" file can be renamed as "Minkowski’s theorem (geometry of numbers)" file since the is another well known theorem of Minkowski on extreme points of a convex set, related to convex geometry. If yes, then one more file "Minkowski’s theorem (convex geometry)" file could be created.

Val

Just wanted to note that this proof is not comprehendible in any way to someone who doesnt have advanced knowledge of Geometry of Numbers. Maybe someone can try and rewrite this more clearly? —Preceding unsigned comment added by 83.237.35.129 (talk) 17:32, 29 September 2008 (UTC)


 * I don't agree. I have no knowledge (to my knowledge) of the Geometry of Numbers, but found the proof comprehensible. It uses concepts from other areas of math that people might not be familiar with--modular arithmetic extended to real numbers, and injective functions. It could probably be rewritten to avoid this "short hand". My point is Geometry of Numbers knowledge isn't a prereq. 67.158.43.41 (talk) 23:54, 1 April 2011 (UTC)

error in proof
The map should to from S to R^2/(2Z^2) not R^2. And the concept of squares stacked on top of each other should be replaced by the concept of a torus (inner tube shape)

92.26.208.58 (talk) 19:03, 30 September 2009 (UTC)

Actually, a better thing would be to send

S -> R^4 (x,y) |-> (sin(x/Pi), cos(x/Pi),sin(y/Pi),cos(x/Pi))

then there is no need to talk about 'mod' although this requires people believing in the concept of area of a surface in 4 space....

92.26.208.58 (talk) 19:06, 30 September 2009 (UTC)
 * Feel free to take a stab at the proof... I would only add that stacking squares using rigid transformations is intuitive without knowledge of differential geometry, even if it does lack in rigor. TotientDragooned (talk) 14:37, 28 October 2009 (UTC)

Theorem is also applicable in case of greater than or equal to 2^n. I don't want to fix it because then proof would be wrong because it only covers the case for strictly greater than. atul (talk) 16:40, 15 February 2012 (UTC)

Assessment comment
Substituted at 02:20, 5 May 2016 (UTC)