Talk:Trigonometry/For Enthusiasts/Hilbert's third Problem

How do we progress this?
JamesCrook (talk) 17:40, 9 November 2010 (UTC)
 * I think we will need a diagram of a dissection puzzle involving pentominos that is provably impossible using an invariant based on black squares and white squares.
 * The explanation of tensor product needs great care not to be too abstract, or we will lose to many people.


 * Vector Spaces and Quotient Spaces are quite difficult to understand on first take. Since they are topics in abstract algebra, to make this topic more approachable for others, we need to link to a article that explains them in great depth or at least briefly describe what they are, rather than jumping in and showing that we can use vector spaces in areas other than just the reals. (Shrig94), 9 November 2010 (UTC)


 * Hmm... I agree.  Most people who have done some calculus will have had some exposure to vector spaces, or at least vectors in 3D and 3x3 matrices.  I can see the problem though.  It's a big jump from being able to calculate the length of a vector using Pythagoras to the idea of being able to construct vector spaces 'to order'.  Quotient Spaces are likely to cause more problem than Vector Spaces will.  Let's see if a 'machinery' box will help. JamesCrook (talk) 11:24, 30 November 2010 (UTC)