Rank-3 scale theorems: Difference between revisions
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A floor-LQ scale ''S'' is LQ since the graph of F(x) = floor(b/a*x) has the desired lattice points: the lattice points are | A floor-LQ scale ''S'' is LQ since the graph of F(x) = floor(b/a*x) has the desired lattice points: the lattice points are | ||
floor({(a,b)t : 0 <= t <= 1}) = floor_x(floor_y({(a,b)t : 0 <= t <= 1})) = floor_x([graph of floor(b/a*x)]). | floor({(a,b)t : 0 <= t <= 1}) = floor_x(floor_y({(a,b)t : 0 <= t <= 1})) = floor_x([graph of floor(b/a*x)]) (*). | ||
Conversely, if a 2-step scale ''S'' is LQ, floor({(a,b)t : 0 <= t <= 1}) gives you the graph of floor(b/a*x) when you connect the dots ( | Conversely, if a 2-step scale ''S'' is LQ, floor({(a,b)t : 0 <= t <= 1}) gives you the graph of floor(b/a*x) when you connect the dots. This follows from the same equation (*). | ||
==== MV3 Theorem 1 (WIP) ==== | ==== MV3 Theorem 1 (WIP) ==== | ||