Create a cartesian system
intro
Figure 6.1
Figure shows slider a and b
Vector u and v are given
the construction shows, vectors a*u and b*v head to tail
vector w = a*u + b*v
this shows that in the 2d plane, we can create any vector w, being compose of two scale non parallel vector.
What requirements from vector space creation are used
Tiling the plane
non parallel Vector u and v can be used to tile the plane
why do we want to tile the plane?
Orthogonal tiling
figure shows vector AB and orthogonal vector CD.
these vectors are used to tile the plane tiling can continue in all directions to infinity
Does this tiling look faliamar
we can now define the cartesian system
have you every used the cartesian system, what is the main use?