A Vector Grid

You are going to use the algebra input line below the graph to create a grid of lattice points according to the following rule: You can only enter expressions of the form A+k*u+j*v where k and j come from the set {-3,-2,-1,0,1,2}.

For example, some allowable inputs are A+2u-3v, A-3u, and A+v. Some that are not allowable are A+4u-2v, u+v, and A+u+v+w.

Enter as many as you possibly can, then answer the questions below.

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(1) Look at all those parallelograms! What is the area of the smallest one?
(2) Drag A to the origin. What do you notice?
(3) Drag A to the tip of one of the vectors. What do you notice?
(4) Drag the tip of one of the vectors to a new point, and answer questions 1, 2, and 3 again.




If you think this looks like the mathlet above, YOU ARE CORRECT!
In the input line below, enter the following commands one at a time so you can see what happens.

(1) SEQUENCE[A+k*u,k,-3,3]
(2) SEQUENCE[A+j*v,j,-2,4]
(3) SEQUENCE[SEQUENCE[A+k*u+j*v,k,-3,3],j,-2,4]


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Go ahead and play around with the sequence command.
Change some of the parameters so you can see what happens!
Drag point A and drag the tips of the two vectors!

Steve Phelps, Created with GeoGebra