Thread: Lattice Points
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rasmhop
#4
Dec9-09, 08:43 AM
P: 424
Lattice Points

I guess crd refers to: http://mathworld.wolfram.com/ which is a math resource, but I don't know the particular write-up he mentioned.

Anyway just work it out in cases. As crd suggested just count the points in the first quadrant (which we can take to include the positive x-axis, but not the positive y-axis because then we get simple rotational symmetry without double-counting), and then use symmetry to deduce the total number. In that case the x-coordinate is 1,2,3,4,5 or 6.

When the x-coordinate is x, then the y-coordinate must be less than or equal to [itex]\sqrt{6^2-x^2}[/itex], so for any x-coordinate you want to count the integers in [tex][0,\sqrt{6^2-x^2}][/tex]


Try to see how far you can get, and if you get stuck at a particular step just ask for more help.