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The cartesian coordinate plane is a virtical line (the y axis) running through a horizontal line (the x axis). It forms a cross which divides the grid that it's placed on into four quadrants. The quadrants are labeled 1, 2, 3, and 4, in counter clockwise direction, starting in the upper right corner. The point where the x and y axis meet, (0,0) is called the origin. You can graph points on the line by counting the amount f points in the first number of the coordinate (x) on the x axis, and then the second on the y. for example the coordinate (1,2) would be one space to the right and two up. Here's a URL for a picture of it.

http://miniurl.com/6307

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Q: How does a Cartesian coordinate system look like?
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What does a coordinate grid look like?

Its like a grid separated in four quadrants with an x and y axis, with labeled coordinated (3,-4)


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Why are spheres rarely used for packaging?

To form an A-B-A-B-... hexagonal close packing of spheres, the coordinate points of the lattice will be the spheres' centers. Suppose, the goal is to fill a box with spheres according to hcp. The box would be placed on the x-y-z coordinate space.First form a row of spheres. The centers will all lie on a straight line. Their x-coordinate will vary by 2r since the distance between each center if the spheres are touching is 2r. The y-coordinate and z-coordinate will be the same. For simplicity, say that the balls are the first row and that their y- and z-coordinates are simply r, so that their surfaces rest on the zero-planes. Coordinates of the centers of the first row will look like (2r, r, r), (4r, r, r), (6r ,r, r), (8r ,r, r), ... . The sphere centered at x = 0 is immediately omitted because part of the sphere would lie outside.Now, form the next row of spheres. Again, the centers will all lie on a straight line with x-coordinate differences of 2r, but there will be a shift of distance r in the x-direction so that the center of every sphere in this row aligns with the x-coordinate of where two spheres touch in the first row. This allows the spheres of the new row to slide in closer to the first row until all spheres in the new row are touching two spheres of the first row. Since the new spheres touch two spheres, their centers form an equilateral triangle with those two neighbors' centers. The side lengths are all 2r, so the height or y-coordinate difference between the rows is . Thus, this row will have coordinates like this: