HandsOn 6 - 1-, 2-, & 3-Dimensions
Fill in a copy of Table 2.4. Now plot the entries in this table on a fresh copy of the log-log graph paper. Along the horizontal axis plot the number of segments and, on the vertical axis, the entries in columns 2, 3, and 4. Draw a line through each set of points and verify that a line, square, and cube are 1-, 2-, and 3-dimensional, respectively.
|l||Number of segments||Number of squares||Number of cubes|
|of length d needed||of side d needed||of edge d needed|
|to span line||to cover square||to fill cube|
|of length L = 100||of area L2 = 10,000||of volume L3 = 106|
Note that in Figure 2.6 the dimension is the exponent in the equation for length or area or volume, as a function of L.
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