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Topic: Logarithmic Graph Paper (Read 557 times) |
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Foolish
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Logarithmic Graph Paper
« on: Dec 1st, 2004, 11:01am » |
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I was thinking earlier today about graphing things on logarithmic paper and semi-logarithmic paper.
Say you graphed a circle, radius r on a sheet of standard 1:1 graph paper, then transcribed it onto semi-log paper, what would the area and circumference become? How about on true logarithmic paper? And then, a sphere in log space (volume and surface area)?
This is perhaps too easy a problem for this forum, but I thought that it was too mathy for the easy or medium sections.
Another thought, what would the shape of the transcribed circles become if they were drawn back onto the 1:1 paper?
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| « Last Edit: Dec 1st, 2004, 7:18pm by Foolish » |
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Aryabhatta
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Re: Logarithmic Graph Paper
« Reply #1 on: Dec 1st, 2004, 10:47pm » |
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On a log paper, if we want to plot the function f(x) do we actually plot ln(f(x)) where ln is the natural logarithm ?
Assuming that we want to log-plot the quadrant sqrt(1-x2) for the area we are looking for the definite integral:
0[int]1 ln[sqrt](1-x2) dx
The substitution x = sin[theta] and using integration by parts seems to do the trick, but we might have problems as ln[sqrt](1-x2) is unbounded in the interval [0,1) (I haven't actually tried to find the value).
I am not sure if that was your intent.. or I understood you correctly.
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| « Last Edit: Dec 1st, 2004, 10:48pm by Aryabhatta » |
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Foolish
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Re: Logarithmic Graph Paper
« Reply #2 on: Dec 1st, 2004, 10:59pm » |
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I will try to clarify what I mean:
-regular graph paper's grid has consistent hash lines of 1 unit each, for both the x and y axis.
-semi-log graph paper has regular hash markings for the x axis, but the y axis has 1, 10, 100, 1000...
-full log paper has the 1, 10, 100, 1000... for both x and y axis
basically, we are just changing the values of the lines on the graph paper, without changing how we draw the shape.
I will make some images if that would be more helpful...
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