Uncovering the Origins of the Symbol 'r' in Mathematics

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The discussion centers on the mathematical symbol 'r', which represents radial distance from an axis, while 'R' denotes resistance. The distinction between lower case 'r' and upper case 'R' is emphasized, particularly in the context of equations involving resistivity. The formula for resistance, R = ρl/A, applies to flat sheets, while dR = ρ dr/A is relevant for cylindrical tubes. The conversation clarifies the proper use of these symbols in mathematical equations. Overall, the participants successfully resolve the initial confusion regarding the symbols and their applications.
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Summary:: I have a question that I don't understand but you may know where r was come from.

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I mentioned about my question on the addition.
 
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Lower case ##r## is radial distance from the axis. Upper case ##R## is resistance. Two different quantities. Besides, you can't have ##dR## on both sides of the equation you are questioning.
 
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##R = {\rho\;l\over A} ## is for a flat sheet with thickness ##l##.
Here ##dR = {\rho \, dr \over A}## is for a tube with radius ##r## and thickness ##dr##. Its area ##A## is ##2\pi Lr##
 
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Okay I get it now. Thanks both of you for attention :)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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