Geometry problem

[borisp]

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I have seen this problem before (it certainly is well known enough to be considered part of mathematical folklore).

One of the nicer ways is to integrate exp(2 \pi i (x+y)) over R (which is of course the same as integrating exp(2\pi i (x+y)) over the union of all of the rectangles ...)

there is another solution involving checkerboards but I am an analyst by heart and by training and so I stick to my most familiar tools [img]/images/graemlins/smile.gif[/img]

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Shut up!!...no offense [img]/images/graemlins/tongue.gif[/img]

[blah_blah]

since the majority of 'recreational' mathematicians are not capable of integrating a complex function over a curve in R^2, I think that I haven't spoiled your problem [img]/images/graemlins/smile.gif[/img]