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Considering an exterior derivative $d$, which may be discretized as the transpose of the boundary operator on a simplicial mesh, I have read and seen that $dd = 0$, but I have not seen an intuitive explanation of this result. I suspect this result is deeply entrenched in the fact that $d$ is defined on an oriented mesh.

Any thoughts?

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What's the boundary of the boundary? The transpose of zero is zero. –  Steve Huntsman Jul 15 '11 at 5:08
    
Calculate some examples and you will see why $d^2=0$. –  Martin Brandenburg Jul 15 '11 at 7:11
    
You could consider the quotation from Henri Cartan's Laudatio on receiving the degree of Doctor Honoris Causa From Oxford University in 1980. It is on the opening of Gelfand and Manin's Methods of Homological Algebra. –  Giuseppe Tortorella Jul 15 '11 at 9:00
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You may enjoy reading answers to these questions mathoverflow.net/questions/10574 mathoverflow.net/questions/21024/… –  j.c. Jul 15 '11 at 14:04
    
I can see through experimentation and examples that this is true, but there must be a geometric argument for why it is the case. –  Brandon Jul 18 '11 at 15:08

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