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## Main Question or Discussion Point

I'm reviewing differential forms again and I believe there is an error in Vladimir Arnold's Mathematical Methods of Classical Mechanics. On page 176 of the hardcover edition of it, in chapter 7, on the section of differential forms, problem 4 he says that dr^2(r^2=x^2+y^2) acting on the 2nd vector in the problem equals -8, I get that is equal 8. I can't understand why there would be a minus sign considering this dr^2, shouldn't it being raised to the 2nd power force the answer to being negative. If anyone can confirm this is not an error I'll be on my way to figuring it out . Thanks