Area of mobius strip

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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. I want that to give a meaning to the notion of area for Mobius strip. I know that Mobius band is nonorientable surface.
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Möbius strip - Wikipedia

You have most likely encountered one-sided objects hundreds of times in your daily life — like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles. This mathematical object is called a Mobius strip. Another mathematician named Listing actually described it a few months earlier, but did not publish his work until The concept of a one-sided object inspired artists like Dutch graphic designer M. For instance, try taking a pair of scissors and cutting the strip in half along the line you just drew.
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Möbius strip

Like the cylinder , it is not a true surface, but rather a surface with boundary Henle , p. According to Madachy , the B. Trott, pers. The coefficients of the first fundamental form for this surface are.
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It can be realized as a ruled surface. For example, any rectangle can be glued left-edge to right-edge with a reversal of orientation. Some, but not all, of these can be smoothly modeled as surfaces in Euclidean space. Such paper models are developable surfaces having zero Gaussian curvature , and can be described by differential-algebraic equations.
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