Orientability facts for kids

A torus is an orientable surface

In the Euclidean space, R³ is called orientable if a two-dimensional figure (for example, ) cannot be moved around the surface and back to where it started so that it looks like its own mirror image (). Otherwise the surface is non-orientable. A concept connected to this is chirality. This means that no matter what, a human right hand, cannot be rotated in such a way that it becomes a human left hand. The right hand is therefore orientable.

Images for kids

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  The Möbius strip is a non-orientable surface. Note that the fiddler crab moving around it has left and right flipped with every complete circulation. This would not happen if the crab were on the torus.

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  The Roman surface is non-orientable

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  In this animation, a simple analogy is made using a gear that rotates according to the right-hand rule on a surface's normal vector. The orientation of the curves given by the boundaries is given by the direction in which the dots move as they are pushed by the moving gear. On a non-orientable surface, such as the Möbius strip, the boundary would have to move in both directions at once, which is not possible.

See also

In Spanish: Orientabilidad para niños