Chirality and handedness

Chiral objects come in pairs, like hands. We have a right and a left hand, and these are, ideally realized , mirror images of each other. The basic mathematical notion that distinguishes the right hand from the left hand is the following  

5 Definition (Orientation) An orientation of means the choice of a sequence (bo.bj.bj) of linearly independent vectors bj, i.e. the choice of an ordered basis of the space considered. Having chosen such an ordered basis (bo, b], bj), another ordered basis (cq, C], cj) is said to have thesome orientation if its determinant has the same sign, 

the choice of (bo,bi,b2) allows to check whether another basis has thesome orientation or the opposite one, depending upon the plus or minus sign of the determinant value. 

Looking from this side, i.e. in the direction of bj means choosing a directional sense. In the case shown above this is the direction of a right-handed screw, so we call this a right-handed orientation, in accordance with the orientation of thumb, index finger and middle finger of the right hand. The opposite case is a left-handed screw or a left-handed orientation. 

the main ingredients needed to dehne right- and left-handedness are 

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R.B. King, Chirality and handedness The Ruch shoe-potato dichotomy in the right-left classification problem. Ann. N.Y. Acad. Sci. 988, 158-170 (2003)... 

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