A propeller is a chiral structure. Propellers can have low or large pitch. This difference can be seen as distinguishing propellers of low and of large chirality.

Is there a general way, given a closed 3d shape, to quantify its chirality? Is there some sort of integral over the shape that yields a number quantifying the degree of chirality of that shape?

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    $\begingroup$ The Hausdorff distance to its mirror image? Or rather, the inf of the distances to the confgruent copies of its mirror image, I guess. $\endgroup$ Oct 28, 2022 at 19:50
  • $\begingroup$ In a word yes, though presumably the underlying intent is a measure satisfying additional conditions: 1. real-valued, 2. easily-calculated, 3. widely-used. Offhand I don't know of anything satisfying both 1. and 2., and nothing satisfying 3. $\endgroup$ Oct 28, 2022 at 19:51
  • $\begingroup$ Where can I read more about the Hausdorff distance? $\endgroup$
    – KlausK
    Oct 29, 2022 at 14:53
  • $\begingroup$ Complex-valued is also ok ... $\endgroup$
    – KlausK
    Oct 29, 2022 at 14:54
  • $\begingroup$ For posterity: re-asked here mathoverflow.net/questions/433487/… $\endgroup$ Oct 30, 2022 at 17:03


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