Talk:Chirality (mathematics)

Organization

Alterations and restructuring are needed to properly represent use and meaning of the word chirality. Please join the multi-disciplinary discussion on Talk:Chirality. --Cigno 22:11, 15 November 2005 (UTC)

Difference between chirality and handedness

From handedness (disambiguation):

Handedness can refer to different things.

• handedness of human beings
• in mathematics, handedness is a common synonym for orientation or chirality

I thought that chirality (mathematics) and handedness (mathematics) were synonyms. For instance, I really cannot see the difference between the chirality of a basis set and the handedness of a basis set. However, I see that in Wikipedia there are several articles somehow referring to the two concepts, and in none of them there's an explicit description of the difference between them.

Etimology. There's no difference between the two words, from an etimological point of view. The prefixes chir- (greek) and hand- (english) mean exactly the same thing.

I suppose that the meaning of the words depends both on the context and on the "object" which they refer to (spiral, propeller, basis set, subatomic particle...). Namely:

• Chirality and handedness (of a basis set on a vector space) are synonyms in the context of linear algebra. The above copied disambiguation says that also orientation is a synonym of handedness, in this context, but I doubt this is exactly true (orientation is only positive or negative...)
• Chirality and handedness (of geometrical objects in general) are also synonims in geometry and physics (where orientation means for sure something else!)
• Left- or right-handedness or chirality is only a special case of handedness or chirality, possible only in 3-D and only for

1. some objects which have both a standard direction of translation along a given axis associated with a prescribed sense of rotation about the same axis (a screw, a propeller) or
2. sets of directed and ordered objects (tern of vectors).
3. ? (is there something else?)

• I mean, there are chiral or handed objects in N-D and even in 3-D that can neither be assigned a left- nor a right- chirality or handedness.

I am not familiar enough with this concept to give a final answer. However, whatever is the truth, in my opinion it should be made clear both in this article and in the article about orientation of a basis set. The disambiguation pages Chirality and Handedness (disambiguation) should be also revised.

Do you agree? I need your opinion. With regards, Paolo.dL 20:35, 25 August 2007 (UTC)

I agree with user Paolo. This article fails to make a clear distinction between orientation and chirality, and what seems to be even important, whether both concepts are needed, or one can be defined in terms of the other. — Preceding unsigned comment added by 67.173.6.105 (talk) 19:25, 26 September 2015 (UTC)

What is the opposite of enantiomorphic; of chiral?

Is there a word similar to enantiomorph which refers to an object which IS equivalent to it's mirror image? I searched Google but haven't found anything.Scot.parker 15:43, 18 October 2007 (UTC)

The best I can come up with is "amphicheiral". That is, if "cheirality" means the same thing. Source: http://users.cecs.anu.edu.au/~hartley/Papers/cheiral/revision/cheiral.pdf

Hendrixjoseph (talk) 13:36, 1 April 2011 (UTC)

2 dimensional chiral objects

The introduction mentioned that the helix and the mobius strip are two-dimensional chiral objects. The helix is not 2-D. It is a 1-D smooth curve in 3-D space. —Preceding unsigned comment added by 96.236.25.168 (talk) 22:57, 14 January 2011 (UTC)

Higher dimensions?

Some discussion of chirality in higher dimensions would not be amiss. — Preceding unsigned comment added by 66.30.115.205 (talk) 18:19, 13 October 2018 (UTC)