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For example:

人間の顔は左右対称ではない
A person's face is asymmetrical.

The above is simple, but how about:

漢字の形が左右対称である。

"The shape of the Kanji character is symmetrical."

The problem I have with the above sentence is "symmetrical" and "左右対称" have different meanings, "symmetrical" is similar to "proportional" whereas "左右対称" has the meaning that if you "flip it over" the shape doesn't change (i.e.金、田、山, etc.). I was thinking "mirror-image", but usually you are contrasting one thing to another.

Any suggestions on how to express the meaning 左右対称 in English correctly in the above sentence?

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Isn't this a question for English Language & Usage rather than Japanese, since you are clear on the Japanese meaning and looking for a way to express it in English...? I hate constantly seeing questions closed here though...

...In any case I disagree that "symmetrical" is closer to "proportional" than "if you flip it over the shape doesn't change". Symmetry is the precise technical term for the latter concept -- there is no more fitting word. To be more descriptive, you could say they have "vertical symmetry", or less ambiguously, "left-right symmetry".

See the Wikipedia article on symmetry.

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+1: After seeing the Wikipedia article, I see the flaw in my thinking, symmetry has two meanings whereas I was only interpreting symmetry in the imprecise sense. Thanks. (I also felt adding "left-right" helps disambiguate the meaning). –  Jesse Good Mar 8 '12 at 2:56
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対称 'symmetry' has many instances. It means that if you switch some set of properties, coordinates, values, etc. in a certain way, the result can be assimilated in some way to the original.

In Japanese high school, students learn about 対称式 (symmetrical polynomials) like "a^2b + ab^2" and 基本対称式 (elementary symmetrical polynomials) like "a+b", "ab". I can also recall my memory from high school that in physics, there are things like CP-対称性 'C(harge)-P(arity) symmetry' or CPT-対称性 'C(harge)-P(arity)-T(ime) symmetry'.

In Japanese elementary school, students usually learn two types of symmetry: 線対称 (line symmetry; symmetry with respect to folding along a straight line) and 点対称 (point symmetry; symmetry with respect to rotation around a point). 左右対称 is a special case of 線対称, particularly when there is a notion of which way is left and which is right. You can also have 上下対称, etc. To express 左右対称の漢字 in English, you can say something like "a Chinese character that is line symmetric with vertical axis" or "a Chinese character that is line symmetric horizontal-wise".

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Everything you said is correct, but my question is How do you translate 左右対称の漢字 into English?. –  Jesse Good Mar 8 '12 at 2:46
    
Sorry, but your translations are not good English. Probably A Chinese character that has left-right (or vertical) symmetry would be best. –  Jesse Good Mar 8 '12 at 3:00
    
@Jesse Maybe you're right. But is that clear enough to mean line symmetry? Seeing the conversation between you and Hyperworm, I think you are forgetting about all the other kinds of symmetry. –  sawa Mar 8 '12 at 3:03
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Well, I don't if it applies in this case, but a lot of this conceptual vocabulary originally came from the West, anyway. It's true that 'symmetry' doesn't express the direction of the symmetry, but your feeling that 'symmetry' is too vague seems to be due more to your own vague understanding of what the English word 'symmetry' means. –  Bathrobe Mar 8 '12 at 12:40
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I do disagree. I learnt "bilateral symmetry" at school. Maybe they don't teach it any more, or perhaps there are places where they don't teach it, but I don't think that that is grounds for saying that Japanese is much clearer than English. I'm also curious how you would understand the word 'symmetrical' -- just a variation on 'proportional'? –  Bathrobe Mar 8 '12 at 23:37
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