So, I’m trying to learn Japanese, being as I live in Japan, so I’ve decided to start this series. I’m armed with a mathematical English-Japanese dictionary, a kanji look-up website, and a willingness to be corrected if I happen to have any Japanese readers. So, this post may not appear correctly if you don’t have Japanese fonts installed, just a warning, and if I explain anything incorrectly, let me know in the comments and I’ll correct the post.
Our first word is “manifold.” Every geometer of every stripe has studied manifolds at some point, and lots of other concepts require manifolds before they can even be defined, so that’s where we’re starting.
The first of these kanji, 多, can be pronounced as “ta,” which seems to be the most common reading. Looking at the actual structure of the kanji, this seems reasonable, as “ta” is written タ in katakana, and the kanji is two copies of this kana. As for meaning, it means “many” or “much” or “frequent,” and is the beginning of a direct translation of manifold.
The second character, 樣, is apparently not a general use character, it only occurs in special situations. Here, it is pronounced “you” (which we should note is two syllables “yo-u”) though can also be pronounced “sama.” Here it seems to be being used to indicate will or “way of” in some sense.
And finally, we get to the last character: 体. Here it is pronounced “tai” (again, ta-i), though it has others. It means “body” or “object.”
So, altogether, “tayoutai” or 多様体 means something like “many ways object” or “diverse bodies,” and translates to “manifold,” which is fairly direct.