What's the difference between 三角 and 三角形?


I just had this terrifying conversation:

> What is "triangle" in Japanese?
>
> me: 三角 right?
>
> Then what's 三角形?
>
> me: Uhh... triangle?

I've confirmed both of these translate to "triangle". Apparently they refer to
different _aspects_ of the triangle in Japan? Is 三角 a symbol and 三角形 a
geometrical form?




It might be something as simple as:

> 三角 (something that is "triangular" where the focus is having attributes
> similar to that of triangles ie: three sides, three corners)
>
> 三角形 (a polygon that IS a triangle)

For example: 「三角屋根」 is a way to describe a roof that is "triangular" in
comparison to other roofs of different shapes. It has attributes similar to
those of "triangles".




As Gradius said, the mathematical term “triangle” is 三角形, and never 三角. As
part of compound words, 三角 also appears; an example is 三角関数 (trigonometric
functions).

(As for the use of 三角 in compounds words, I think that there is a general
tendency to prefer to two-kanji words than three-kanji words when they are
used adjectivally in compound words. See also Chocolate’s comment on the
question “[What is the difference between 日曜日 and
日曜?](https://japanese.stackexchange.com/questions/6368/what-is-the-difference-
between-%E6%97%A5%E6%9B%9C%E6%97%A5%E3%80%90%E3%81%AB%E3%81%A1%E3%82%88%E3%81%86%E3%81%B3%E3%80%91and-%E6%97%A5%E6%9B%9C%E3%80%90%E3%81%AB%E3%81%A1%E3%82%88%E3%81%86%E3%80%91)”
by BabyAzerty.)

As a non-technical word, 三角形 is more formal and 三角 is less formal. I do not
recognize any difference in their meanings.

