Out of curiosity,s+v...為何可替換成curious,s+v.....誰可以用英文文法跟我解釋一下？最好附上例子?

"out of curiosity" ~ 出於好奇 (curiosity - noun)
"out of somthing" is a prepositional phrase acting as adverbial - used to show the reason why something is done.

e.g. I opened the letter out of curiosity.
= I opened the letter because of curiosity.

The adverbial phrase can also be placed in the begining of sentene:
Out of curiosity, I opened the letter.

The sentence can be rewritten using adverbial clause:
As I was curious, I opened the letter.
(where "curious" is an adjective)

The sentence can be further reduced with the adverbial clause converted into a participle phrase:
Being curious, I opened the letter.

Although the participle phrase ("being curious") is adjectival (modifying the subject "I"), it has a cause-and-effect relation with the main clause in meaning.

The participle phrase with the format "Being + adjective / adjectival phrase" can normally be reduced with the "being" removed. However, they could have slightly different meanings.

Example:
- The curious man opened the letter.
- Curious, the man opened the letter.
- The man, curious about what was inside, opened the letter.