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I know that

I am curious what would happen

is a perfectly valid usage. What I don't understand is why there is no preposition to connect "curious" and "what would happen", which is acting like a noun clause. It seems to me that the sentence is not grammatical and needs "about" between curious and what would happen. Why is it an acceptable usage? Is there a grammar rule behind it?

1

Check out this link: https://www.grammarly.com/blog/prepositions/

There's no preposition, because you don't need it. When you take a technical writing course, there's a lot of focus on removing unnecessary prepositions, and that was the first thing I thought of when I read your question.

I don't think "I'm curious about what would happen" is wrong, it's just superfluous.

Try extending the thought of the original sentence: I am curious about what would happen if I open that door.

vs

I am curious what would happen if I open that door.

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Both forms are idiomatic. With the version without the preposition, curious is treated as if it means "desiring to know".

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