你理想中的一天是什么？

[soft fable]

"what's your ideal day?" (DeepL translation)
i know all the characters here but the function of 中 kinda confuses me.

[frigid wasp]

理想 here is a noun which means "ideal, dream" so the using 中 would make it "within your ideals"

[soft fable]

oh i see, could you provide another example of how 中 could be used like that? i don't think i've seen it before

[wind charm]

I've leaned something similar yesterday. 在 + Topic + 上. When you're talking about something, you can say the topic + 上。
For example, 这件事情上应该问老师 - about this matter, you should ask the teacher

It's almost the same for 中
example, 在这个故事中, would be like, in this story...
在这些画作中，in these paintings....

like the same use for "inside something" 在商店里， but for books, movies, paintings, dreams

but I'm still leaning this, so maybe I'm wrong

中 brings the idea of among/within, "among these paintings" - 在这些画中

[soft fable]

interesting, sounds kinda literary, no?

although i'm learning as well so lol

[soft fable]

i've tried to find more examples and that does sound very accurate, just still not sure how frequent that expression is

[wind charm]

I don't know either. The use of 在。。。中，seems like i will be like the use of 都 and 就 to me, the more I see them the more I feel where in sentence it's more natural to use them

[soft fable]

yeah, that's why it sounds a bit literary

to me

[wind charm]

it feels really nice to say 中 out loud in the middle of a sentence, like 都

[soft fable]

lol

[soft fable]

btw, i've heard of 在 + topic + 上 before and thought it's mostly used to express literally "on"

cool to find more uses

[wind charm]

oh yes, it can also means at the top of something

but it can be more abstract subjects

很有趣

[ornate echo]

不是 这问题是在问什么 😅

[past sentinel]

i know all the characters here but the function of 中 kinda confuses me.
中 indicates the position, like 上 and 下, so in English, we would call it a preposition. However, since these particles come after the thing they're modifying, these are technically postpositions in Chinese.
中 means "middle", so when used as a position particle, it means "in the midst of", "in", "amongst", etc. It's like how 上 means "up", so as a preposition, it can mean "on", "above", etc.
里 also means "inside", but is used for concrete things that you can have other things inside. 中 is more often used for more abstract notions of "inside".
In that sense, 中 would seem to be more literary, but there are certain things you cannot use 里 with because they're not concrete enough, and there are certain concrete things with which you can use both (e.g. 浓雾 and 他们手 in your examples).
In the case of 理想中的一天, 中 is not strictly necessary because 理想的 is enough to modify 一天 to give the same meaning. However, it's good to know that this construction is also possible.