Мы заметили красоту природы.

Because красоту is in the accusative case, which is the case usually used for a direct object.

• Dictionary form: красота = beauty
• In the sentence, beauty is the thing that was noticed, so it becomes the direct object.
• For most feminine nouns ending in -а, the accusative singular changes -а to -у.

So:

• красота → красоту

That is why Мы заметили красоту природы uses красоту.

Here природы is in the genitive case.

The phrase красота природы means the beauty of nature. In Russian, this kind of of relationship is often shown by the genitive case rather than by a separate word like English of.

So:

• природа = nature
• природы = of nature

Together:

• красота природы = the beauty of nature

Because Russian often expresses of by using the genitive case instead of a separate word.

English says:

• the beauty of nature

Russian says:

• красота природы

Literally, this is something like beauty [of] nature, where the of idea is built into the form природы.

This is very common in Russian:

• дом брата = brother’s house / the house of the brother
• цвет неба = the color of the sky
• красота природы = the beauty of nature

Заметили is the past plural form of the verb заметить, which usually means:

• to notice
• to observe
• sometimes to spot

In this sentence, Мы заметили красоту природы means that we became aware of or noticed nature’s beauty.

It is not exactly the same as увидели (saw).
Заметили emphasizes that something caught your attention or that you noticed it, not just that it was visible.

Because the subject is мы, which means we.

Russian past tense agrees with the subject in gender/number:

• я заметил = I noticed (masculine speaker)
• я заметила = I noticed (feminine speaker)
• мы заметили = we noticed

Since мы is plural, the verb takes the plural past ending -и:

• заметили

The dictionary form is заметить.

This is the infinitive, meaning to notice.

From that infinitive, the past tense forms are built like this:

• заметил = he noticed
• заметила = she noticed
• заметило = it noticed
• заметили = they/we noticed

So заметили is simply the plural past form of заметить.

Заметить is perfective.

That matters because Russian verbs often come in aspect pairs:

• замечать = imperfective
• заметить = perfective

Very roughly:

• imperfective focuses on the process, repetition, or general action
• perfective focuses on a completed action or result

So:

• Мы замечали красоту природы would suggest we used to notice or were noticing the beauty of nature
• Мы заметили красоту природы means we noticed it as a completed event

In this sentence, the perfective verb makes good sense because it presents the noticing as a single completed realization.

Yes, but it would mean something a little different.

• Мы заметили красоту природы = We noticed the beauty of nature
  A completed act of noticing, perhaps at a particular moment.

• Мы замечали красоту природы = We were noticing / used to notice the beauty of nature
  More about repeated noticing, an ongoing experience, or a general pattern.

So both are grammatical, but they do not express exactly the same idea.

Yes, мы can often be omitted in Russian, because the verb ending already shows who the subject is.

• Мы заметили красоту природы
• Заметили красоту природы

Both can mean We noticed the beauty of nature, depending on context.

However, including мы can be useful:

• for clarity
• for emphasis
• when introducing a new subject
• when contrasting with someone else

So Russian often drops subject pronouns, but not always.

Yes. Russian word order is more flexible than English word order because case endings show grammatical roles.

The neutral order here is:

• Мы заметили красоту природы.

But you may also see:

• Красоту природы мы заметили.
• Мы красоту природы заметили.

These versions can sound more emphatic or stylistically marked. For example:

• Красоту природы мы заметили may emphasize the beauty of nature
• Мы at the beginning may emphasize we

Even though the word order changes, the case endings still show that:

• мы is the subject
• красоту is the direct object
• природы depends on красоту

Yes, it is very natural.

Красота природы is a common phrase meaning:

• the beauty of nature
• nature’s beauty

It sounds normal in both everyday and literary Russian. It can be used in many contexts, for example:

• Мы восхищались красотой природы. = We admired the beauty of nature.
• Он любил красоту природы. = He loved the beauty of nature.

So this is a very useful phrase to learn.

You know mainly because of the cases.

• мы is the nominative form of we, which is typically the subject form
• красоту is accusative, which marks it as the direct object
• природы is genitive, showing of nature

So even without relying much on word order, the forms tell you the structure:

• мы = subject
• заметили = verb
• красоту природы = object phrase

This is one of the most important differences between Russian and English: Russian depends much more on endings.

Not exactly.

• Мы заметили красоту природы = We noticed the beauty of nature
• Мы заметили красоту в природе = We noticed beauty in nature

These are similar, but not identical.

Красота природы treats the beauty of nature as a single noun phrase.
Красота в природе focuses more on beauty that exists within nature.

The original sentence is the more direct and idiomatic match for the beauty of nature.