杜甫是中国唐代著名的诗人，他的诗歌以深刻的社会洞察和精湛的艺术表现力著称。以下是三首杜甫的诗作及其英文翻译：

《春望》

国破山河在，城春草木深。

感时花溅泪，恨别鸟惊心。

烽火连三月，家书抵万金。

白头搔更短，浑欲不胜簪。

英文翻译：

The country falls, yet mountains and rivers remain;

Spring comes to the city, where grass and trees grow amain.

Grieved by the times, flowers shed tears; parting makes birds' hearts strain.

For three months the beacon fires burn, home letters are worth their weight in gold.

With hoary hair that grows shorter as I scratch my head,

I find it hard to keep even my hairpins from falling out.

《登高》

风急天高猿啸哀，渚清沙白鸟飞回。

无边落木萧萧下，不尽长江滚滚来。

万里悲秋常作客，百年多病独登台。

艰难苦恨繁霜鬓，潦倒新停浊酒杯。

英文翻译：

The wind is sharp, the sky high, and apes wail mournfully;

On clear shoals white sand and birds wheel back and forth.

Endless fallen leaves rustle down; the great river rolls on without end.

Wandering ten thousand miles in autumn's sorrow, often a guest;

In a hundred years of illness, alone I ascend this platform.

Bitter regrets for hardships have turned my hair to frost;

In my destitution, I've just stopped drinking muddy wine.

《茅屋为秋风所破歌》

八月秋高风怒号，卷我屋上三重茅。

茅飞渡江洒江郊，高者挂罥长林梢，

下者飘转沉塘坳。

英文翻译：

In the eighth month when autumn winds howl fiercely,

They tore off three layers of thatch from my roof.

The straw flew across the river, scattering over the riverside suburbs,

Higher ones got caught in tall treetops,

Lower ones drifted and sank into the depressions of ponds.

以上是三首杜甫的经典诗作及其英文翻译。通过这些翻译，我们可以感受到杜甫对自然景观的细腻描绘以及他对人生百态的深切关怀。