How did communism win in both China and Korea if the US had nuclear weapons?

china is close to Russia which was the birth place of the form of government that eventually collapsed on itself, and so we Korea.  Now moving on to why the US failed to stop the spreading of communism, the use of nuclear weapons was unnecessarily devastating to the country and the aftermath of the detonation of a nuclear warhead would leave the land uninhabitable from the radiation.  And for using a nuclear weapon in war without needing to, the relations between every other country in the world would worsen with the united states (It's hard to know how the world would react to it but it wouldn't be positively).  For a short story: using nuclear weapons as a regular payload should and must be refrained from usage as much as possible.

Explanation:

according to the map, most industrialization in europe occurred in the northwest.

the production of coal and lignite deposits was profitable throughout western europe.

the building of railroads transport goods throughout europe.

according to the map, the population trend indicates that more people are moving into cities.

northwest

coal and lignite depostis

railroads

cities

the revival of interest in greek and roman influences also stimulated developments in math and science. the mathematical traditions that governed the conception of the universe were based in greek mathematics that had been preserved and built upon by scientists in muslim lands, such as nasir al-din in the 13th century. the catholic church endorsed the views of ptolemy, the greek philosopher and astronomer who constructed a geocentric theory where all planets, the moon, and the sun revolved around the earth. using calculations from al-din, polish monk and mathematician, nicholas copernicus, concluded that the geocentric theory did not make sense. instead, his data indicated that the earth and all the other planets rotated around the sun, a conclusion that he did not share widely, for fear of retaliation from the church. in fact, his heliocentric theory was not published until after his death in 1543.

the scientist that really got into trouble over the heliocentric theory was italian galileo galilei, who strengthened and improved copernicus' theory. other scientists, such as johannes kepler, had demonstrated that planets also moved in elliptical orbits, and galileo confirmed those theories as well. perhaps most famously, he built a telescope that allowed him to observe the phenomena directly, recording details of heavenly bodies that the ancients could never have known about. galileo's theories were published in the starry messenger in 1610, a highly controversial book criticized by other scientists, as well as officials of the church. galileo made the mistake of making fun of people that disagreed with him, and he was arrested and put on trial, eventually recanting his theory publicly in order to save his own life.