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Zheng He made his first voyage to other countries to show Chinese superiority by giving gifts so other countries would bow down and respect the Chinese.
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Prince Henry founds the first navigation school in Portugal. These schools give Portugal an edge in exploration later on.
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After Zheng He's seventh voyage, his patron died. His patron's successors weren't interested in exploring. Instead of using the money for exploration, they built the Great Wall of China and withdrew into isolation.
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Christopher Columbus from Spain convinced his patron to fund his exploration. He attempted a route to Asia but landed in the Americas because he misjudged the size of the Earth.
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Spain and Portugal had both explored into the Americas, and they were fighting over land until they got the Pope involved. The Pope divided the land between them.
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da Gama from Portugal used Diaz's route to set up a port in Calicut. He comes back to India later to stop corruption in India but he died trying to stop it.
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Later in the 1600s, Tokugawa Ieyasu completes the unification of Japan. None of the previous shoguns could complete the unification of Japan such as Nobunaga and Hideyoshi. The project to unify Japan was started by Hideyoshi.
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Beforehand, the Manchus had conquered Korea and their next target was the Chinese empire because of all the riches that had been built up in their time of isolation. However, in 1644, the Manchus conquered the Chinese. They made them shave their heads and grow a ponytail to humiliate them. Later on, the Chinese began to respect the Manchus because they acknowledged the Chinese's Confucian beliefs.