Final answer:
Columbus used navigation techniques involving the stars to cross the ocean, but he was mistaken in his estimate of the Earth's size, thinking that it was much smaller. He believed he had reached Asia and never realized that he had encountered a new world, which was only confirmed after his death.
Step-by-step explanation:
Christopher Columbus was able to cross the ocean by using navigation techniques like dead reckoning, and he also relied on celestial navigation, which involves using the stars to guide his path. However, when it comes to Columbus's understanding of the Earth's shape and size, he was partially correct and partially mistaken. Columbus knew that the Earth was round, which was a common understanding among educated people of his time.
Columbus never realized he had discovered a "new world". Until his death, he believed that the lands he reached were part of Asia, specifically the East Indies. The true extent of his discovery was only confirmed much later, when further explorations were conducted by others, such as Ferdinand Magellan's fleet which circumnavigated the globe and proved the presence of a massive ocean and unknown continents separating Europe from East Asia.