Why did Columbus sail west instead of east if he wanted to reach India?

After studying maps drawn by Ptolemy during AD 100 as well as Italian scholar Paolo Toscanelli, Columbus came to the conclusion that Japan lay about 4,400 kilometers west of the Canary Islands near Spain. He hoped to establish a trading post in Japan heading towards India. Since the distance was short, he thought it would be a fairly simple voyage to travel in the western direction.

But he underestimated the size of the Earth by about 16,000 kilometers, because the direct route from the Canaries to Japan is about 20,000 kilometers. His plan to reach India by sailing west was supported by Queen Isabella of Spain, who gave him 3 ships and 90 sailors. He set sail on August 3, 1492 and, after three weeks the fleet sighted land — one of the Islands of Bahamas in the Caribbean Sea. (See the illustration above.)

Contrary to popular belief, Columbus never saw the mainland of what is now the United States of America during any of his three voyages. Columbus was convinced that he had found the Indies (south-eastern Asia), which is why Caribbean Islands are known as the West Indies to this day.

Additional reading:
Christopher Columbus (Wikipedia)

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