Final answer:
The Netherlands explored what is now the state of New York, establishing the colony of New Netherland with its center at New Amsterdam, and also being active in the Caribbean region, contributing to Amsterdam becoming a vital trade hub in the 17th century.
Step-by-step explanation:
The Netherlands actively explored parts of the New World under the auspices of the Dutch East India Company (DEIC) and later the Dutch West India Company (DWIC). In 1609, Henry Hudson, while searching for the Northwest Passage on behalf of the DEIC, sailed into what is now known as the Hudson River and Delaware Bay. This allowed the Dutch to lay claim to the area, naming it New Netherland, with its hub at New Amsterdam on modern-day Manhattan. The region, known for its fur trade—especially beaver pelts—became a valuable Dutch colony. Additionally, the Dutch established Fort Orange near present-day Albany. Beyond this region, the Dutch were also commercially active in the Caribbean, focusing on areas like Aruba, Bonaire, and Curaçao due to the lucrative sugar production. Amsterdam flourished as a central trade hub during this era, bolstering the Dutch as a significant colonial power in the 17th century.