Manhattan refers both to the Island of Manhattan which borders the lower Hudson River, and also to the Borough of Manhattan (one of the five boroughs of New York City), which includes the Island of Manhattan itself, as well as several other smaller islands and a small portion of the mainland (see geography). The borough is coterminous with New York County, and addresses within the borough of Manhattan are typically designated as New York, NY. As of the United States 2000 Census, the population comprised 1,537,195 people, but the county is geographically among the smallest in the United States with only 23.7 square miles (61.4 km˛) of land. With 64.9 thousand people per square mile (25 thousand/km˛), it is by far the most densely populated county in both New York State and the entire United States.

Manhattan is the largest central business district in the United States. The name Manhattan derives from the word Manna-hata so written earliest in the 1609 log book of Robert Juet, an officer of the Dutch East India Company yacht Halve Maen or Half Moon. The ship was captained by Henry Hudson, who, in the service of the Dutch Republic, was (covertly) commissioned to seek a north-west passage to China. The Half Moon first entered Upper New York Bay on September 11, 1609, and sailing up the lower Hudson River, anchored off the tip of northern Manhattan that night. As emissary of Holland’s Lord-Lieutenant Maurits he named the river he discovered after him; the Mauritius River.

A manuscript map of 1610 depicts the name Manahata twice, on the west as well as the east side of the Mauritius, Hudson River, thereby referring to the tribes that dwelled at the mouth of the river as the Manahata Indians. In 1625, Johannes de Laet, Director of the Dutch West India Company wrote in his “New World”: “The great North River of New-Netherland is called by some the Manhattas River from the people who dwell near its mouth; but by our countrymen it is generally called the Great River”. In the 1630 edition he continues to write of “another fort of greater importance at the mouth of the same North River, upon an island which our people call Manhattas or Manhattans Island, because of this nation of Indians happened to possess the same, and by them it has been sold to the company”. He thus confirmed that the island had been purchased in 1626 by Peter Minuit, the third director of New Netherland from the native Mannahatans for 60 guilders worth of trade goods (translated to about $24 which at a 4% annual inflation rate would be 71.3 million dollars today).
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