It is called Rapa Nui by the natives, Isla de Pascua by the Spaniards - it was named Easter Island by James Cook who "discovered it" on Easter Sunday in 1722. A late Peruvian invasion which brought smallpox and took away slaves was the main cause of loss of population. It is not a very hospitable place for agriculture and the Rapa Nuins cut down most of the trees (probably trying to turn it into farmland) which made it difficult to build new sea-going canoes which among other things were needed for fishing.
These were the first Moai that we saw:
Another view of a few of them and some more current additions.
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