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They are commonly known as Areca Nuts. The nuts are seeds of the Areca palm found in the tropical Pacific, Asia, and parts of east Africa. Technically, they are not nuts, the areca is a fruit and can be found in similar forms as our typical fruits such as dried and fresh.
Believe it or not, the betel nut can be chewed wrapped in betel leaves. Hence, the Betel Nut name it is commonly known as. Why are these chewed? When the nuts are chewed, there is a stimulant effect on the person. The effect varies by person, but usually it's no more than a cup of coffee. The fruits are found to cause many cancers in the mouth. From what I can tell, the areca are as common in Asia as peanuts or raisins for instance in the US.
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Below are pictures of the Areca Nuts you might find interesting. The fruit uncut, and the inside of the fruit and the trees from which they come.
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Photos were pulled from Wikipedia.