proteins - Why are 3 nucleotides used as codons for amino-acid mapping in DNA?

DNA is made of 4 unique nucleotides. When coding for a protein, a sequence of 3 nucleotides is used to code for each amino acid. Why are codons 3 nucleotides in length?

A related question can be found here: why-are-there-exactly-four-nucleobases-in-dna