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Think in terms of the trinity, and you've got one reason. One of the major mysteries of the Christian faith is how the divinity can be three in one: father, son, and holy spirit. In Satan's three faces, Dante gives us an inverted trinity. Other trios also come from Christian theology. It is not Dante who invented purgatory, which gives a tri-part afterlife, but the larger Christian tradition. Likewise, when he finds himself in the middle of the forest and his life at the start of the poem, he is given a natural triad: the present, the past, and the future.
three is an important number. dante expresses a lot of religious beliefs and 3 stands for the holy trinity! 3 books with 33 cantos plus the 1 canto as a preface equals 100.
Dante also writes in terza rima-verses of three lines with the rhyme scheme aba bcb cdc. It's a very difficult rhyme scheme to use in English, but it works well in Italian where so many more words rhyme.
The numbers 3 and 7 are the most sacred books in the Christian Bible. Three was the number of the trinity, the three parts of God. In fact, the number 3 is referenced 467 times in the bible. The number 2 was a symbol of completeness and perfection. Dante was a Christian so he would have been well aware of this fact and would have written it into his work.
Not only that, but Dante lived during the time of the Renaissance. Renaissance art was heavily peppered with the number of three. Figures were painted in sets of three, within triangles of three. The number 3 is also referenced many times in the book of Revelation, which foretells the end of the world as we know it.
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