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.
The number 3 is everywhere in Dante Alighieri's Divine Comedy. For one thing, the poem itself is structured according to the rhyme scheme terza rima, which uses stanzas of three lines that employ interlocking rhymes (aba bcb cdc, etc.). Additionally, there are nine circles of Hell (three multiplied by three), Satan has three faces, and three beasts (a lion, a leopard, and a wolf) threaten Dante at the beginning of the Inferno. There are many more examples of three, but the overall important thing to understand is that the number three largely governs the structure of Dante's poem. Indeed, you can think of the number three as the scaffolding on which the rest of the poem's content is hung. This number is significant because three is a central number in the Judeo-Christian tradition, especially in terms of the Trinity (Father, Son, and Holy Spirit). As such, just as the whole of the Christian world is governed by a three-in-one God, Dante's poem is governed by the number three. Thus, Dante's obsession with the number three mirrors the prevalence of three in the Christian tradition.
3 was his favorite number. Also 9 circles of Hell are depicted in the Inferno. 3 also represents the father, son and the holy spirit.
The first four odd numbers have great religious and spiritual significance. One refers to the individual, as we all are. Three can refer to the Holy Trinity, or to the life cycle created as two parents produce a child. Five is the number of main appendages on the human body, contributing to the star and pentagram symbols, and seven is even more mysterious as it is referenced in many fantasy novel cycles as being one of the numbers most closely associated with a deity figure. So, due to the Judeo-Christian source material that writers such as Dante Alighieri and John Milton based their classic works on, the prevalence of numbers such as these is not surprising.
In medieval Italy, the period and place in which Dante lived, many people believed that numbers had metaphysical significance. In “Dante’s Inferno” we see the number three appear many times. The church was central in Italian culture during medieval times, and three is a significant number in Christianity and to Dante because it represents the Holy Trinity. Each verse of the canto has three lines, Hell has three divisions, it takes Dante three days to travel through the inferno, and there are nine circles of Hell, which is three multiplied by three – these are just a few examples of the presence of the number three in "Dante's Inferno."
Dante's Comedia is a thoroughly Christian work with deep ties to theology, church tradition, and Biblical allusions. The number three is highly significant in Christian tradition in that it links to the Trinity - Father, Son, and Holy Ghost - as well as to Jesus' death and resurrection, as he was crucified and rose again three days later. Dante weaves the number three throughout his work down to the meter itself, which he invented specifically for the work. The meter is called terza rima with the rhyme scheme aba bcb cdc, which further illustrates the Biblical mystery he's trying to convey in that the three parts of the rhyme scheme, representing the three parts of the Trinity, all work together to form the whole of the line. Additionally, the three parts of the Comedia - Inferno, Purgatorio, and Paradiso - all work together to form the whole of Dante's journey. As far as the three heads of Dante's Satan, they represent an inversion of the Trinity, which is the perfect image of Satan for Dante. The reason for Satan's downfall was that he tried to be like and usurp God - who is the ultimate Trinity.
I hope that helps you understand Dante's work better! Good luck!
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.
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.