Throughout his Comedia, and especially within the Inferno, Dante draws much use from numerology. Numbers pervade the work as a whole, and not only divide individual cantos within the text from each other, but also partition the physical locations that the poem describes, distinguish the caste of each individual sinner or saint, and generally do the work of assigning a fixed, specific value to each and every concrete item in the poem. Because he is so meticulously logical in his approach to writing, almost everything in Dante's work has its number, and almost every number has its own meaning. It is interesting, then, to consider why it is that certain numbers among those that Dante puts to use are repeated to the degree that they are. Threes, for instance, are quite literally everywhere in the Inferno, stretching from Dante's first encounter with the opening encounter with the three different beasts of Canto I to the three mouths of Satan, the poem's final image. It has been said that no shape is as powerful as the triangle, and as much use as Dante makes of numbers in the Comedia, no digit gets nearly the amount of attention that the number three does, except perhaps for its multiples. Threes provide a structure not only for the poetry and overall design of Dante's work, but also for it's landscape, for the attributes of creatures that populate the Inferno, and finally, for the punishment of sinners that are damned eternally.

The most immediate uses of threes that appear in the Inferno are found in the poem's overall structure and its rhyme scheme. There are, most obviously, three books to the Comedia itself (Inferno, Purgatorio, and Paradisio), each with thirty-three cantos apiece if one does not count the opening, introductory canto of the Inferno. Important events tend to occur in cantos that are multiples of three - Charon appears in III, Cerberus in VI, Dis in IX, the Plain of Fire in XII, Malebolge in XVIII, and so on. The poem also employs a unique, interlocking terza rima rhyme scheme (aba bcb cdc...) that seems to be Dante's own invention. With this device, the number three can literally permeate the whole of the Comedia, since each line of the poem finds a rhyme with two others (excepting the couplets that close each canto, of course).
Threes also saturate the physical landscape of the Inferno. Nine circles - three times three - compose the whole of Hell's organization, dividing up sinners according to one of three distinct categories: incontinence, violence, or, worst of all, fraud. Three separate ferrymen are required for passage across three distinct rivers - Acheron, Styx, and Phlegethon - the first of which appears in Canto III. This canto also denotes Dante's arrival at Hell; likewise, the hellish metropolis Dis begins at the sixth circle (in the ninth canto) and contains within it three circles, the Plain of Fire, Malebolge, and the Pit, respectively.

Creatures that appear in the Inferno almost always represent the number three in some way, either through some single attribute that has triplicate aspect or by appearing with two other identical monsters. Three beasts, the leopard, the wolf, and the lion - which perhaps correspond to the three categories of sin mentioned above - intercept Dante in Canto I and find their opposites in the three saints, Lucy, the Virgin Mary, and (of course) Beatrice, described to Dante in Canto II. Cerberus, himself in the third circle of hell, is a demon composed of three heads, and three Furies assault Dante just outside of the gates of Dis. The monster Geryon - whom John Ciardi notes as "a mythical king of Spain represented as a giant with three heads and three bodies" - contains three animal aspects in Dante, a scaly, reptilian body, hairy lion's arms, and a scorpion's tail, each of which - again - can possibly be aligned with the three different categories of sin. Finally, the Satan that the reader encounters in Canto XXXIV of the Inferno possesses three mouths for chewing three separate sinners, Brutus, Cassius, and Judas Iscariot.

Sinners who are punished in the Inferno themselves are often categorized by or found in threes. Dante finds, for instance, three sinners linked together in a wheel in Canto XVI and three in Satan's mouth. Also, as previously mentioned, three castes of sin divide all of the sinners from each other: incontinence, violence, and fraud. Violence itself can be broken down into three separate categories, that which is enacted towards others, that which is directed at the self, and that which is violent towards God; for this reason, circle seven of the Inferno has three rings. Furthermore, violence towards God manifests itself, according to Dante, in one of three different ways: as direct violence towards the Almighty (blasphemy), as violence towards Nature (sodomy), or as violence towards Art (usury). God, Nature, and Art themselves have a familial relation, the first being the father of the second, which itself is the parent of the third.

Another interesting formula of note in the Inferno is the three-plus-one equation. Three saints plus Virgil are introduced in Canto II of the poem, three monsters plus one are encountered before Dis, nine plus one pouches compose the geography of Malebolge, sins of Betrayal contain four sub-categories, and thirty-three plus one cantos make up the work itself. This is perhaps because there are three components to the Holy Trinity and one overarching Unity.

This Trinity itself provides one possible reason for each of the poems threes: Dante, obviously, wrote the Comedia as a deeply Christian work, and would have understood three to be a deeply theological number. Each of the tertiary structures in his poem can therefore be rationalized as a miniature religious reference to itself, and it makes a sort of logical sense that a poem that itself can be viewed as a reworking of the Bible would be composed so neatly and so fully out of the number three.

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