Dante's Underworld

In writing his wonderful poem, the Divine Comedy, Dante Alighieri described very precisely the structure of the three worlds visited in his journey. It is sure that the Poet saw, in his mind, concrete shapes and dimensions, and he tried, through his verses, to explain to us that the Hell, the Purgatory and the Heaven are real. Starting from several quantitative information included in the Comedy, it is possible to obtain physical features of the worlds imagined by Dante, such as the depth of the Hell, or the width of the circles, the height of the Purgatory and also the strange shape of the Heaven, impossible to describe with a three-dimensional geometry. Using elementary mathematical relations, I will show that the structure of the three kingdoms is consistent and, finally, I will point out Alighieri’s genius not only in term of poetical ability, but also on a scientific basis.