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In Flatland, the story is told of how a 2D sphere, S^2, passing through a place, R^2, would appear as a point (at first tangency), then grow to a maximum equatorial circle, then shrink to a point as it leaves the plane.

Taking the analogous geometry in one higher dimension. Dante's sphere was S^3 slicing R^3, which yields a sphere growing from Heaven Tthrough the "equatorial" terrestrial sphere to Hell. This cosmology resolved an apparent paradox of how could concentric sphere's be arranged between Heaven and Hell, focussed respectively on the point-like poles of God and Satan. (Thanks to Freccero for drawing attention to an article in which this cosmology appeared.)

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