Post #557473

2026-02-27 11:18 UTC

In 1948, François Le Lionnais (1901–84) published an essay in which he distinguished two types of beauty in mathematics: • ‘Classical’ mathematical beauty, which impressed by its control and austerity. • ‘Romantic’ mathematical beauty, which manifested in wildness, non-conformity, and strangeness. Classical beauty was found where there was unification, such as in the 9-point circle of a triangle (see 1st attached image), or how the circle, ellipse, hyperbola, and parabola all arise from the focus–directrix construction (see 2nd attached image) and from conic sections, and can transformed into one another by projective transformations. 1/3 #MathematicalBeauty #ClassicalBeauty #Classicism #RomanticBeauty #Romanticism #ClassicalVsRomantic #aesthetics

Replies (1)

@ajcain@mathstodon.xyz 2026-02-27 11:20

Romantic beauty could arise from unexpectedness, such as the formulae for the volumes and surface areas of $n$-dimensional unit spheres reaching their maximums at non-integer values (see 1st attached image). The tractroid pseudosphere (see 2nd attached image) also had romantic beauty, for it was in some ways close to the sphere, having constant Gaussian curvature (negative, while the sphere's is positive), and the same surface area as the sphere, and finite volume (equal to half of the sphere), but was in other respects wild, having infinite extent. The cycloid had both classical beauty – in its simple definition — and romantic beauty — in its unexpected appearance as the solutions to the tautochrone and brachistochrone problems, contrary to intuition. 2/3

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