Post #1670119

2026-02-27 11:20 UTC

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

Replies (1)

@ajcain@mathstodon.xyz 2026-02-27 11:21

References • A.J. Cain. ‘Form & Number: A History of Mathematical Beauty’. Lisbon, 2024. URL: https://archive.org/details/cain_formandnumber_ebook_large pp.671–7. • F. Le Lionnais. ‘La Beauté en Mathématiques’. In: F. Le Lionnais, ed. ‘Les Grands Courants de la Pensée Mathématique’. L'Humanisme Scientifique de Demain. Cahiers du Sud, 1948. • F. Le Lionnais. ‘Beauty in Mathematics’. In: F. Le Lionnais, ed. ‘Great Currents in Mathematical Thought’, vol.2. New York: Dover, 1971. ISBN: 978-0-486-62724-3. URL: https://archive.org/details/greatcurrentsofm0000leli/page/121 (Note: translation is sometimes very free, and some quotations have been distorted by being translated from English to French and back.) Images from ‘Form & Number’, figures 19.3, 19.4, 19.5, and 19.6. 3/3

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