- Italian mathematician
who pioneered modern non-Euclidean geometry. His work ranged over
almost the whole field of pure and applied mathematics, but especially
theories of surfaces and space of constant curvature.
Beltrami was born in Cremona, Lombardy, and studied mathematics at
Pavia. He held academic posts at Bologna, Pisa, Pavia, and Rome.
In 1862 he published his first paper, an analysis of the differential
geometry of curves, to which he would return in his most important
paper, 'Saggio di interpretazione della geometria non-euclidia' 1868.
This advanced a theory of hyperbolic space that laid the analytical
base for the development of non-Euclidean geometry.
Beltrami demonstrated that the concepts and formulae of Russian mathematician
Nikolai Lobachevsky's geometry are realized for geodesics on surfaces
of constant negative curvature. He showed also that there are rotation
surfaces of this kind - he called them 'pseudospherical surfaces'.
He also demonstrated the usefulness of employing differential parameters
in surface theory, thereby beginning the use of invariant methods
in differential geometry.
After 1872 Beltrami switched his attention to questions of applied
mathematics, especially problems in elasticity and electromagnetism.
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