differential geometry of surfaces造句

• A treatise covering virtually every aspect of the 19th century differential geometry of surfaces.
• Between 1844 and 1867 he published a series of papers on the differential geometry of surfaces.
• The differential geometry of surfaces captures many of the key ideas and techniques characteristic of this field.
• Monge Amp鑢e equations frequently arise in differential geometry, for example, in the Minkowski problems in differential geometry of surfaces.
• It is a very broad and abstract generalization of the differential geometry of surfaces in "'R "'3.
• Phys ., " 1905, 18, p . 941 ) founded his theory of aberrations on the differential geometry of surfaces.
• Established the theory of surfaces, and introduced the idea of principal curvatures, laying the foundation for subsequent developments in the differential geometry of surfaces.
• Riemann found the correct way to extend into " n " dimensions the differential geometry of surfaces, which Gauss himself proved in his " theorema egregium ".
• For a more elementary discussion see the article on curvature which discusses the curvature of curves and surfaces in 2 and 3 dimensions, as well as the differential geometry of surfaces.
• Darboux's contribution to the differential geometry of surfaces appears in the four-volume collection of studies he published between 1887 and 1896; see links below for access to these texts.
• Although Gauss was the first to study the differential geometry of surfaces in "'E "'3, it was not until Riemann's Habilitationsschrift of 1854 that the notion of a Riemannian space was introduced.
• In 1896 he made two important contributions : he proved the prime number theorem, using complex function theory ( also proved independently by Charles Jean de la Vall閑-Poussin ); and he was awarded the Bordin Prize of the French Academy of Sciences for his work on geodesics in the differential geometry of surfaces and dynamical systems.
• He " attributed his interest in geometry both to his work at Wesleyan and Goettingen and to summers spent working on his grandfather's farm . " His particular interests were in the fields of the geometry of curves and surfaces ( curves, differential geometry of surfaces ), algebraic planes and twisted curves ( algebraic geometry, algebraic curves, twisted curves ), homeomorphic sets of lines in a plane ( line coordinates ), the theory of invariants, relativity in mechanics, and correspondences.