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27 de abr. de 2024 · Some concepts considered here, such as those of a group by Galois or a topos by Grothendieck, were more radically innovative. Still, however, they had connections with earlier concepts, such as (putting aside the earlier history of which) those of Adrien-Marie Legendre in the case of a group and those of category theory in the case of a topos.
27 de abr. de 2024 · Galois’s and Riemann’s concepts, such as that of a group by Galois and that of a manifold [Manningfaltigkeit] by Riemann, both especially central to this chapter, were more radically innovative, but still not completely, because they had continuities with earlier concepts, such as (among others) those of Adrien-Marie Legendre in the case of Galois and those of Karl Friedrich Gauss in the ...
Hace 12 horas · In 1783, in a paper sent to the Académie, Adrien-Marie Legendre had introduced what are now known as associated Legendre functions. If two points in a plane have polar coordinates (r, θ) and (r ', θ'), where r ' ≥ r, then, by elementary manipulation, the reciprocal of the distance between the points, d, can be written as:
