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===History===
An early form of height function was proposed by [[Giambattista Benedetti]] (c. 1563), who argued that the [[consonance]] of a [[interval (music)|musical interval]] could be measured by the product of its numerator and denominator (in reduced form); see {{slink|Giambattista Benedetti|Music}}.{{cn|date=November 2022}}
Heights in Diophantine geometry were initially developed by [[André Weil]] and [[Douglas Northcott]] beginning in the 1920s.<ref>{{harvs|txt||last=Weil|authorlink=André Weil|year=1929}}</ref> Innovations in 1960s were the [[Néron–Tate height]] and the realization that heights were linked to projective representations in much the same way that [[ample line bundle]]s are in other parts of [[algebraic geometry]]. In the 1970s, [[Suren Arakelov]] developed Arakelov heights in [[Arakelov theory]].<ref>{{harvs|txt|last=Lang|authorlink=Serge Lang|year=1988}}</ref> In 1983, Faltings developed his theory of Faltings heights in his proof of Faltings's theorem.<ref>{{harvs|txt|last=Faltings|authorlink=Gerd Faltings|year=1983}}</ref>
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