{"title":"Peano on definition of surface area","authors":"G. H. Greco, S. Mazzucchi, Enrico Pagani","doi":"10.4171/RLM/734","DOIUrl":null,"url":null,"abstract":"In this paper we investigate the evolution of the concept of area in Peano's works, taking into account the main role played by Grassmann's geometric-vector calculus and Peano's theory on derivative of measures. Geometric (1887) and bi-vectorial (1888) Peano's approaches to surface area mark the development of this topic during the first half of the last century. In the sequel we will present some significative contributions on surface area that are inspired and/or closely related to Peano's definition.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/RLM/734","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper we investigate the evolution of the concept of area in Peano's works, taking into account the main role played by Grassmann's geometric-vector calculus and Peano's theory on derivative of measures. Geometric (1887) and bi-vectorial (1888) Peano's approaches to surface area mark the development of this topic during the first half of the last century. In the sequel we will present some significative contributions on surface area that are inspired and/or closely related to Peano's definition.
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