17th century arguments for the impossibility of the indefinite and the definite circle quadrature
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17th century arguments for the impossibility of the indefinite and the definite circle quadrature. / Lützen, Jesper.
I: Revue d'histoire des Mathematiques, Bind 20, Nr. 2, 2014, s. 211-251.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - 17th century arguments for the impossibility of the indefinite and the definite circle quadrature
AU - Lützen, Jesper
PY - 2014
Y1 - 2014
N2 - The classical problem of the quadrature (or equivalently the rectification) of the circle enjoyed a renaissance in the second half of the 17th century. The new analytic methods provided the means for the discovery of infinite expressions of and for the first attempts to prove impossibility statements related to the quadrature of the circle. In this paper the impossibility arguments put forward by Wallis, Gregory, Leibniz and Newton are analyzed and the controversies they gave rise to are discussed. They all deal with the impossibility of finding an algebraic expression of the area of a sector of a circle in terms of its radius and cord, or of the area of the entire circle. It is argued that the controversies were partly due to a lack of precision in the formulation of the results. The impossibility results were all part of a constructive problem solving mathematical enterprise. They were intended to show that certain solutions of the quadrature problem were the best possible because simpler (analytic) solutions were impossible.
AB - The classical problem of the quadrature (or equivalently the rectification) of the circle enjoyed a renaissance in the second half of the 17th century. The new analytic methods provided the means for the discovery of infinite expressions of and for the first attempts to prove impossibility statements related to the quadrature of the circle. In this paper the impossibility arguments put forward by Wallis, Gregory, Leibniz and Newton are analyzed and the controversies they gave rise to are discussed. They all deal with the impossibility of finding an algebraic expression of the area of a sector of a circle in terms of its radius and cord, or of the area of the entire circle. It is argued that the controversies were partly due to a lack of precision in the formulation of the results. The impossibility results were all part of a constructive problem solving mathematical enterprise. They were intended to show that certain solutions of the quadrature problem were the best possible because simpler (analytic) solutions were impossible.
KW - Faculty of Science
KW - Matematikkens historie
KW - Cirklens kvadratur
KW - Wallis
KW - Gregory
KW - Leibniz
KW - Newton
M3 - Journal article
VL - 20
SP - 211
EP - 251
JO - Revue d'Histoire des Mathematiques
JF - Revue d'Histoire des Mathematiques
SN - 1262-022X
IS - 2
ER -
ID: 129881711