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.

In: Revue d'histoire des Mathematiques, Vol. 20, No. 2, 2014, p. 211-251.

Research output: Contribution to journalJournal articleResearchpeer-review

Harvard

Lützen, J 2014, '17th century arguments for the impossibility of the indefinite and the definite circle quadrature', Revue d'histoire des Mathematiques, vol. 20, no. 2, pp. 211-251.

APA

Lützen, J. (2014). 17th century arguments for the impossibility of the indefinite and the definite circle quadrature. Revue d'histoire des Mathematiques, 20(2), 211-251.

Vancouver

Lützen J. 17th century arguments for the impossibility of the indefinite and the definite circle quadrature. Revue d'histoire des Mathematiques. 2014;20(2):211-251.

Author

Lützen, Jesper. / 17th century arguments for the impossibility of the indefinite and the definite circle quadrature. In: Revue d'histoire des Mathematiques. 2014 ; Vol. 20, No. 2. pp. 211-251.

Bibtex

@article{4569cc9344d74a028d0f6cef34b98615,
title = "17th century arguments for the impossibility of the indefinite and the definite circle quadrature",
abstract = "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. ",
keywords = "Faculty of Science, Matematikkens historie, Cirklens kvadratur, Wallis, Gregory, Leibniz, Newton",
author = "Jesper L{\"u}tzen",
year = "2014",
language = "English",
volume = "20",
pages = "211--251",
journal = "Revue d'histoire des Mathematiques",
issn = "1262-022X",
publisher = "Societe Mathematique de France",
number = "2",

}

RIS

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