The Geometrical Work of Girard Desargues

Field, J. V.; Gray, Jeremy; Desargues, Gérard

doi:10.1007/978-1-4613-8692-6

Cited by 62 publications

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“…In the course of the fifteenth and sixteenth centuries, the interest in the technique of linear perspective moved from artistic circles to scientific and mathematical ones (mathematicians such as Commandino, Benedetti and Danti can be mentioned here). Desargues was the first who described a new method of making an accurate perspective drawing (in 1636 and in 1639), and the modern term 'point at infinity' appeared for the first time (Field & Gray, 1987). Given such innovative work, it may seem surprising that the subject did not develop rapidly in the following years.…”

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confidence: 96%

“…Geometrical roots of actual infinity lie in the fifteenth century and are closely related to the development of new art forms, in particular to perspective drawing, with which artists wanted to achieve an illusion of a third dimension. 'De pictura' by Leone Battista Alberti (1404-1472) is the earliest surviving account of a perspective construction (Field & Gray, 1987). He formulated the theory based on planar projections, or how all lines in the object that are perpendicular to the plane of the picture meet at the 'vanishing point' when they are represented in perspective in the picture.…”

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Analysis of factors influencing the understanding of the concept of infinity

Kolar

Čadež

2011

Educ Stud Math

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The article discusses the understanding of infinity in children, teachers and primary teacher students. It focuses on a number of difficulties that people cope with when dealing with problems related to infinity such as its abstract nature, understanding of infinity as an ongoing process which never ends, understanding of infinity as a set of an infinite number of elements and understanding of well-known paradoxes. In the empirical section of the article, a study is described that was conducted at the Faculty of Education, University of Ljubljana, Slovenia. It encompassed 93 third-year students of the Primary Teacher Education study programme with the aim of researching their understanding of the concept of infinity. The focus was on finding out how primary teacher students who received no in-depth instruction on abstract mathematical content understand different types of infinity: infinitely large, infinitely many and infinitely close, what argumentation they provide for their answers to problems on infinity and what their basic misunderstandings about infinity are. The results show that the respondents' understanding of infinity depends on the type of the task and on the context of the task. The respondents' justifications for the solutions are based both on actual and on potential infinity. When solving tasks of the types 'infinitely large' and 'infinitely many', they provide justifications based on actual infinity. When solving tasks of the type 'infinitely close', they use arguments based on potential infinity. We conclude that when they feel unsure of themselves, they resort to their primary method of dealing with infinity, that is, to potential infinity.Keywords Infinity . Concept of infinity . Potential infinity . Actual infinity . Primary teacher students Potential and actual infinityIn the literature, the understanding of the notion of infinity is associated with two different concepts-the concept of potential infinity and the concept of actual infinity (Dubinsky, Educ Stud Math (2012) 80:389-412

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Analysis of factors influencing the understanding of the concept of infinity

Kolar

Čadež

2011

Educ Stud Math

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“…We use this diagram not only because of its Desargues's theorem as illustrated by Bosse, from [11]. We have enlarged the labels from the original diagram.…”

Section: Drawing On Coxetermentioning

confidence: 99%

Drawing on Desargues

Crannell

Douglas

2012

Math Intelligencer

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“…Nevertheless, Desargues first studied the projective properties in a systematic manner. As to Desargues' works, see Desargues, 1951 andDesargues, 2011. As to the literature, without any claim to be exhaustive, we mention: Andersen, 1991;Catastini & Ghione, 2005a;Catastini & Ghione, 2005b;Field & Gray, 1987;Hogendijk, 1991;Le Goff, 1993;Le Goff 1994;Le Goff, 2005;Lenger, 1950;Swinden, 1950. With regard to the whole history of geometry a fundamental reference point is Chasles, 1837.…”

Section: Introduction: Federigo Enriques and His Geometrymentioning

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The Geometrical Foundation of Federigo Enriques’ Gnoseology and Epistemology

Bussotti¹,

Pisano²

2015

AHS

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The purpose of this paper is to valuate the role of geometry inside Enriques' theory of knowledge and epistemology. Our thesis is that such a role is prominent. We offer a particular interpretation of Enriques' gnoseology, according to which geometry is the cornerstone to fully catch also the way in which he framed his conception of the history of science, of the origin of philosophy and of mathematics' foundations. Our argumentation is divided into three sections: in the first one, we provide the reader with Enriques' ideas on the physiological and conceptual bases of geometry. We distinguish between the primary and the secondary intuitions and expound the role Enriques ascribes to history inside the construction of human mind. In the second section, Enriques' idea that philosophy was born as a rational geometry is expounded. In the third section we see what foundations of mathematics means in Enriques' speculation. The reader will be in front of a thinker, whose theories are not separated one from the other, rather they are strictly connected. Geometry is the link which ties the various parts of Enriques' theories and contributions. The Italian mathematician was an important thinker inside the European cultural milieu oriented towards scientific philosophy. In different forms, and with different ideas, mathematicians, philosophers, scientists as Mach, Poincaré, Hilbert, Painlevé-only to mention the most famous oneswere members of such a milieu, which, between the end of the 19 th century and the beginning of the first world war, hoped to construct a philosophy based on science, whose value should have not been only scientific, but socio-anthropological, as well.

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The Geometrical Work of Girard Desargues

Cited by 62 publications

References 0 publications

Analysis of factors influencing the understanding of the concept of infinity

Analysis of factors influencing the understanding of the concept of infinity

Drawing on Desargues

The Geometrical Foundation of Federigo Enriques’ Gnoseology and Epistemology

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