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1 — 50 / 177
  1. added 2020-05-21
    Are the Notions of Past, Present and Future Compatible with the General Theory of Relativity?Daniel David Sega Neuman & Daniel Galviz - manuscript
    The notions of time and causality are revisited, as well as the A- and B-theory of time, in order to determine which theory of time is most compatible with relativistic spacetimes. By considering orientable spacetimes and defining a time-orientation, we formalize the concepts of a time-series in relativistic spacetimes; A-theory and B-theory are given mathematical descriptions within the formalism of General Relativity. As a result, in time-orientable spacetimes, the notions of events being in the future and in the past, which (...)
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  2. added 2020-03-20
    Ancient Greek Geometry of Motion and its Further Development by Galileo and Newton.Mario Bacelar Valente - manuscript
    in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first (...)
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  3. added 2020-03-20
    From Practical to Pure Geometry and Back.Mario Bacelar Valente - manuscript
    The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically (...)
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  4. added 2020-02-11
    Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Michael Boylan - 1983 - Philosophy of Science 50 (4):665-668.
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  5. added 2020-01-27
    Andalò di Negro’s De Compositione Astrolabii: A Critical Edition with English Translation and Notes.Bernardo Mota, Samuel Gessner & Dominique Raynaud - 2019 - Archive for History of Exact Sciences 73 (6):551-617.
    In this article, we publish the critical edition of Andalò di Negro’s De compositione astrolabii, with English translation and commentary. The mathematician and astronomer Andalò di Negro presumably redacted this treatise on the astrolabe in the 1330s, while residing at the court of King Robert of Naples. The present edition has three purposes: first, to make available a text missing from the previous compilations of works by Andalò di Negro; second, to revise a privately circulated edition of the text; and (...)
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  6. added 2020-01-20
    Figure..Stephen Lester Thompson - manuscript
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  7. added 2020-01-05
    Continua.Lu Chen - 2020 - Dissertation, University of Massachusetts Amherst
    The subject of my dissertation is the structure of continua and, in particular, of physical space and time. Consider the region of space you occupy: is it composed of indivisible parts? Are the indivisible parts, if any, extended? Are there infinitesimal parts? The standard view that space is composed of unextended points faces both \textit{a priori} and empirical difficulties. In my dissertation, I develop and evaluate several novel approaches to these questions based on metaphysical, mathematical and physical considerations. In particular, (...)
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  8. added 2019-12-11
    Jeremy J. Gray. János Bolyai, Non‐Euclidean Geometry, and the Nature of Space. Viii + 185 Pp., Illus., Table, Apps. Cambridge, Mass.: MIT Press, 2004. $20. [REVIEW]Joan Richards - 2006 - Isis 97 (2):363-364.
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  9. added 2019-12-11
    How Euclidean Geometry has Misled Metaphysics.Graham Nerlich - 1991 - Journal of Philosophy 88 (4):169-189.
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  10. added 2019-12-11
    Non-Euclidean Geometry and Weierstrassian Mathematics.Thomas Hawkins - 1983 - In Joseph Warren Dauben & Virginia Staudt Sexton (eds.), History and Philosophy of Science: Selected Papers. New York Academy of Sciences.
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  11. added 2019-12-11
    Euclidean Nostalgia.J. Grünfeld - 1983 - International Logic Review 27:41-50.
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  12. added 2019-12-11
    Is Visual Space Euclidean?Patrick Suppes - 1977 - Synthese 35 (4):397 - 421.
  13. added 2019-12-11
    La Géométrie Et le Problème de L'Espace.J. H. Tummers - 1962 - Dialectica 16 (1):56-60.
    RésuméDans cet article, l'auteur discute les principes qui ont guidé M. Gonseth dans ses recherches sur la géométrie et le problème de l'espace. M. Gonseth défend la thèse selon laquelle avant de tenter de résoudre le problème de la géométrie, on doit disposer des facultés d'intuition, de déduction et d'une connaissance expérimentale de l'espace.M. Tummers a publié trois brochures sur la géométrie: 1. De Opbouw der Meetkunde ; 2. De Meetkunde en de Ervaring ; 3. Wijsgerige Verantwoording van het Paralelenpostulaat (...)
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  14. added 2019-10-09
    Explicaciones Geométrico-Diagramáticas en Física desde una Perspectiva Inferencial.Javier Anta - 2019 - Revista Colombiana de Filosofía de la Ciencia 38 (19).
    El primer objetivo de este artículo es mostrar que explicaciones genuinamente geométricas/matemáticas e intrínsecamente diagramáticas de fenómenos físicos no solo son posibles en la práctica científica, sino que además comportan un potencial epistémico que sus contrapartes simbólico-verbales carecen. Como ejemplo representativo utilizaremos la metodología geométrica de John Wheeler (1963) para calcular cantidades físicas en una reacción nuclear. Como segundo objetivo pretendemos analizar, desde un marco inferencial, la garantía epistémica de este tipo de explicaciones en términos de dependencia sintáctica y semántica (...)
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  15. added 2019-09-30
    Kant and the Impossibility of Non‐Euclidean Space.Tufan Kıymaz - 2019 - Philosophical Forum 50 (4):485-491.
    In this paper, I discuss the problem raised by the non-Euclidean geometries for the Kantian claim that the axioms of Euclidean geometry are synthetic a priori, and hence necessarily true. Although the Kantian view of geometry faces a serious challenge from non-Euclidean geometries, there are some aspects of Kant’s view about geometry that can still be plausible. I argue that Euclidean geometry, as a science, cannot be synthetic a priori, but the empirical world can still be necessarily Euclidean.
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  16. added 2019-09-05
    Perceptual Foundations of Euclidean Geometry.Pierre Pica, Elizabeth Spelke & Véronique Izard - manuscript
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  17. added 2019-09-04
    Fine-Structure Constant From Sommerfeld to Feynman.Michael A. Sherbon - 2019 - Journal of Advances in Physics 16 (1):335-343.
    The fine-structure constant, which determines the strength of the electromagnetic interaction, is briefly reviewed beginning with its introduction by Arnold Sommerfeld and also includes the interest of Wolfgang Pauli, Paul Dirac, Richard Feynman and others. Sommerfeld was very much a Pythagorean and sometimes compared to Johannes Kepler. The archetypal Pythagorean triangle has long been known as a hiding place for the golden ratio. More recently, the quartic polynomial has also been found as a hiding place for the golden ratio. The (...)
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  18. added 2019-06-29
    Points as Higher-Order Constructs: Whitehead’s Method of Extensive Abstraction.Achille C. Varzi - forthcoming - In Stewart Shapiro & Geoffrey Hellman (eds.), The Continuous. Oxford: Oxford University Press.
    Euclid’s definition of a point as “that which has no part” has been a major source of controversy in relation to the epistemological and ontological presuppositions of classical geometry, from the medieval and modern disputes on indivisibilism to the full development of point-free geometries in the 20th century. Such theories stem from the general idea that all talk of points as putative lower-dimensional entities must and can be recovered in terms of suitable higher-order constructs involving only extended regions (or bodies). (...)
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  19. added 2019-06-06
    Jesper Lützen. Mechanistic Images in Geometric Form: Heinrich Hertz's Principles of Mechanics. [REVIEW]Christopher Pincock - 2008 - Philosophia Mathematica 16 (1):140-144.
    Philosophers unacquainted with the workings of actual scientific practice are prone to imagine that our best scientific theories deliver univocal representations of the physical world that we can use to calibrate our metaphysics and epistemology. Those few philosophers who are also scientists, like Heinrich Hertz, tend to contest this assumption. As Jesper Lützen relates in his scholarly and engaging book, Hertz's Principles of Mechanics contributed to a lively debate about the content of classical mechanics and what, if anything, this highly (...)
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  20. added 2019-06-06
    What Frege Meant When He Said: Kant is Right About Geometry.Teri Merrick - 2006 - Philosophia Mathematica 14 (1):44-75.
    This paper argues that Frege's notoriously long commitment to Kant's thesis that Euclidean geometry is synthetic _a priori_ is best explained by realizing that Frege uses ‘intuition’ in two senses. Frege sometimes adopts the usage presented in Hermann Helmholtz's sign theory of perception. However, when using ‘intuition’ to denote the source of geometric knowledge, he is appealing to Hermann Cohen's use of Kantian terminology. We will see that Cohen reinterpreted Kantian notions, stripping them of any psychological connotation. Cohen's defense of (...)
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  21. added 2019-06-06
    Coloured Quadrangles. A Guide to the Tenth Book of Euclid's Elements. [REVIEW]Ivor Bulmer-Thomas - 1983 - The Classical Review 33 (1):143-144.
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  22. added 2019-06-06
    Technology and Instruments Stephen K. Victor Practical Geometry in the High Middle Ages. Artis Cuiuslibet Consummatio, and the Pratike de Geometrie. Philadelphia: American Philosophical Society, 1979. Pp. Xii + 638. [REVIEW]Joann Morse - 1983 - British Journal for the History of Science 16 (2):211-212.
  23. added 2019-06-06
    Philosophy of Geometry From Riemann to Poincaré. [REVIEW]S. L. - 1982 - Review of Metaphysics 35 (3):633-634.
    This deeply researched, carefully constructed and very thoughtful book is fascinating in its own right as well as being indispensable background material for anyone interested in current philosophical thought about space, time, and geometry.
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  24. added 2019-01-31
    Review of 'Inconsistent Geometry', by Chris Mortensen. [REVIEW]Zach Weber - 2012 - Australasian Journal of Philosophy 90 (3):611-614.
    Australasian Journal of Philosophy, Volume 90, Issue 3, Page 611-614, September 2012.
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  25. added 2019-01-28
    What Is the Validity Domain of Einstein’s Equations? Distributional Solutions Over Singularities and Topological Links in Geometrodynamics.Elias Zafiris - 2016 - 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year.
    The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...)
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  26. added 2019-01-28
    The Nature of Local/Global Distinctions, Group Actions and Phases: A Sheaf=Theoretic Approach to Quantum Geometric Spectra.Elias Zafiris - 2015 - In Vera Bühlmann, Ludger Hovestadt & Vahid Moosavi (eds.), Coding as Literacy - Metalithicum IV. Basel: BIRKHÄUSER. pp. 172-186.
  27. added 2019-01-27
    Differential Sheaves and Connections: A Natural Approach to Physical Geometry.Anastasios Mallios & Elias Zafiris - 2015 - World Scientific.
    This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to "physical geometry". In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory (...)
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  28. added 2018-12-29
    Is Geometry Analytic?David Mwakima - 2017 - Dianoia 1 (4):66 - 78.
    In this paper I present critical evaluations of Ayer and Putnam's views on the analyticity of geometry. By drawing on the historico-philosophical work of Michael Friedman on the relativized apriori; and Roberto Torretti on the foundations of geometry, I show how we can make sense of the assertion that pure geometry is analytic in Carnap's sense.
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  29. added 2018-12-15
    The Value of Pi in the Bible (And What It Tells Us About Biblical Hermeneutics).James H. Cumming - manuscript
    This short two-page essay provides irrefutable evidence that the Bible was encoded by its original redactors. Critical scholarship on the Bible needs to take ancient Jewish hermeneutical methods seriously.
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  30. added 2018-12-12
    A Philosopher Looks at Non-Commutative Geometry.Nick Huggett - manuscript
    This paper introduces some basic ideas and formalism of physics in non-commutative geometry. My goals are three-fold: first to introduce the basic formal and conceptual ideas of non-commutative geometry, and second to raise and address some philosophical questions about it. Third, more generally to illuminate the point that deriving spacetime from a more fundamental theory requires discovering new modes of `physically salient' derivation.
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  31. added 2018-11-08
    A Priori Concepts in Euclidean Proof.Peter Fisher Epstein - 2018 - Proceedings of the Aristotelian Society 118 (3):407-417.
    With the discovery of consistent non-Euclidean geometries, the a priori status of Euclidean proof was radically undermined. In response, philosophers proposed two revisionary interpretations of the practice: some argued that Euclidean proof is a purely formal system of deductive logic; others suggested that Euclidean reasoning is empirical, employing concepts derived from experience. I argue that both interpretations fail to capture the true nature of our geometrical thought. Euclidean proof is not a system of pure logic, but one in which our (...)
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  32. added 2018-10-21
    Prolegomena to a Cognitive Investigation of Euclidean Diagrammatic Reasoning.Yacin Hamami & John Mumma - 2013 - Journal of Logic, Language and Information 22 (4):421-448.
    Euclidean diagrammatic reasoning refers to the diagrammatic inferential practice that originated in the geometrical proofs of Euclid’s Elements. A seminal philosophical analysis of this practice by Manders (‘The Euclidean diagram’, 2008) has revealed that a systematic method of reasoning underlies the use of diagrams in Euclid’s proofs, leading in turn to a logical analysis aiming to capture this method formally via proof systems. The central premise of this paper is that our understanding of Euclidean diagrammatic reasoning can be fruitfully advanced (...)
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  33. added 2018-06-06
    Poincaré on the Foundation of Geometry in the Understanding.Jeremy Shipley - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Springer. pp. 19-37.
    This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...)
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  34. added 2018-03-30
    Fundamental Physics and the Fine-Structure Constant.Michael A. Sherbon - 2017 - International Journal of Physical Research 5 (2):46-48.
    From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.
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  35. added 2018-03-21
    A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
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  36. added 2018-02-18
    John von Neumann's Mathematical “Utopia” in Quantum Theory.Giovanni Valente - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):860-871.
    This paper surveys John von Neumann's work on the mathematical foundations of quantum theories in the light of Hilbert's Sixth Problem concerning the geometrical axiomatization of physics. We argue that in von Neumann's view geometry was so tied to logic that he ultimately developed a logical interpretation of quantum probabilities. That motivated his abandonment of Hilbert space in favor of von Neumann algebras, specifically the type II1II1 factors, as the proper limit of quantum mechanics in infinite dimensions. Finally, we present (...)
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  37. added 2018-01-28
    On the Chow Ring of a Flag.Christian Wenzel - 1997 - Mathematische Nachrichten 188:293-310.
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  38. added 2018-01-28
    On the Structure of Non-Reduced Parabolic Subgroup-Schemes.Christian Wenzel - 1994 - Proceedings of Symposia in Pure Mathematics 56 (1):291-297.
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  39. added 2018-01-28
    Rationality of G/P for a Non-Reduced Parabolic Subgroup Scheme P.Christian Wenzel - 1993 - Proceedings of the American Mathematical Society 117 (4):899-904.
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  40. added 2018-01-28
    Classification of All Parabolic Subgroup Schemes of a Reductive Linear Algebraic Group Over an Algebraically Closed Field.Christian Wenzel - 1993 - Transactions of the American Mathematical Society 337 (1):211-218.
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  41. added 2018-01-22
    Géométrie pratique. Géomètres, ingénieurs, architectes, XVIe-XVIIIe siècles.Dominique Raynaud (ed.) - 2015 - Besançon: Presses universitaires de Franche-Comté.
    Actes du colloque de Grenoble (8-9 octobre 2009), avec les contributions de Samuel Gessner (Lisbone), Eberhard Knobloch (Berlin), Jorge Galindo Díaz (Bogotá), Joël Sakarovitch (Paris) et Dominique Raynaud (Grenoble).
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  42. added 2017-12-01
    Vitale Giordano: Un matematico bitontino nella Roma barocca.Francesco Tampoia - 2005 - Rome: Armando.
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  43. added 2017-11-25
    Iter Italicum and Leibniz/Giordano Correspondence.Francesco Tampoia - manuscript
    Letters exchanged by scientists are a crucial source by which to trace the process that accompanies their scientific evolution. In this paper -accomplished through a historical approach- I aim to throw new light on Leibniz's continuing interest in classical geometry and to stress the significance of his correspondence with the Italian mathematician Vitale Giordano.
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  44. added 2017-11-01
    Inequivalent Representations of Geometric Relation Algebras.Steven Givant - 2003 - Journal of Symbolic Logic 68 (1):267-310.
    It is shown that the automorphism group of a relation algebra ${\cal B}_P$ constructed from a projective geometry P is isomorphic to the collineation group of P. Also, the base automorphism group of a representation of ${\cal B}_P$ over an affine geometry D is isomorphic to the quotient of the collineation group of D by the dilatation subgroup. Consequently, the total number of inequivalent representations of ${\cal B}_P$ , for finite geometries P, is the sum of the numbers ${\mid Col(P)\mid\over (...)
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  45. added 2017-10-30
    Erratum and Addendum To: The BV-Energy of Maps Into a Manifold: Relaxation and Density Results.Mariano Giaquinta & Domenico Mucci - 2007 - Annali della Scuola Normale Superiore di Pisa 6 (1):185-194.
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  46. added 2017-10-30
    The BV-Energy of Maps Into a Manifold: Relaxation and Density Results.Mariano Giaquinta & Domenico Mucci - 2006 - Annali della Scuola Normale Superiore di Pisa 5 (4):483-548.
    Let ${\cal Y}$ be a smooth compact oriented riemannian manifoldwithout boundary, and assume that its $1$-homology group has notorsion. Weak limits of graphs of smooth maps $u_k:B^n\rightarrow {\cal Y}$ with equibounded total variation give riseto equivalence classes of cartesian currents in $\mathop {\rm cart}\nolimits ^{1,1}$ for which we introduce a natural$BV$-energy.Assume moreover that the first homotopy group of ${\cal Y}$ iscommutative. In any dimension $n$ we prove that every element $T$ in $\mathop {\rm cart}\nolimits ^{1,1}$ can be approximatedweakly in the (...)
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  47. added 2017-10-26
    Philosophy of Science and Scientific Controversy: A Variety of Physical Conceptions and of Philosophical Interpretations of Quantum Physics.Olival Freire Júnior - 2013 - Scientiae Studia 11 (4):937-962.
    Este ensaio introdutório faz uma breve apresentação do tratado de óptica atribuído a Euclides de Alexandria, inserindo-o no contexto das teorias sobre a visão formuladas pelas doutrinas filosóficas antigas. Ressalta-se o antagonismo entre a análise geométrica da visão, empreendida por Euclides, e as considerações filosóficas acerca dos processos físicos subjacentes à sensação visual. Pretende-se mostrar que o objeto da óptica euclidiana é a percepção visual daquilo que Aristóteles denomina "sensível comum". This introductory essay provides an abridged presentation of the optical (...)
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  48. added 2017-10-13
    The Point or the Primary Geometric Object.ZERARI Fathi - manuscript
    The definition of a point in geometry is primordial in order to understand the different elements of this branch of mathematics ( line, surface, solids…). This paper aims at shedding fresh light on the concept to demonstrate that it is related to another one named, here, the Primary Geometric Object; both concepts concur to understand the multiplicity of geometries and to provide hints as concerns a new understanding of some concepts in physics such as time, energy, mass….
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  49. added 2017-09-23
    Linear and Geometric Algebra.Alan Macdonald - 2012 - North Charleston, SC: CreateSpace.
    This textbook for the second year undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. -/- Geometric algebra and its extension to geometric calculus simplify, unify, and generalize vast areas of mathematics that involve geometric ideas. Geometric algebra is an extension of linear algebra. The treatment of many linear algebra topics is enhanced by geometric algebra, for example, determinants and orthogonal transformations. And geometric algebra does much (...)
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  50. added 2017-08-31
    Poincaré on the Foundations of Arithmetic and Geometry. Part 2: Intuition and Unity in Mathematics.Katherine Dunlop - 2017 - Hopos: The Journal of the International Society for the History of Philosophy of Science 7 (1):88-107.
    Part 1 of this article exposed a tension between Poincaré’s views of arithmetic and geometry and argued that it could not be resolved by taking geometry to depend on arithmetic. Part 2 aims to resolve the tension by supposing not merely that intuition’s role is to justify induction on the natural numbers but rather that it also functions to acquaint us with the unity of orders and structures and show practices to fit or harmonize with experience. I argue that in (...)
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