Relevant bibliographies by topics / Hermann Grassmann

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Academic literature on the topic 'Hermann Grassmann'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Hermann Grassmann"

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Stewart, Ian. "Mathematics: Hermann Grassmann was right." Nature 321, no. 6065 (1986): 17. http://dx.doi.org/10.1038/321017a0.

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Achtner, Wolfgang. "From Religion to Dialectics and Mathematics." Studies in Logic, Grammar and Rhetoric 44, no. 1 (2016): 111–31. http://dx.doi.org/10.1515/slgr-2016-0007.

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Abstract Hermann Grassmann is known to be the founder of modern vector and tensor calculus. Having as a theologian no formal education in mathematics at a university he got his basic ideas for this mathematical innovation at least to some extent from listening to Schleiermacher’s lectures on Dialectics and, together with his brother Robert, reading its publication in 1839. The paper shows how the idea of unity and various levels of reality first formulated in Schleiermacher’s talks about religion in 1799 were transformed by him into a philosophical system in his dialectics and then were picked up by Grassmann and operationalized in his philosophical-mathematical treatise on the extension theory (German: Ausdehnungslehre) in 1844.
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Otte, Michael. "The ideas of Hermann Grassmann in the context of the mathematical and philosophical tradition since Leibniz." Historia Mathematica 16, no. 1 (1989): 1–35. http://dx.doi.org/10.1016/0315-0860(89)90096-7.

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Hyder, David Jalal. "Physiological Optics and Physical Geometry." Science in Context 14, no. 3 (2001): 419–56. http://dx.doi.org/10.1017/s0269889701000151.

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ArgumentHermann von Helmholtz’s distinction between “pure intuitive” and “physical” geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant’s claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz’s understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz’s development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz’s arguments concerning geometry.
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Schubring, Gert. "Hermann Grassmann. Extension Theory. Translated by, Lloyd C. Kannenberg. (History of Mathematics Sources, 19.) 411 pp., frontis., figs., apps., indexes. Providence, R.I.: American Mathematical Society, 2000. $75 (paper)." Isis 94, no. 2 (2003): 386–87. http://dx.doi.org/10.1086/379450.

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Petsche, Hans-Joachim. "The ‘Chemistry of Space’: The Sources of Hermann Grassmann's Scientific Achievements." Annals of Science 71, no. 4 (2014): 522–76. http://dx.doi.org/10.1080/00033790.2013.877339.

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Arguedas T, Vernor. "Hermann Graßmann: Un poli-matemático extraodinario." Revista Digital: Matemática, Educación e Internet 18, no. 2 (2018). http://dx.doi.org/10.18845/rdmei.v18i2.3526.

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"Conference on Hermann G. Grassmann in 1994." Historia Mathematica 19, no. 1 (1992): 81. http://dx.doi.org/10.1016/0315-0860(92)90060-o.

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"Hermann Gunther Grassman (1809–1877) Visionary Mathematician, Scientist and Neohumanist Scholar. Papers from a Sesquicentennial Conference Editor: Gert Schubring." Advances in Applied Clifford Algebras 7, no. 2 (1997): 171–72. http://dx.doi.org/10.1007/bf03041227.

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Dissertations / Theses on the topic "Hermann Grassmann"

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Damion, Robin A. "Grassmann variables and pseudoclassical Nuclear Magnetic Resonance." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-214290.

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The concept of a propagator is useful and is a well-known object in diffusion NMR experiments. Here, we investigate the related concept; the propagator for the magnetization or the Green’s function of the Torrey-Bloch equations. The magnetization propagator is constructed by defining functions such as the Hamiltonian and Lagrangian and using these to define a path integral. It is shown that the equations of motion derived from the Lagrangian produce complex-valued trajectories (classical paths) and it is conjectured that the end-points of these trajectories are real-valued. The complex nature of the trajectories also suggests that the spin degrees of freedom are also encoded into the trajectories and this idea is explored by explicitly modeling the spin or precessing magnetization by anticommuting Grassmann variables. A pseudoclassical Lagrangian is constructed by combining the diffusive (bosonic) Lagrangian with the Grassmann (fermionic) Lagrangian, and performing the path integral over the Grassmann variables recovers the original Lagrangian that was used in the construction of the propagator for the magnetization. The trajectories of the pseudoclassical model also provide some insight into the nature of the end-points.
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Servidoni, Maria do Carmo Pereira. "A axiomatização da aritmética e a contribuição de Hermann Günther Grabmann." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11103.

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Made available in DSpace on 2016-04-27T16:57:50Z (GMT). No. of bitstreams: 1 EDM - Maria do Carmo P Servidoni.pdf: 866161 bytes, checksum: 8e9e034ec8ba50f2872318b1cea8c98d (MD5) Previous issue date: 2006-11-07<br>Secretaria da Educação do Estado de São Paulo<br>This research had as purpose the epistemology development of the knowledge object, number, in its formation as mathematical entity. It became evident that, in the end of the XIX century, the need of this formation caused many controversies, because number was understood as gift by God and consequently, considered something perfect. To the development of this research, we had as references Gramanns works, the first mathematician to consider, even if, in an unconscious form, the Axiomatization of Arithmetic. The main reference was the article entitled: The debate about the Axiomatization of Arithmetic: Otto Hölder against Robert Gramann by Mircea Radu (2003), in which, there is a debate about Axiomatization of Arithmetic under two points of view, on the other hand, we have Otto Hölder who believed in the synthetic nature of Mathematics, in such case, he rejected the axiomatical method as base for itself, and otherwise, Hermann Gramann and Robert Gramann that agree with the same idea, but they reject the axiomatical method. However, Gramann didnt understand so well his treatment of Arithmetic, because the laws that would define the natural numbers belonged to Algebra, another discipline that Grassmann considered as originated for all the other ones. In the development of this research, we indicated that the bases of the Axiomatization of Arithmetic were in the salience of big transformations occurred in Mathematics in the time of XIX century and beginning of XX one: the appearing of the non-Euclidean Geometries, the Algebra s release of Arithmetics veins and the intricate process of Arithmetization of Analysis. In this period, it also developed the relevancy or not of the use of axiomatic method as a basis of Arithmetic. We concluded that, in spite of all controversies of this period, 11 the possibility of Axiomatization of Arithmetic and the adoption of the axiomatical source in formal sciences contributed for the exact sciences<br>Esta pesquisa teve como objetivo o desenvolvimento epistemológico do objeto de conhecimento número em sua constituição como entidade matemática. Ficou evidenciado que, no final do século XIX, a necessidade dessa constituição gerou muitas controvérsias, porque número era concebido como presente de Deus e, conseqüentemente, considerado algo perfeito. Para o desenvolvimento dessa pesquisa, tivemos como referência os trabalhos de Grassmann, o primeiro matemático a propor, mesmo que, de forma inconsciente, a Axiomatização da Aritmética. A referência principal foi o artigo intitulado: A debate about the axiomatization of arithmetic: Otto Hölder against Robert Gramann de Mircea Radu (2003), no qual se encontra um debate a respeito da Axiomatização da Aritmética sob dois pontos de vista; por um lado, temos Otto Hölder que acreditava na natureza sintética da Matemática, sendo assim rejeitava o método axiomático como base para a mesma; por outro lado, Robert Grassmann e Hermann Grassmann que, também, concordam com a idéia de Hölder, pois rejeitam o método axiomático. No entanto, apresentaram uma abordagem da Aritmética, aparentemente, axiomática. Na verdade, Grassmann não entendia assim seu tratamento da Aritmética, pois as leis que definiriam os números naturais pertenciam à Álgebra, outra disciplina que Grassmann considerou como geradora de todas as outras. No desenvolvimento dessa pesquisa, indicamos que as bases da axiomatização da Aritmética estavam no bojo das grandes transformações ocorridas na Matemática durante o século XIX e início do XX: o aparecimento das Geometrias não-euclidianas, a libertação da Álgebra das veias da Aritmética e o processo intrincado da Aritmetização da Análise. Nesse período, também, desenvolveu-se a discussão da pertinência ou não do uso do método 9 axiomático, como um fundamento da Aritmética. Concluiu-se que apesar de toda a polêmica desse período, a possibilidade da axiomatização da Aritmética e a adoção do princípio axiomático nas ciências formais contribuíram para o avanço das ciências exatas
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Books on the topic "Hermann Grassmann"

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), Hans-Joachim Petsche; Lloyd Kannenberg; Gottfried Kessler; Jolanta Liskowacka (eds. Hermann Grassmann roots and traces. Birkhäuser, 2009.

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Petsche, Hans-Joachim. Hermann Grassmann: From past to future : Grassmann's work in context : Grassmann Bicentennial Conference, September 2009. Birkhäuser, 2011.

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Hermann Grassmann: Roots and traces : autographs and unknown documents. Birkhäuser, 2009.

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1809-1877, Grassmann Hermann, and Schubring Gert, eds. Hermann Günther Grassmann (1809-1877): Visionary mathematician, scientist and neohumanist scholar : papers from a sesquicentennial conference. Kluwer Academic Publishers, 1996.

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Nolte, David D. Geometry on my Mind. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0005.

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This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics. Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics. Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems in chaos theory. Motion cannot exist without space—trajectories are the tracks of points, mathematical or physical, through it.
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Book chapters on the topic "Hermann Grassmann"

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Kuehni, Rolf G. "Grassmann, Hermann Günther." In Encyclopedia of Color Science and Technology. Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4419-8071-7_290.

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Kuehni, Rolf. "Grassmann, Hermann Günther." In Encyclopedia of Color Science and Technology. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-27851-8_290-1.

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Shamey, Renzo, and Rolf G. Kuehni. "Grassmann, Hermann Günther 1809–1877." In Pioneers of Color Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-319-30811-1_38.

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Scholz, Erhard. "The Influence of Justus Grassmann’s Crystallographic Works on Hermann Grassmann." In Boston Studies in the Philosophy of Science. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8753-2_5.

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Otte, Michael. "Justus and Hermann Grassmann: philosophy and mathematics." In From Past to Future: Graßmann's Work in Context. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0405-5_6.

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Russ, Steve. "Concepts and contrasts: Hermann Grassmann and Bernard Bolzano." In From Past to Future: Graßmann's Work in Context. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0405-5_11.

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Sühring, Peter. "Calculation and emotion: Hermann Grassmann and Gustav Jacobsthal’s musicology." In From Past to Future: Graßmann's Work in Context. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0405-5_34.

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Heuser, Marie-Luise. "The Significance of Naturphilosophie for Justus and Hermann Grassmann." In From Past to Future: Graßmann's Work in Context. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0405-5_5.

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Peckhaus, Volker. "The Influence of Hermann Günther Grassmann and Robert Grassmann on Ernst Schröder’s Algebra of Logic." In Boston Studies in the Philosophy of Science. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8753-2_18.

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Ohala, John J. "Hermann Grassmann: his contributions to historical linguistics and speech acoustics." In From Past to Future: Graßmann's Work in Context. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0405-5_30.

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