Historia scientiarum. Second series : international journal of the History of Science Society of Japan, 2006
In the paper we try to demonstrate that the geometric procedure, used in the division of trapezoi... more In the paper we try to demonstrate that the geometric procedure, used in the division of trapezoidal figures, could also be applied, and in a general way, in this type of figures; with this method the Babylonian scribes knew how to calculate any of their unknown magnitudes.
Logic is a set of well-formed formulae, along with an inference relation. But the Classical Logic... more Logic is a set of well-formed formulae, along with an inference relation. But the Classical Logic is bivalent; for this reason, very limited to solve problems with uncertainty on the data. It is well-known that Artificial Intelligence requires Logic. Because its Classical version shows too many insufficiencies, it is very necessary to introduce more sophisticated tools, as may be Non- Classical Logics; amongst them, Fuzzy Logic, Modal Logic, Non-Monotonic Logic, Para-consistent Logic, and so on. All them in the same line: against the dogmatism and the dualistic vision of the world: absolutely true vs. absolutely false, black vs. white, good or bad by nature, Yes vs. No, 0 vs. 1, Full vs. Empty, etc. We attempt to analyze here some of these very interesting Classical and modern Non-Classical Logics.
In ancient Mesopotamia were not practiced neither autopsies nor dissections, so the internal orga... more In ancient Mesopotamia were not practiced neither autopsies nor dissections, so the internal organs of human body were known only from occasional inspections on wounds and injuries. The brain was considered as a part of the head and was not related to mental activity. However, Babylonian and Assyrian physicians were able to identify the symptoms of many diseases that affect this organ. We will make here a brief overview of them.
RESUMEN : La geometria griega incorpora una serie de elementos que carecen de consistencia en el ... more RESUMEN : La geometria griega incorpora una serie de elementos que carecen de consistencia en el mundo sensible, como son el punto , la linea y el plano, pero que surgen por la necesidad de superar la indefinicion que la idea de infini to suscitaba en las mentes de los filosofos griegos. La intro duccion de estos elementos en la composicion de cuadratu ras origino una serie de paradojas y contradicciones que persistieron hasta el descubrimiento , en pleno siglo XVII, del calculo integral . Aqui se revisan algunos conceptos esen ciales de la geometria euclidea y se analizan brevemente los metodos de exhaucion practicados por Hipocrates, Euclides y Arquimedes, observando como este ultimo se encuentra mas proximo a las tradiciones practicas provenientes de Meso potamia, mientras Euclides continua fiel a la corriente pla tonico-aristotelica . DESCRIPTORES : Exhaucion, Filosofia griega, Geometria griega.
... Robson provides a detailed study of this tablet (Robson 1999, 208-217); as does Friberg (Frib... more ... Robson provides a detailed study of this tablet (Robson 1999, 208-217); as does Friberg (Friberg 2007, 126 ... 20 the coefficient of a grain-field D17: 5(u) 6(diš) 4(u) DAL šà A ... Akkadian and Sumerian logograms that name all of these geometric forms.19 Exercises numbers 2, 4 (col. ...
Theoria Revista De Teoria Historia Y Fundamentos De La Ciencia, 2005
RESUMEN. Con la ayuda de un diagrama y aplicando la fórmula del agrimensor, los matemáticos de la... more RESUMEN. Con la ayuda de un diagrama y aplicando la fórmula del agrimensor, los matemáticos de la Antigua Babilonia descubrieron un método sencillo y elegante de bisecar figuras trapezoidales. En este trabajo intentaremos demostrar, únicamente como conjetura, que en el "Problema de los Seis hermanos"-Tablilla AO 17264-se pudo haber manejado este mismo procedimiento, aunque ampliado y generalizado. Descriptores: Matemática babilónica, Tablilla AO 17264, Problema de los seis hermanos, Tablilla YBC 4675, Geometría Antigua, Partición de trapecios, Trapecios bisecados. ABSTRACT. The Mathematicians of the Old Babylonian Period, with the aid of a diagram and applying the surveyor formula, discovered a simple and smart method to bisect trapezoidal figures. In this paper, we will try to demonstrate, only as a conjecture, that in the Problem of Six Brothers, Tablet AO 17264, it could be used the same procedure, although extended and generalized.
Theoria an International Journal For Theory History and Foundations of Science, Nov 25, 2008
RESUMEN: En este ensayo presento un análisis comparativo entre los diversos procedimientos creado... more RESUMEN: En este ensayo presento un análisis comparativo entre los diversos procedimientos creados, respectivamente, por los matemáticos babilonios y Diofanto de Alejandría para resolver ecuaciones de segundo grado. Observaremos cómo los primeros recurrieron a la composición de diagramas mientras Diofanto aplicó un algoritmo abstracto que no consiguió generalizar. Descriptores: matemáticas en Mesopotamia, álgebra, Diofanto de Alejandría, ecuaciones cuadráticas, algoritmos.
Historia Scientiarum Second Series International Journal of the History of Science Society of Japan, Jul 31, 2008
In this paper we propose that there is a school geometric exercise from the Old Babylonian Period... more In this paper we propose that there is a school geometric exercise from the Old Babylonian Period in which the students would learn how to compute the surface of an isosceles trapezoid, beginning with the calculation of its height. This problem text can be found on tablet YBC 8633.
Historia scientiarum: international journal of the History of Science Society of Japan
The Old Babylonian problem text VAT 8393 raises the construction of a succession of isosceles tra... more The Old Babylonian problem text VAT 8393 raises the construction of a succession of isosceles trapezoids with the same measure of their diagonals. This paper suggests a geometric procedure of resolution very close to the context at hand.
Historia scientiarum. Second series : international journal of the History of Science Society of Japan, 2006
In the paper we try to demonstrate that the geometric procedure, used in the division of trapezoi... more In the paper we try to demonstrate that the geometric procedure, used in the division of trapezoidal figures, could also be applied, and in a general way, in this type of figures; with this method the Babylonian scribes knew how to calculate any of their unknown magnitudes.
Logic is a set of well-formed formulae, along with an inference relation. But the Classical Logic... more Logic is a set of well-formed formulae, along with an inference relation. But the Classical Logic is bivalent; for this reason, very limited to solve problems with uncertainty on the data. It is well-known that Artificial Intelligence requires Logic. Because its Classical version shows too many insufficiencies, it is very necessary to introduce more sophisticated tools, as may be Non- Classical Logics; amongst them, Fuzzy Logic, Modal Logic, Non-Monotonic Logic, Para-consistent Logic, and so on. All them in the same line: against the dogmatism and the dualistic vision of the world: absolutely true vs. absolutely false, black vs. white, good or bad by nature, Yes vs. No, 0 vs. 1, Full vs. Empty, etc. We attempt to analyze here some of these very interesting Classical and modern Non-Classical Logics.
In ancient Mesopotamia were not practiced neither autopsies nor dissections, so the internal orga... more In ancient Mesopotamia were not practiced neither autopsies nor dissections, so the internal organs of human body were known only from occasional inspections on wounds and injuries. The brain was considered as a part of the head and was not related to mental activity. However, Babylonian and Assyrian physicians were able to identify the symptoms of many diseases that affect this organ. We will make here a brief overview of them.
RESUMEN : La geometria griega incorpora una serie de elementos que carecen de consistencia en el ... more RESUMEN : La geometria griega incorpora una serie de elementos que carecen de consistencia en el mundo sensible, como son el punto , la linea y el plano, pero que surgen por la necesidad de superar la indefinicion que la idea de infini to suscitaba en las mentes de los filosofos griegos. La intro duccion de estos elementos en la composicion de cuadratu ras origino una serie de paradojas y contradicciones que persistieron hasta el descubrimiento , en pleno siglo XVII, del calculo integral . Aqui se revisan algunos conceptos esen ciales de la geometria euclidea y se analizan brevemente los metodos de exhaucion practicados por Hipocrates, Euclides y Arquimedes, observando como este ultimo se encuentra mas proximo a las tradiciones practicas provenientes de Meso potamia, mientras Euclides continua fiel a la corriente pla tonico-aristotelica . DESCRIPTORES : Exhaucion, Filosofia griega, Geometria griega.
... Robson provides a detailed study of this tablet (Robson 1999, 208-217); as does Friberg (Frib... more ... Robson provides a detailed study of this tablet (Robson 1999, 208-217); as does Friberg (Friberg 2007, 126 ... 20 the coefficient of a grain-field D17: 5(u) 6(diš) 4(u) DAL šà A ... Akkadian and Sumerian logograms that name all of these geometric forms.19 Exercises numbers 2, 4 (col. ...
Theoria Revista De Teoria Historia Y Fundamentos De La Ciencia, 2005
RESUMEN. Con la ayuda de un diagrama y aplicando la fórmula del agrimensor, los matemáticos de la... more RESUMEN. Con la ayuda de un diagrama y aplicando la fórmula del agrimensor, los matemáticos de la Antigua Babilonia descubrieron un método sencillo y elegante de bisecar figuras trapezoidales. En este trabajo intentaremos demostrar, únicamente como conjetura, que en el "Problema de los Seis hermanos"-Tablilla AO 17264-se pudo haber manejado este mismo procedimiento, aunque ampliado y generalizado. Descriptores: Matemática babilónica, Tablilla AO 17264, Problema de los seis hermanos, Tablilla YBC 4675, Geometría Antigua, Partición de trapecios, Trapecios bisecados. ABSTRACT. The Mathematicians of the Old Babylonian Period, with the aid of a diagram and applying the surveyor formula, discovered a simple and smart method to bisect trapezoidal figures. In this paper, we will try to demonstrate, only as a conjecture, that in the Problem of Six Brothers, Tablet AO 17264, it could be used the same procedure, although extended and generalized.
Theoria an International Journal For Theory History and Foundations of Science, Nov 25, 2008
RESUMEN: En este ensayo presento un análisis comparativo entre los diversos procedimientos creado... more RESUMEN: En este ensayo presento un análisis comparativo entre los diversos procedimientos creados, respectivamente, por los matemáticos babilonios y Diofanto de Alejandría para resolver ecuaciones de segundo grado. Observaremos cómo los primeros recurrieron a la composición de diagramas mientras Diofanto aplicó un algoritmo abstracto que no consiguió generalizar. Descriptores: matemáticas en Mesopotamia, álgebra, Diofanto de Alejandría, ecuaciones cuadráticas, algoritmos.
Historia Scientiarum Second Series International Journal of the History of Science Society of Japan, Jul 31, 2008
In this paper we propose that there is a school geometric exercise from the Old Babylonian Period... more In this paper we propose that there is a school geometric exercise from the Old Babylonian Period in which the students would learn how to compute the surface of an isosceles trapezoid, beginning with the calculation of its height. This problem text can be found on tablet YBC 8633.
Historia scientiarum: international journal of the History of Science Society of Japan
The Old Babylonian problem text VAT 8393 raises the construction of a succession of isosceles tra... more The Old Babylonian problem text VAT 8393 raises the construction of a succession of isosceles trapezoids with the same measure of their diagonals. This paper suggests a geometric procedure of resolution very close to the context at hand.
Uploads
Papers by Piedad Yuste