The sphere is a common object in uncountable engineering problems, which not only appears in structural elements like domes but also in thousands of mechanisms normally used in diverse kinds of machines. To design, ca...The sphere is a common object in uncountable engineering problems, which not only appears in structural elements like domes but also in thousands of mechanisms normally used in diverse kinds of machines. To design, calculate and analyze the behaviour on service of spherical elements, it is essential to have a good method to create an ordered group of discrete points of the spherical surface from the parametric equations commonly used to define the sphere continuously. One of the best known and widely used in high-level programming environment is MATLAB. The programming language has thousands of functions, lots of them specially designed for engineering processes. One of these functions generates a sphere knowing a given radius and shows the result. Nevertheless, this function is really imprecise because it is based on parallels and meridians besides the obtained vertices do not keep a constant distance each other. This causes the fact that it would be appropriate to design a new function to generate accurate discrete approximations of the sphere. The objective of this paper is to create a low-level function in MATLAB to obtain a discrete sphere with high regularity and high approximation in order to provide a good base to solve sphere-based engineering problems. To ensure a perfect symmetry and high regularity platonic bodies, MATLAB will be used as a base to divide the continuous spherical surface in a finite number of regular triangles. The obtained results for the different seed bodies will be represented graphically and compared to each other. The accuracy of each method will be evaluated and compared too.展开更多
The present paper has a double aim： （1） it attempts to present an aspect of Plotinus＇ philosophical and hermeneutical methodology on the basis of relevant remarks in the treatise ＂On Eternity and Time＂; （2） it...The present paper has a double aim： （1） it attempts to present an aspect of Plotinus＇ philosophical and hermeneutical methodology on the basis of relevant remarks in the treatise ＂On Eternity and Time＂; （2） it seeks to connect this attitude with contemporary methodological questions concerning the relation between philosophy and history of philosophy. After an introduction where it is emphasized that the term ＂Neo-Platonism＂ is of recent coinage, I exploit David Sedley＇s remarks regarding the function of ancient philosophical schools： the quest for the ＂correct＂ interpretation of the school＇s founder as a philosophical enterprise in itself is not an exclusively Neoplatonic characteristic. Nonetheless, the example of Plotinus＇ Enneads III.7, owing to the complexity of its theme, shows that Plotinus does not pay attention only to the Platonic teachings regarding eternity and time, but also to all the other philosophical schools＇ theories, including the Epicurean. The aim is the ascertainment of the truth inherent in them and its apt interpretation. Hence, I follow Steven K. Strange （1950-2009）, who relates the Plotinian methodology to Aristotle＇s endoxic method. After a presentation of similarities and differences between the two philosophers, I conclude that the problematic features posed by several philosophical theories are resolved via an innovative Plotinian reading of Plato. Thus, the non-Platonic theories play a role in the more adequate interpretation of Plato, which is identified with the successful answer to the philosophical problems. This fact makes us wonder as to the best characterization of Plotinus＇ enterprise： philosophy or history of philosophy？ Although the question is somehow anachronistic, Plotinus gives an explicit response in his aforementioned tractate： to the extent that he is interested in solving philosophical problems, rather than compiling a ＂catalogue＂ of past philosophical positions, his enterprise is not historical, but philosophical. Two final corollaries stem from this： （i） to a certain extent, the previous enunciation explains the Neoplatonic reading of Plato; （ii） it teaches us that the difference between philosophizing and a historical treatment of philosophy does not lie only on the content, but also on the manner according to which the interpreter approaches past or contemporary philosophers.展开更多
文摘The sphere is a common object in uncountable engineering problems, which not only appears in structural elements like domes but also in thousands of mechanisms normally used in diverse kinds of machines. To design, calculate and analyze the behaviour on service of spherical elements, it is essential to have a good method to create an ordered group of discrete points of the spherical surface from the parametric equations commonly used to define the sphere continuously. One of the best known and widely used in high-level programming environment is MATLAB. The programming language has thousands of functions, lots of them specially designed for engineering processes. One of these functions generates a sphere knowing a given radius and shows the result. Nevertheless, this function is really imprecise because it is based on parallels and meridians besides the obtained vertices do not keep a constant distance each other. This causes the fact that it would be appropriate to design a new function to generate accurate discrete approximations of the sphere. The objective of this paper is to create a low-level function in MATLAB to obtain a discrete sphere with high regularity and high approximation in order to provide a good base to solve sphere-based engineering problems. To ensure a perfect symmetry and high regularity platonic bodies, MATLAB will be used as a base to divide the continuous spherical surface in a finite number of regular triangles. The obtained results for the different seed bodies will be represented graphically and compared to each other. The accuracy of each method will be evaluated and compared too.
文摘The present paper has a double aim： （1） it attempts to present an aspect of Plotinus＇ philosophical and hermeneutical methodology on the basis of relevant remarks in the treatise ＂On Eternity and Time＂; （2） it seeks to connect this attitude with contemporary methodological questions concerning the relation between philosophy and history of philosophy. After an introduction where it is emphasized that the term ＂Neo-Platonism＂ is of recent coinage, I exploit David Sedley＇s remarks regarding the function of ancient philosophical schools： the quest for the ＂correct＂ interpretation of the school＇s founder as a philosophical enterprise in itself is not an exclusively Neoplatonic characteristic. Nonetheless, the example of Plotinus＇ Enneads III.7, owing to the complexity of its theme, shows that Plotinus does not pay attention only to the Platonic teachings regarding eternity and time, but also to all the other philosophical schools＇ theories, including the Epicurean. The aim is the ascertainment of the truth inherent in them and its apt interpretation. Hence, I follow Steven K. Strange （1950-2009）, who relates the Plotinian methodology to Aristotle＇s endoxic method. After a presentation of similarities and differences between the two philosophers, I conclude that the problematic features posed by several philosophical theories are resolved via an innovative Plotinian reading of Plato. Thus, the non-Platonic theories play a role in the more adequate interpretation of Plato, which is identified with the successful answer to the philosophical problems. This fact makes us wonder as to the best characterization of Plotinus＇ enterprise： philosophy or history of philosophy？ Although the question is somehow anachronistic, Plotinus gives an explicit response in his aforementioned tractate： to the extent that he is interested in solving philosophical problems, rather than compiling a ＂catalogue＂ of past philosophical positions, his enterprise is not historical, but philosophical. Two final corollaries stem from this： （i） to a certain extent, the previous enunciation explains the Neoplatonic reading of Plato; （ii） it teaches us that the difference between philosophizing and a historical treatment of philosophy does not lie only on the content, but also on the manner according to which the interpreter approaches past or contemporary philosophers.
