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 influence of particle characteristics,such as shape,size,and volume fraction,on the permeability of porous media was investigated by combining the randomly packed beds of Platonic particles with the lattice Boltzm...The influence of particle characteristics,such as shape,size,and volume fraction,on the permeability of porous media was investigated by combining the randomly packed beds of Platonic particles with the lattice Boltzmann method.Quantitative solutions of the permeability as a function of these characteristic parameters in mono-sized particle packing structures were obtained.The D3Q19 model is presented here,which was tested by three simple benchmark tests.A series of packed beds of Platonic particles as well as spherical particles were generated in a random manner.Numerical studies on factors influencing the permeability of materials were carried out to comprehensively study their impacts.The results revealed that the permeability significantly increased with increasing equivalent diameter of the particles(or decreasing volume fraction).At a fixed size and volume fraction of particles,the permeability of the Platonic particle packing structures was also influenced by particle morphology:permeability significantly reduced as the particle sphericity decreased.The permeability of tetrahedral particle packing structures dropped by more than 40%compared with that of corresponding spherical particle systems.展开更多
We investigate the orientably regular non-abelian coverings of regular maps.A complete classification of dihedral coverings of the Platonic maps for branching over faces(or,dually,vertices)is given.As a result,we gene...We investigate the orientably regular non-abelian coverings of regular maps.A complete classification of dihedral coverings of the Platonic maps for branching over faces(or,dually,vertices)is given.As a result,we generalise the results of Jones and Surowski on regular cyclic coverings of the Platonic maps.展开更多
The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result <em>R</em>&...The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result <em>R</em><sub><em>V</em></sub> = π <span style="white-space:nowrap;"><span style="white-space:nowrap;">⋅</span></span> <em><em style="white-space:normal;">φ</em></em><sup>5</sup>, where <img src="Edit_83decbce-7252-44ed-a822-fef13e43fd2a.bmp" alt="" /> is the golden mean. It is important that the number <em>φ</em><sup>5</sup> is a fundamental constant of nature describing phase transition from microscopic to cosmic scale. In this contribution the relatively small volume ratio of the Great Pyramid was compared to that of selected convex polyhedral solids such as the <em>Platonic </em>solids respectively the face-rich truncated icosahedron (bucky ball) as one of <em>Archimedes</em>’ solids leading to effective filling of the polyhedron by its in-sphere and therefore the highest volume ratio of the selected examples. The smallest ratio was found for the Great Pyramid. A regression analysis delivers the highly reliable volume ratio relation <img src="Edit_79e766ce-5580-4ae0-a706-570e0f3f1bd8.bmp" alt="" />, where <em>nF</em> represents the number of polyhedron faces and b approximates the silver mean. For less-symmetrical solids with a unique axis (tetragonal pyramids) the in-sphere can be replaced by a biaxial ellipsoid of maximum volume to adjust the <em>R</em><sub><em>V</em></sub> relation more reliably.展开更多
Love and moral are the main themes of Iris Murdoch' s literary works.As the combination of the two main themes,her Eros theory plays a significant role in her works.On the basis of her personal perception of Plato...Love and moral are the main themes of Iris Murdoch' s literary works.As the combination of the two main themes,her Eros theory plays a significant role in her works.On the basis of her personal perception of Platonic Eros and Freudian Eros,Murdoch establishes her own Eros Theory.To unveil this important theory,this paper tries to trace the sources of Murdoch' s Eros theory from Platonic Eros and Freudian Eros.展开更多
We are discussing one of the most unlikely hypotheses in the history of mathematics—Proclus’ hypothesis, which overturns a traditional view on Euclid’s Elements and the history of mathematics, starting since Euclid...We are discussing one of the most unlikely hypotheses in the history of mathematics—Proclus’ hypothesis, which overturns a traditional view on Euclid’s Elements and the history of mathematics, starting since Euclid. According to Proclus, the main goal of Euclid, when writing the Elements, was to build a complete geometric theory of Platonic solids (Book XIII), associated in the ancient philosophy (Pythagoras, Plato) with the Universe harmony. To construct this theory, Euclid introduced in Book II the problem of dividing a segment into extreme and mean ratio (the “golden section”). It follows from Proclus’ hypothesis that Euclid’s Elements are the first attempt to create the “Mathematical Theory of the Universe Harmony”, based on Platonic solids and the “golden section”.展开更多
Alexander of Aphrodisias’s Commentary on Aristotle’s Metaphysics is an important testimony to understand Plato’s philosophy.In fact,Alexander uses some lost Aristotelian books,especially a work On the Good,from whi...Alexander of Aphrodisias’s Commentary on Aristotle’s Metaphysics is an important testimony to understand Plato’s philosophy.In fact,Alexander uses some lost Aristotelian books,especially a work On the Good,from which we learn that Plato’s metaphysics is adialectical metaphysics,founded on an original opposition of two principles that shapes the whole reality—these principles being the One and the indefinite Dyad.Sensible things participate in ideas(they receive their being from ideas)and the intermediate mathematical entities lie between these two realities.However,ideas can be traced back to ideal numbers and the principles of ideal numbers are the One and the indefinite Dyad.Thus,these principles constitute their metaphysical foundation of ideas and,through the ideas,of the whole reality.展开更多
This paper will discuss Plato＇s view of love in The Symposium, in particular the arguments presented by the Diotima character, but not neglecting all the other views of love presented therein. The paper, as the title...This paper will discuss Plato＇s view of love in The Symposium, in particular the arguments presented by the Diotima character, but not neglecting all the other views of love presented therein. The paper, as the title indicates, will be confined to a comparison and evaluation of Platonic love against love as articulated within Christianity. Both forms of love will be analyzed and I will attempt to show that although Plato, through Socrates （and Socrates through the Diotima character）, tries to redeem the traditional understanding of love in the ancient Greek society that he was living in, Platonic love is still very different from the Christian concept of love.展开更多
Plato’s last dialogue,the Laws,occupies an anomalous position within his larger body of work.An individual identified as the“Athenian stranger”replaces Socrates and reverses key Socratic teachings,most notably by e...Plato’s last dialogue,the Laws,occupies an anomalous position within his larger body of work.An individual identified as the“Athenian stranger”replaces Socrates and reverses key Socratic teachings,most notably by endorsing tyranny.Scholars conclude that Plato abandoned his earlier political recommendations in favor of a more pragmatic vision.In that case,the Laws should be treated as Plato’s definitive work,the ultimate statement of his thought,when in fact,much more attention is paid to earlier dialogues,particularly the Republic.The problem is resolved and the true significance of the Laws revealed when the text is read as Plato’s ironic critique of his brilliant-but-rebellious student,Aristotle.Reasoning from Aristotelian premises,the Athenian stranger arrives at conclusions that Platonists and Aristotelians alike would find unpalatable or absurd.The alleged rupture between Plato’s earlier and later work disappears.The esoteric writings that are thought to have been the product of Aristotle’s later career are shown to have emerged from ideas that Plato himself was familiar with and rejected.展开更多
The article addresses the issue of leisure in the sense of ancient ＂schole.＂ It strives to uncover the relationship between Aristotelian concept of theoretical activity and ＂schole＂ as vacuity. It shows a paradoxi...The article addresses the issue of leisure in the sense of ancient ＂schole.＂ It strives to uncover the relationship between Aristotelian concept of theoretical activity and ＂schole＂ as vacuity. It shows a paradoxical character of ＂schole＂ as purposeless time that forms condition for a meaningful activity. How, then, to restore ＂schole＂ as vacuity today, when colonization of time expands？展开更多
Initiation was one of the most substantial experiences undergone in Antiquity.The term Les rites de passage introduced by Arnold van Gennep,accommodates the multifaceted significance of initiation in the social struct...Initiation was one of the most substantial experiences undergone in Antiquity.The term Les rites de passage introduced by Arnold van Gennep,accommodates the multifaceted significance of initiation in the social structure.The two main aspects of initiation were defined as the social and that which belonged to the religious sphere;or,the profane and the sacred.Initiation or rites of passage in the social realm were intended to delineate the transition from childhood to adult status,while the sacred initiation was intended to promise eternal life and a merging with the divine.As van Gennep has indicated,however,acts of apprenticeship of any kind were enveloped in ceremonies,since no act was entirely free of the sacred.Sacred initiations were intended to remain secret in Antiquity,thus explicit depictions of sacred rituals are rare in ancient art.As this study will demonstrate,however,signifiers of such initiation can nonetheless be found in Roman wall paintings and mosaics depicting mythological protagonists.The point of departure here is that initiation is the main issue manifested metaphorically in the depictions under discussion,with the sacred initiation rather than the social mostly featuring in the visual images.The analysis is based on literary and philosophical sources,and focuses on four personalities:Narcissus,Endymion,and Achilles,who are represented in their mythological context on wall paintings from Pompeii,and Heracles,who is shown in Roman mosaics in a scene familiar as the“Drinking Contest between Heracles and Dionysus”.展开更多
The cube is the only regular hexahedron among the Platonic solids,but supramolecules with a cubic configuration have rarely been reported.Herein,two isostructural metal–organic cubes VMOC-6 and VMOC-7 with large cavi...The cube is the only regular hexahedron among the Platonic solids,but supramolecules with a cubic configuration have rarely been reported.Herein,two isostructural metal–organic cubes VMOC-6 and VMOC-7 with large cavities are successfully synthesized by face-directed self-assembly of concave hexanuclear vanadium clusters[V_(6)O_(6)(OCH_(3))_(9)(XO_(4))(COO)_(3)]^(n−)(X=S,n=2;X=V,n=1)and large-size nitrogen-containing tetravalent ligands.VMOC-6 and VMOC-7 are the largest metal–organic cubes based on metal clusters with an outer diameter of 28.47×28.17×28.44Å^(3) and an inner cavity volume of 7785.657Å^(3).Moreover,the cages can capture volatile iodine vapor with an uptake value of up to 1.83 g g^(−1),which is superior to those of most metal–organic materials.Mechanistic studies have shown that their good adsorption capacity is closely related to the presence of large internal cavities,electron-donating pyridine groups and redox-active V sites.The present work shows the potential application of these mesoporous MOPs in the treatment of iodine-containing nuclear waste.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.
基金The authors gratefully acknowledge financial support from the National Natural Science Foundation of Chinavia GrantNos.51461135001,51878152 and the Ministry of Science and Technology of China 973 Plan via Grant No.2015CB655102.
文摘The influence of particle characteristics,such as shape,size,and volume fraction,on the permeability of porous media was investigated by combining the randomly packed beds of Platonic particles with the lattice Boltzmann method.Quantitative solutions of the permeability as a function of these characteristic parameters in mono-sized particle packing structures were obtained.The D3Q19 model is presented here,which was tested by three simple benchmark tests.A series of packed beds of Platonic particles as well as spherical particles were generated in a random manner.Numerical studies on factors influencing the permeability of materials were carried out to comprehensively study their impacts.The results revealed that the permeability significantly increased with increasing equivalent diameter of the particles(or decreasing volume fraction).At a fixed size and volume fraction of particles,the permeability of the Platonic particle packing structures was also influenced by particle morphology:permeability significantly reduced as the particle sphericity decreased.The permeability of tetrahedral particle packing structures dropped by more than 40%compared with that of corresponding spherical particle systems.
文摘We investigate the orientably regular non-abelian coverings of regular maps.A complete classification of dihedral coverings of the Platonic maps for branching over faces(or,dually,vertices)is given.As a result,we generalise the results of Jones and Surowski on regular cyclic coverings of the Platonic maps.
文摘The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result <em>R</em><sub><em>V</em></sub> = π <span style="white-space:nowrap;"><span style="white-space:nowrap;">⋅</span></span> <em><em style="white-space:normal;">φ</em></em><sup>5</sup>, where <img src="Edit_83decbce-7252-44ed-a822-fef13e43fd2a.bmp" alt="" /> is the golden mean. It is important that the number <em>φ</em><sup>5</sup> is a fundamental constant of nature describing phase transition from microscopic to cosmic scale. In this contribution the relatively small volume ratio of the Great Pyramid was compared to that of selected convex polyhedral solids such as the <em>Platonic </em>solids respectively the face-rich truncated icosahedron (bucky ball) as one of <em>Archimedes</em>’ solids leading to effective filling of the polyhedron by its in-sphere and therefore the highest volume ratio of the selected examples. The smallest ratio was found for the Great Pyramid. A regression analysis delivers the highly reliable volume ratio relation <img src="Edit_79e766ce-5580-4ae0-a706-570e0f3f1bd8.bmp" alt="" />, where <em>nF</em> represents the number of polyhedron faces and b approximates the silver mean. For less-symmetrical solids with a unique axis (tetragonal pyramids) the in-sphere can be replaced by a biaxial ellipsoid of maximum volume to adjust the <em>R</em><sub><em>V</em></sub> relation more reliably.
文摘Love and moral are the main themes of Iris Murdoch' s literary works.As the combination of the two main themes,her Eros theory plays a significant role in her works.On the basis of her personal perception of Platonic Eros and Freudian Eros,Murdoch establishes her own Eros Theory.To unveil this important theory,this paper tries to trace the sources of Murdoch' s Eros theory from Platonic Eros and Freudian Eros.
文摘We are discussing one of the most unlikely hypotheses in the history of mathematics—Proclus’ hypothesis, which overturns a traditional view on Euclid’s Elements and the history of mathematics, starting since Euclid. According to Proclus, the main goal of Euclid, when writing the Elements, was to build a complete geometric theory of Platonic solids (Book XIII), associated in the ancient philosophy (Pythagoras, Plato) with the Universe harmony. To construct this theory, Euclid introduced in Book II the problem of dividing a segment into extreme and mean ratio (the “golden section”). It follows from Proclus’ hypothesis that Euclid’s Elements are the first attempt to create the “Mathematical Theory of the Universe Harmony”, based on Platonic solids and the “golden section”.
文摘Alexander of Aphrodisias’s Commentary on Aristotle’s Metaphysics is an important testimony to understand Plato’s philosophy.In fact,Alexander uses some lost Aristotelian books,especially a work On the Good,from which we learn that Plato’s metaphysics is adialectical metaphysics,founded on an original opposition of two principles that shapes the whole reality—these principles being the One and the indefinite Dyad.Sensible things participate in ideas(they receive their being from ideas)and the intermediate mathematical entities lie between these two realities.However,ideas can be traced back to ideal numbers and the principles of ideal numbers are the One and the indefinite Dyad.Thus,these principles constitute their metaphysical foundation of ideas and,through the ideas,of the whole reality.
文摘This paper will discuss Plato＇s view of love in The Symposium, in particular the arguments presented by the Diotima character, but not neglecting all the other views of love presented therein. The paper, as the title indicates, will be confined to a comparison and evaluation of Platonic love against love as articulated within Christianity. Both forms of love will be analyzed and I will attempt to show that although Plato, through Socrates （and Socrates through the Diotima character）, tries to redeem the traditional understanding of love in the ancient Greek society that he was living in, Platonic love is still very different from the Christian concept of love.
文摘Plato’s last dialogue,the Laws,occupies an anomalous position within his larger body of work.An individual identified as the“Athenian stranger”replaces Socrates and reverses key Socratic teachings,most notably by endorsing tyranny.Scholars conclude that Plato abandoned his earlier political recommendations in favor of a more pragmatic vision.In that case,the Laws should be treated as Plato’s definitive work,the ultimate statement of his thought,when in fact,much more attention is paid to earlier dialogues,particularly the Republic.The problem is resolved and the true significance of the Laws revealed when the text is read as Plato’s ironic critique of his brilliant-but-rebellious student,Aristotle.Reasoning from Aristotelian premises,the Athenian stranger arrives at conclusions that Platonists and Aristotelians alike would find unpalatable or absurd.The alleged rupture between Plato’s earlier and later work disappears.The esoteric writings that are thought to have been the product of Aristotle’s later career are shown to have emerged from ideas that Plato himself was familiar with and rejected.
文摘The article addresses the issue of leisure in the sense of ancient ＂schole.＂ It strives to uncover the relationship between Aristotelian concept of theoretical activity and ＂schole＂ as vacuity. It shows a paradoxical character of ＂schole＂ as purposeless time that forms condition for a meaningful activity. How, then, to restore ＂schole＂ as vacuity today, when colonization of time expands？
文摘Initiation was one of the most substantial experiences undergone in Antiquity.The term Les rites de passage introduced by Arnold van Gennep,accommodates the multifaceted significance of initiation in the social structure.The two main aspects of initiation were defined as the social and that which belonged to the religious sphere;or,the profane and the sacred.Initiation or rites of passage in the social realm were intended to delineate the transition from childhood to adult status,while the sacred initiation was intended to promise eternal life and a merging with the divine.As van Gennep has indicated,however,acts of apprenticeship of any kind were enveloped in ceremonies,since no act was entirely free of the sacred.Sacred initiations were intended to remain secret in Antiquity,thus explicit depictions of sacred rituals are rare in ancient art.As this study will demonstrate,however,signifiers of such initiation can nonetheless be found in Roman wall paintings and mosaics depicting mythological protagonists.The point of departure here is that initiation is the main issue manifested metaphorically in the depictions under discussion,with the sacred initiation rather than the social mostly featuring in the visual images.The analysis is based on literary and philosophical sources,and focuses on four personalities:Narcissus,Endymion,and Achilles,who are represented in their mythological context on wall paintings from Pompeii,and Heracles,who is shown in Roman mosaics in a scene familiar as the“Drinking Contest between Heracles and Dionysus”.
基金financially supported by the NSFC of China(No.22271023,22175033).
文摘The cube is the only regular hexahedron among the Platonic solids,but supramolecules with a cubic configuration have rarely been reported.Herein,two isostructural metal–organic cubes VMOC-6 and VMOC-7 with large cavities are successfully synthesized by face-directed self-assembly of concave hexanuclear vanadium clusters[V_(6)O_(6)(OCH_(3))_(9)(XO_(4))(COO)_(3)]^(n−)(X=S,n=2;X=V,n=1)and large-size nitrogen-containing tetravalent ligands.VMOC-6 and VMOC-7 are the largest metal–organic cubes based on metal clusters with an outer diameter of 28.47×28.17×28.44Å^(3) and an inner cavity volume of 7785.657Å^(3).Moreover,the cages can capture volatile iodine vapor with an uptake value of up to 1.83 g g^(−1),which is superior to those of most metal–organic materials.Mechanistic studies have shown that their good adsorption capacity is closely related to the presence of large internal cavities,electron-donating pyridine groups and redox-active V sites.The present work shows the potential application of these mesoporous MOPs in the treatment of iodine-containing nuclear waste.
