This paper is focused on the study of the urban form of Tomar, which was founded in Portugal by the Order of the Temple during the 12th century. It is centered on the site where the Order of the Temple was created, Je...This paper is focused on the study of the urban form of Tomar, which was founded in Portugal by the Order of the Temple during the 12th century. It is centered on the site where the Order of the Temple was created, Jerusalem, and also on the Templar European headquarters, Paris, in Marais neighborhood; as well as on its headquarters in Portugal, Tomar; and finally, on Angra which was set up in Azores at the beginning of the Portuguese discoveries in 1427. While exploring possible Templar principles on setting up medieval geometric cities, the aim of this paper is to expose that Tomar is a truly relevant case on that process and, therefore, that Portugal have had a significant role on medieval geometric urbanism. The achievements of this paper show that the selected territories share common settlement principles which are based on both similar geometric rules and analogous hierarchy schemes. Regarding that, it will be possible to state that cultural and population exchanges with France should not be considered as the sole factor to shape European medieval urbanity. Portugal should have had a role on that process, too. At least, it should be possible to explore other hypothesis on further pieces of research, according to the exposed arguments.展开更多
Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 ...Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 is an associative submanifold of R^7 if and only if M is almost complex in S^6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S^6 are the equation for primitive maps associated to the 6-symmetric space G2/T^2, and use this to explain some of the known results. Moreover, the equation for S^1-symmetric almost complex curves in S^6 is the periodic Toda lattice, and a discussion of periodic solutions is given.展开更多
文摘This paper is focused on the study of the urban form of Tomar, which was founded in Portugal by the Order of the Temple during the 12th century. It is centered on the site where the Order of the Temple was created, Jerusalem, and also on the Templar European headquarters, Paris, in Marais neighborhood; as well as on its headquarters in Portugal, Tomar; and finally, on Angra which was set up in Azores at the beginning of the Portuguese discoveries in 1427. While exploring possible Templar principles on setting up medieval geometric cities, the aim of this paper is to expose that Tomar is a truly relevant case on that process and, therefore, that Portugal have had a significant role on medieval geometric urbanism. The achievements of this paper show that the selected territories share common settlement principles which are based on both similar geometric rules and analogous hierarchy schemes. Regarding that, it will be possible to state that cultural and population exchanges with France should not be considered as the sole factor to shape European medieval urbanity. Portugal should have had a role on that process, too. At least, it should be possible to explore other hypothesis on further pieces of research, according to the exposed arguments.
文摘Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 is an associative submanifold of R^7 if and only if M is almost complex in S^6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S^6 are the equation for primitive maps associated to the 6-symmetric space G2/T^2, and use this to explain some of the known results. Moreover, the equation for S^1-symmetric almost complex curves in S^6 is the periodic Toda lattice, and a discussion of periodic solutions is given.
