The Armenian highlands contain numerous remote sites featuring petroglyphs. Many of these rock carvings are pastoral depictions of animals, while others are abstract and complex, and one example of the latter, believed by archaeologists to date back to the Late Bronze Age (LBA), is found on an isolated site on Sevsar Mountain at an altitude of about 2700 m. The most accepted theory about the significance of these carvings dates back to the 1980s and suggests that they were representative of a lunisolar calendar. During our two recent expeditions to the site in 2017 and 2019, we noticed a cup mark in the largest circular petroglyph, deep enough to hold a vertical wooden pole, and from this we inferred a more extensive astronomical function for the carvings. In particular, the petroglyph’s intricate design of a radiating spiral and three concentric circles placed at non-equidistant radii from the centre made us consider its possible use as a sundial, with the inscribed circles representing the noon shadow lengths on solstices and equinoxes. We measured the radii of the circles north–south and the orientation of the main landscape features using a Suunto clinometer and compass. Our analysis shows that the dimensions of the petroglyph closely match actual shadow lengths in the LBA, and that the petroglyph can be reconstructed to high accuracy from theoretical ellipses. Additionally, the remote location of this site further suggests that the movement of the Sun was important to the builders, as the site may have also served as a ritualistic and initiation destination.
En el mes de mayo de 2019 se cumplió el aniversario número quinientos del fallecimiento del Hombre Universal por excelencia: Leonardo de Vinci. Entre las muchas disciplinas que Leonardo cultivó están la pintura y otras formas de creación artística; sin embargo, su interés y curiosidad lo llevaron a abarcar un sinnúmero de ramas de la Ciencia: Matemática, Física, Ingeniería, Botánica, Anatomía, etc. El enfoque de Leonardo a todas ellas era integral; no podía separar el arte de la ciencia, ni la física de la ingeniería ni de la matemática. Por ello, hacemos un acercamiento geométrico a una de sus más famosas creaciones: La MonaLisa. El eje geométrico está representado por la llamada Flor de la Vida, que desde tiempos inmemoriales ha ocupado un lugar entre las culturas del mundo. En este trabajo se da cuenta de esta aproximación; describiendo una posible manera en la que Leonardo pudo haber hecho uso de la Flor de la Vida para lograr la armonía y balance de la Mona Lisa.
We develop the classical and quantum theory of a spinning particle moving in a Möbius strip. We first propose a Lagrangian for such a system and then we proceed to quantize the system via the constraint Hamiltonian system formalism. Our results may be of particular interest in several physical scenarios, including solid state physics and optics. In fact, the present work may shed some new light on the recent discoveries on condensed matter concerning topological insulators.
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