996 resultados para Ravizza, Giovita, 1476-1553


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Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann Müller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician

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Meir Kayserling

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Raphael Strauß

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An integrated instrument package for measuring and understanding the surface radiation budget of sea ice is presented, along with results from its first deployment. The setup simultaneously measures broadband fluxes of upwelling and downwelling terrestrial and solar radiation (four components separately), spectral fluxes of incident and reflected solar radiation, and supporting data such as air temperature and humidity, surface temperature, and location (GPS), in addition to photographing the sky and observed surface during each measurement. The instruments are mounted on a small sled, allowing measurements of the radiation budget to be made at many locations in the study area to see the effect of small-scale surface processes on the large-scale radiation budget. Such observations have many applications, from calibration and validation of remote sensing products to improving our understanding of surface processes that affect atmosphere-snow-ice interactions and drive feedbacks, ultimately leading to the potential to improve climate modelling of ice-covered regions of the ocean. The photographs, spectral data, and other observations allow for improved analysis of the broadband data. An example of this is shown by using the observations made during a partly cloudy day, which show erratic variations due to passing clouds, and creating a careful estimate of what the radiation budget along the observed line would have been under uniform sky conditions, clear or overcast. Other data from the setup's first deployment, in June 2011 on fast ice near Point Barrow, Alaska, are also shown; these illustrate the rapid changes of the radiation budget during a cold period that led to refreezing and new snow well into the melt season.