A obra de triangulis omnimodis libri quinque de Johann Müller Regiomontanus (1436 1476): uma contribuição para o desenvolvimento da trigonometria

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

Ecologia humana e manejo participativo da pesca do búzio Anomalocardia brasiliana (Gmelin, 1791) (Bivalvia: Veneridae) na Reserva de Desenvolvimento Sustentável Estadual Ponta do Tubarão (RN)

Coastal and marine protected areas are created to protect habitat, avoid biodiversity loss, and to help maintain viable fisheries. However, most of these areas in tropical countries occurs in impoverished regions and directly affect the livelihood and survival of coastal communities which directly depend on fisheries and shellfisheries. Therefore, socioeconomic and conservation goals overlap. In this context, fishers should have a central place in resource management. They are critical resource users and their behavior directly affects the system. Shellfish resources are important sources of food, employment and income to fishing communities in Latin America. But despite its widespread use for food and income, there is an urgent need of more research on shellfish management. This research discusses the artisanal fisheries of Venus clam (Anomalocardia brasiliana) (Gmelin, 1791) (Bivalvia: Veneridae) in Brazil, and points out strategies to improve the system. Venus clam is a small and commonly exploited species for food and income on the Brazilian coast. This research was carried out at Ponta do Tubarão Sustainable Development Reserve (Brazilian Northeast coast), where there was no information available about who harvest, where or how much Venus clam has been harvested, despite this resource being exploited for generations. Clam fishery follows the pattern of socio-economic invisibility that general clam exploitation has in Brazil. Methods used were interviews, participatory monitoring and focal follow observation from January 2010 to May 2011. Results include: (a) the identification of shell fishers, (b) how harvest and meat processing are performed (mollusk beds, time spent, gross and net production), (c) the analisis of shell fisher income and their economic sustentability, and (d) the involvement of shell fisher families in data gathering and analyses for the first time. Based on the acquired knowledge, we propose a new institutional arrangement for clam fishery including co-management, fisheries agreement, compensatory arrangements and improvements for the Venus clam value chain such as the establishment of a minimum price for clam meat. This research also includes two other results: a general description for Venus clam harvesting in the Brazilian Northeast coast and a specific discussion about co-management of Venus clam in Brazil. The first one was possible through the meeting of several shell fisherwomen from other states during activities promoted by People of the Tides (PoT) project. PoT was an international initiative aiming to develop coastal communities that depend on mollusk for their livelihood. The second one is a comparison between PoT and Venus clam management at Pirajubaé Marine Extractive Reserve (Santa Catarina). It evaluates the success and failures of these only two initiatives involving co-management of A. brasiliana in Brazil