Ernst Bloch: esperança e educação em tempos de niilismo

This work aims give evidence of that The hope principle, the philosophical system devised by the German philosopher Ernst Bloch, in which hope assumes an ontological character, offers cognitive support that allows overcoming the void imposed by nihilism today, especially in the field of education. But while it offers cognitive support, it also presents a need that is fulfilled by an educational proposal based on a not-yet-conscious being. An education based on hope has four essential pillars: learning to know, learning to do, learning to be, learning to live together and, most of all, immerging into in the seas of uncertainty. In times when school is a promoter of certainties at the expense of uncertainties, education must not forsake the notion of the unpredictable and immeasurable, nor the need to find ways to enable better understanding of aspect related to the not-yet-be. The employed theoretical and methodological elements in this work paint a corpus through an interactive process in which layers of additional texts are subjected to analysis

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