A remarkable property of cycloidal curves

The purpose of this theoretical work is to establish a connection between the most important properties of plane curves: cycloids and sinusoids. For this, a drawing mechanism is considered, which simultaneously draws a sinusoid and two cycloids. Based on the results obtained using this mechanical method of obtaining curves, the following important, previously unknown, theoretical facts are established. Firstly, new in theoretical terms is that the sinusoid is not represented as a graph of a trigonometric function, but as a locus of points equidistant from the current points of two cycloids: an ordinary and another cycloid congruent to the original one, inverted and shifted along the axis by half a period. Secondly, the line passing through the current points of these cycloids is nothing like a normal to the resulting sinusoid. This property greatly simplifies the graphical construction of such a normal. And, finally, a simple trigonometric relationship was established between the angle of rotation of the generating circle and the angle of deviation of the normal from the vertical.

On an Increasingly Yield Curve of Knowledge

The paper examines the behaviour of the yield curve of the knowledge considered as production factor. The concepts of complementarity and substitutability among classical production factors are revisited in order to put the bases to analyse the special production factor (a species of the neo-production factors) namely knowledge. In this context, some distinctions are made between information and knowledge putting in view the added value of knowledge related to information. Some graphical construction and algebraic formalisms are convoked in order to better ground the final conclusions regarding the increasing nature of the knowledge yield curve in the knowledge-based society. The approach is preponderantly logic and conceptualized, trying to get general results which could then be tested, by other researchers, in order either to corroborate or to reject them.

CONSTRUCTION OF GRAPHICS IN CHEMISTRY: AN ESSENTIAL COMPETENCE IN INVESTIGATIVE ACTIVITIES

Teaching processes that promote knowledge integration must consider the relevance of graphical literacy, an essential competence to investigative activities in natural science education. The aim of this study is to analyze the treatment given to the domain of construct-ing graphics in the official documents related to scholar curriculum in Brazil and to debate it at the light of classroom practices. So, the recent literature on the topic is analyzed, as well as Brazilian official pedagogical orientations. Also, an activity on graphical construc-tion was proposed to high school students and a teacher was interviewed. The results ob-tained indicate a twilight zone for graphical construction in the official documents, which extends to teaching training and reflects into classroom practices, creating a vicious circle composed by the incongruence in the orientations, limitations in teaching training and therefore in students’ learning, which demonstrate a heuristic and a superficial vision of graphical construction when solving Chemistry problems. The implications of these results point out the urge to broaden this debate in order to include this topic in teaching training undergraduate programs, besides emphasizing the exploration of this issue in the classroom. Keywords: chemistry teaching, construction of graphics, graphical literacy.