A New Look at the So-Called Trammel of Archimedes

The paper begins with an elementary treatment of a standard trammel (trammel of Archimedes), a line segment of fixed length whose ends slide along two perpendicular axes. During the motion, points on the trammel trace ellipses, and the trammel produces an astroid as an envelope that is also the envelope of the family of traced ellipses. Two generalizations are introduced: a zigzag trammel, obtained by dividing a standard trammel into several hinged pieces, and a flexible trammel whose length may vary during the motion. All properties regarding traces and envelopes of a standard trammel are extended to these more general trammels. Applications of zigzag trammels are given to problems involving folding doors. Flexible trammels provide not only a deeper understanding of the standard trammel but also a new solution of a classical problem of determining the envelope of a family of straight lines. They also reveal unexpected connections between various classical curves; for example, the cycloid and the quadratrix of Hippias, curves known from antiquity

Blogging in the physics classroom: A research-based approach to shaping students' attitudes towards physics

Even though there has been a tremendous amount of research done in how to help students learn physics, students are still coming away missing a crucial piece of the puzzle: why bother with physics? Students learn fundamental laws and how to calculate, but come out of a general physics course without a deep understanding of how physics has transformed the world around them. In other words, they get the "how" but not the "why". Studies have shown that students leave introductory physics courses almost universally with decreased expectations and with a more negative attitude. This paper will detail an experiment to address this problem: a course weblog or "blog" which discusses real-world applications of physics and engages students in discussion and thinking outside of class. Specifically, students' attitudes towards the value of physics and its applicability to the real-world were probed using a 26-question Likert scale survey over the course of four semesters in an introductory physics course at a comprehensive Jesuit university. We found that students who did not participate in the blog study generally exhibited a deterioration in attitude towards physics as seen previously. However, students who read, commented, and were involved with the blog maintained their initially positive attitudes towards physics. Student response to the blog was overwhelmingly positive, with students claiming that the blog made the things we studied in the classroom come alive for them and seem much more relevant.Comment: 20 pages, 6 figure

Using a free open source software to teach mathematics

We present the experience of the authors teaching mathematics to freshmen engineering students with the help of the open source computer algebra system Sage. We describe some teaching resources and present an ad hoc distribution of Sage used by the authors

Flamingo, 15 December, 1933, Vol. 8, No. 2

Monthly magazine of creative and other writings from undergraduates and faculty of Rollins College, sponsored by the Rollins English Department.https://scholarship.rollins.edu/flamingo/1070/thumbnail.jp

Scientific, Technical and Economic Committee for Fisheries (STECF) - Landing Obligation - Part 6 (Fisheries targeting demersal species in the Mediterranean Sea) (STECF-15-19)

Sala, Antonello ... et al.-- This report was reviewed by the STECF during its winter plenary meeting held from 9 to 13 November 2015 in Brussels.-- 269 pages, 166 figures, 7 tables, 5 annexesThis report presents the responses of the Scientific, Technical and Economic Committee for Fisheries to requests from the Eur opean Commission for advice on the implementation of the EU Common Fisheries Policy. Advice is given in relation to the following: Landing Obligation (Fisheries targeting demersal species in the Mediterranean Sea)Peer Reviewe

Bycatch and discard issues in the Adriatic demersal fisheries

Commercial fisheries exploiting the demersal resources of Western Adriatic Sea produce high bycatch and discard rates; the most important are bottom trawls, hydraulic dredges and passive nets. The five papers here published assess these fisheries’ impacts and investigate the potential of specific solutions to promote more sustainable exploitation. Papers I, II, III focused on bottom trawl fishery. Paper I compared the catch performance of the two legal codends by accounting for the entire species community in trawl catches. 50% of the catch in weight and 80% in count numbers consisted of discarded species, highlighting the severe impact of this fishery. Paper II estimated the selectivity of experimental codend having meshes turned 90° (T90) and of traditional diamond mesh codend with same mesh size. The T90 codend improved the size selection for all the target species. Paper III investigated the use of T90 meshes in the extension piece together with a reduction in mesh number at extension circumference. Results revealed that both these changes applied in the extension piece did not improve the selectivity of the main target species. Paper IV focused on hydraulic dredge fishery targeting the striped venus clam by assessing the clams’ size selection process operated by the dredge. 25% of the clams caught were not size selected due to clogging phenomenon in the dredge. The clam length with 50% retention probability was 18.9 mm, highlighting that the additional size selection process of sorting sieve is necessary to land only the legal clams >22 mm. Paper V compared the catch performance of innovative fish pots and of traditional trammel net. A similar catch efficiency between the two gears for the commercial portion was observed, while the trammel net produced significantly more discards in terms of species number and weight. All the results are discussed in fisheries management perspective

Suomalaisten ja chileläisten alaluokkien opettajien esille tuomia uskomuksia ongelmanratkaisusta

Peer reviewe

On Holditch's theorem and related kinematics

El teorema de Holditch es un resultado clásico sobre áreas de curvas planas generadas por el movimiento de segmentos. Esta construcción está estrechamente relacionada con otros tipos de curvas como, por ejemplo, curvas paralelas, curvas de anchura constante o curvas de bicicletas. Se compilan las propiedades básicas de este tipo de curvas y se da una revisión histórica sobre el teorema de Holditch y teoremas relacionados de cinemática. Primero, la situación plana de Holditch se define rigurosamente y se consideran ciertos problemas como la existencia de dicha construcción o el modo de evitar movimientos retrógrados en el segmento que se va moviendo. En el enunciado del teorema de Holditch aparece el área de una elipse oculta. En este trabajo se utiliza una aproximación poligonal a dicho teorema para mostrar geométricamente de dónde proviene esta elipse. También es posible dar generalizaciones inmediatas de este teorema y de otros relacionados con la cinemática en otros contextos y situaciones. Así, en la segunda parte, se da una introducción a la geometría no euclidiana y se presenta la extensión de los resultados mencionados a superficies de curvatura constante. Además, se encuentran curvas cerradas ocultas en la superficie de curvatura constante relacionadas con el enunciado generalizado de Holditch. Finalmente, se obtiene una nueva extensión natural del teorema de Holditch para curvas espaciales, lo cual nos lleva al concepto de superficie de Holditch.Holditch's theorem is a classical result on areas of planar curves generated by moving chords. The construction is closely related to other kinds of curves such as parallel curves, constant width curves or bicycle curves. The basic properties of these curves are compiled and a historical review on Holditch's theorem and related theorems in kinematics is given. First, the Holditch planar setting is rigorously defined and problems such as the existence of that construction or the avoidance of retrograde movements of the moving chord are considered. In the statement of Holditch's theorem, the area of a hidden ellipse appears. A polygonal approach to the theorem is used to show geometrically where this ellipse comes from. Moreover, immediate generalizations of Holditch's theorem and related results to other contexts are possible. So, in the second part, an introduction to non-Euclidean geometry is given and the extension of such results to constant curvature surfaces is presented. In addition, hidden closed curves in the constant curvature manifold related to the generalized statement of Holditch's theorem are found. Finally, a new extension of Holditch's theorem to space curves is derived in a natural way leading to the concept of Holditch surface

Peer coaching: To what extent can it support the development of professional attributes required to be a teacher?

Students on a science PGCE course were introduced to peer coaching. This article describes the structures developed to enhance student teachers’ professional attributes and then reports the results. The students were given questionnaires to ascertain to what extent they felt they had developed their professional attributes as a result of being involved in peer coaching. The questionnaire design provided both qualitative and quantitative data. The evidence indicates that the peer coaching procedures had a positive impact on student teachers’ professional development. Data was analysed and has been used to draw conclusions to inform peer coaching in an education setting