Multiple representations and GeoGebra-based learning environments

The dynamic mathematics software GeoGebra offers the possibility of generating interactive applets for use in learning environments. Its graphics, algebra, computer algebra and spreadsheet views combine multiple mathematical representations with each other in an interactive and connected way. On the one hand, the software facilitates the visualization of mathematical concepts and facts. On the other hand, GeoGebra supports the interaction of different forms of representation of mathematical objects. In this paper, the use of GeoGebra applets is particularly addressed concerning tablet computers, which are becoming increasingly important and are distinguished by their intuitive operation with fingers. Abstract mathematics now becomes available at students’ fingertips allowing a very direct form of interaction with mathematical concepts and objects. One way to implement such learning environments are collections of interactive applets in so called “GeoGebraBooks” which are presented in this paper

Gaining momentum: GeoGebra inspires educators and students around the world

The use of technology is slowly becoming a substantial part of today’s education. Although due to the increased accessibility of affordable computing technologies in the 1980s and 90s it was predicted that computers would become rapidly integrated into mathematics teaching and learning (Kaput, 1992), technology uptake in schools has been considerably slow. The current expansion of technology use took a new unconventional direction: a bottom-up, community-based collaborative development, catalyzed by Internet-based communities and increasingly available community-developed software packages. During the past decades it has been demonstrated that a large number of enthusiasts can alter conventional thinking and models of development and innovation. The success of open source projects like Linux, Firefox, Moodle, and Wikipedia shows that collaboration and sharing can produce valuable resources in a variety of areas of life. While working on the open-source project GeoGebra we are witnessing the emergence of an enthusiastic international community around the software

CP asymmetries in chargino production and decay: the three-body decay case

We study CP violation in chargino production and decay in the Minimal Supersymmetric Standard Model (MSSM) with complex parameters at an e^+ e^- linear collider with longitudinally polarized beams. We investigate CP-sensitive asymmetries by means of triple product correlations and study their dependence on the complex parameters M_1 and mu. We give numerical predictions for the asymmetries and their measurability at the future International Linear Collider. Our results show that the CP asymmetries can be measured in a large region of the MSSM parameter space.Comment: 22 pages, LaTeX, 8 figures; v2: structural changes and references added, main conclusions unchanged, published versio

Deciding geometric properties symbolically in GeoGebra

It is well known that Dynamic Geometry (DGS) software systems can be useful tools in the teaching/learning of reasoning and proof. GeoGebra 5.0 was recently extended by an Automated Theorem Prover (ATP) subsystem that is able to compute proofs of Euclidean geometry statements. Free availability and portability of GeoGebra has made it possible to harness these novel techniques on tablets, smartphones and computers. Then, we think it is urgently necessary to address the new challenges posed by the availability of geometric ATP?s to millions of students worldwide

Fracture behavior of high strength pearlitic steel wires

Steel wires are widely used in various industrial applications. Hence, the drawing process and the resulting mechanical properties are of significant scientific and industrial importance. In this investigation the focus is on pearlitic steel wires with relatively high drawing strains and resulting high ultimate tensile strengths up to several GPa. The fracture behavior was investigated for two different wires with a drawing strain of 3.10 and 6.52 with a diameter of about 100 µm and 20 µm, respectively. The resulting ultimate tensile strength varies between 4 and 7 GPa [1]. The fracture toughness was measured with crack propagation direction in drawing direction and perpendicular to it. To test the fracture toughness of the samples in drawing direction micro-bending beams were fabricated utilizing a focused ion beam (FIB). For investigating the direction perpendicular to the drawing direction, the wires were notched with a FIB and tested under tensile and bending loading. The fracture toughness experiments for both directions were performed in-situ in the SEM. In addition, some samples of the perpendicular direction were tested ex-situ as well. The results of the fracture experiments show a strong anisotropy of the fracture behavior. It was revealed that in drawing direction the wires show a significantly lower fracture toughness than perpendicular to it. This is further supported by the in-situ and ex-situ bending experiments of the second testing direction, where the crack kinks into the drawing direction

Effects of Lepton Flavour Violation on Chargino Production at the Linear Collider

We study the effects of lepton flavour violation (LFV) on the production processes e+e- --> \chi+_i \chi-_j at a linear collider with longitudinal e+ and e- beam polarizations. In the case of LFV the sneutrino mass eigenstates have no definite flavour, therefore, in the t-channel more than one sneutrino mass eigenstate can contribute to the chargino production cross sections. Our framework is the Minimal Supersymmetric Standard Model (MSSM) including LFV terms. We show that in spite of the restrictions on the LFV parameters due to the current limits on rare lepton decays, the cross section \sigma(e+e- --> \chi+_1 \chi-_1) can change by a factor of 2 or more when varying the LFV mixing angles. We point out that even if the present bound on BR(tau- --> e- gamma) improves by a factor of thousand the influence of LFV on the chargino production cross section can be significant. These results could have an important impact on the strategies for determining the underlying model parameters at the linear collider.Comment: 11pp; final version for JHE

Femtosecond laser and FIB: A revolutionary approach in rapid micro- mechanical sample preparation

The established Focused Ion Beam (FIB) technique usually poses a bottleneck in the preparation of samples for micro-mechanical experiments. This is due to its limited material removal rate. Especially for tungsten, the sputter yield of the Ga+ ion beam is very low. Therefore the practical sample size is restricted to dimensions of a few micrometers. On the contrary a femtosecond laser offers ablation rates 4-6 orders of magnitude higher compared to a Ga+ FIB [1] and therefore allows a rapid fabrication of specimens on the meso-scale. A prototype, which combines both methods, has been developed on the basis of the Zeiss Auriga Laser platform [2]. This system consists of the main chamber, where the FIB milling is conducted, and a separated airlock chamber for the femtosecond laser ablation. This setup prevents the contamination of the main chamber with laser ablated material and allows laser processing under atmospheric, inert gas or vacuum conditions. Fracture toughness experiments on single crystal tungsten in the micro-regime [3] exhibit a different behavior compared to specimens on the macro-scale [4]. The rapid processing of specimens with the novel laser system allows to sample the transition region from a discrete flow behavior of the micro-sized cantilevers to macroscopic plasticity. An analysis of fracture experiments for sample sizes ranging from 20 x 20 x 100 µm^3 to 200 x 200 x 1000 µm^3 is conducted. In addition to that, the quality of the laser processed samples is analyzed regarding the influence of processing parameters. Please click Additional Files below to see the full abstract

Wolfgang Borchert: A Representative of "Trümmerliteratur"?

This investigation examines whether Wolfgang Borchert's short stories are representative of "Trümmerliteratur". By "Trümmerliteratur" I am referring to that short period in 20th century German Literature which was manifested by the causes and effects of World War II (1945-1947). Borchert's biographical data, the events leading to the emergence of "Trümmerliteratur" and a definition for and discussion of this literary phenomenon, and an analysis of four of Borchert's "Kurzgeschichten", ''Die Hundeblume", "Vier Soldaten", "Der Kaffee ist undefinierbar", and "Er hatte auch viel Ärger mit den Kriegen", are presented. Investigation includes as well an extensive bibliography