GeoGebra is a free, open-source, and multi-platform software that combines dynamic geometry, algebra and calculus in one easy-to-use package. Students from middle-school to university can use it in classrooms and at home. In this workshop, we will introduce the features of GeoGebra with a special focus on not very common applications of a dynamic geometry program. We will inform about plans for developing training and research networks connected to GeoGebra. We can expect that at the time of the conference a spreadsheet will be integrated into GeoGebra which offers new ways teaching mathematics using the interplay between the features of a spreadsheet and the objects of dynamic geometry.

GeoGebra is a free, open-source, and multi-platform software that combines dynamic geometry, algebra and calculus in one easy-to-use package. Students from middle-school to university can use it in classrooms and at home. In this workshop, we will introduce the features of GeoGebra with a special focus on not very common applications of a dynamic geometry program. We will inform about plans for developing training and research networks connected to GeoGebra. We can expect that at the time of the conference a spreadsheet will be integrated into GeoGebra which offers new ways teaching mathematics using the interplay between the features of a spreadsheet and the objects of dynamic geometry.

Submitted by Cristiane Chim (cristiane.chim@ucpel.edu.br) on 2018-05-08T17:34:22Z No. of bitstreams: 1 Vagner Guidotti Furtado (1).pdf: 2942442 bytes, checksum: a43c18ecb28456284d4b6c622f11210d (MD5) / Made available in DSpace on 2018-05-08T17:34:22Z (GMT). No. of bitstreams: 1 Vagner Guidotti Furtado (1).pdf: 2942442 bytes, checksum: a43c18ecb28456284d4b6c622f11210d (MD5) Previous issue date: 2017-12-07 / The division operation in digital systems has its relevance because it is a necessary function in several applications, such as general purpose processors, digital signal processors and microcontrollers. The digital divider circuit is of great architectural complexity and may occupy a considerable area in the design of an integrated circuit, and as a consequence may have a great influence on the static and dynamic power dissipation of the circuit as a whole. In relation to the application of dividing circuits in circuits of the Digital Signal Processing (DSP) area, adaptive filters have a particular appeal, especially when using algorithms that perform a normalization in the input signals. In view of the above, this work focuses on the proposition of algorithms, techniques for reducing energy consumption and logical area, proposition and implementation of efficient dividing circuit architectures for use in adaptive filters. The Newton-Raphson and Goldschmidt iterative dividing circuits both operating at fixed-point were specifically addressed. The results of the synthesis of the implemented architectures of the divisors with the proposed algorithms and techniques showed considerable reduction of power and logical area of the circuits. In particular, the dividing circuits were applied in adaptive filter architectures based on the NLMS (Normalized least Mean Square) algorithm, seeking to add to these filters, characteristics of good convergence speed, combined with the improvement in energy efficiency. The adaptive filters implemented are used in the case study of harmonic cancellation on electrocardiogram signals / A operação de divisão em sistemas digitais tem sua relevância por se tratar de uma função necessária em diversas aplicações, tais como processadores de propósito geral, processadores digitais de sinais e microcontroladores. O circuito divisor digital é de grande complexidade arquitetural, podendo ocupar uma área considerável no projeto de um circuito integrado, e por consequência pode ter uma grande influência na dissipação de potência estática e dinâmica do circuito como um todo. Em relação à aplicação de circuitos divisores em circuitos da área DSP (Digital Signal Processing), os filtros adaptativos têm um particular apelo, principalmente quando são utilizados algoritmos que realizam uma normalização nos sinais de entrada. Diante do exposto, este trabalho foca na proposição de algoritmos, técnicas de redução de consumo de energia e área lógica, proposição e implementação de arquiteturas de circuitos divisores eficientes para utilização em filtros adaptativos. Foram abordados em específico os circuitos divisores iterativos Newton-Raphson e Goldschmidt ambos operando em ponto-fixo. Os resultados da síntese das arquiteturas implementadas dos divisores com os algoritmos e técnicas propostas mostraram considerável redução de potência e área lógica dos circuitos. Em particular, os circuitos divisores foram aplicados em arquiteturas de filtros adaptativos baseadas no algoritmo NLMS (Normalized least Mean Square), buscando agregar a esses filtros, características de boa velocidade de convergência, aliada à melhoria na eficiência energética. Os filtros adaptativos implementados são utilizados no estudo de caso de cancelamento de harmônicas em sinais de eletrocardiograma (ECG)