Pengembangan lembar kerja siswa materi garis singgung lingkaran untuk pembelajaran menggunakan model inquiry

Based on observations at PPL in SMP 21 Malang in 2012/2013, many student of class 8^th and 9^th are forget how to calculate the length of common tangent. The purpose of this development is to produce a student worksheet on the material tangent for activity learning using Inquiry model which is valid, practical, and effective.Development of student worksheet on tangen material for activity learning using Inquiry models was adapting by Plomp model. In developing a learning media consists of five phases: (1) initial investigation phase, (2) the design phase, (3) phase of realization / construction, (4) phase of the test, evaluation, and revision (5) the implementation phase. According from validation and the results of field trial the student worksheets were developed was valid by percentage of 88.3 percent, practically by percentage of 87.5 percent, and called effective because the scores that were obtained by six students in to answer evaluation had passed the minimum passing score which is given is 75. Berdasarkan observasi saat PPL di SMP Negeri 21 Malang tahun 2012/2013, banyak siswa kelas VIII dan IX lupa saat ditanya bagaimana cara menghitung panjang garis singgung persekutuan dua lingkaran. Tujuan dari pengembangan ini untuk mengembangkan lembar kerja siswa dengan materi garis singgung lingkaran untuk pembelajaran menggunakan model Inquiry yang valid, praktis dan efektif. Pengembangan lembar kerja siswa materi garis singgung lingkaran untuk pembelajaran model Inquiry ini dikembangkan dengan mengadaptasi model Plomp. Dalam mengembangkan media pembelajaran terdiri menjadi lima fase yaitu : (1) fase investigasi awal, (2) fase desain, (3) fase realisasi/konstruksi, (4) fase tes, evaluasi, dan revisi (5) fase implementasi. Berdasarkan hasil validasi dan uji coba lapangan lembar kerja siswa yang dikembangkan valid dengan persentase 88,3 persen, praktis dengan persentase 87,5 persen, dan dikatakan valid karena nilai evaluasi yang didapatkan oleh enam siswa memenuhi kriteria kelulusan minimal yang diberikan yaitu 75

Non-acyclic SL2-representations of Twist Knots, -3-Dehn Surgeries, and L-functions

We study irreducible $\mathop{\textrm{SL}}\nolimits _2$-representations of twist knots. We first determine all non-acyclic $\mathop{\textrm{SL}}\nolimits _2({\mathbb{C}})$-representations, which turn out to lie on a line denoted as $x=y$ in ${\mathbb{R}}^2$. Our main tools are character variety, Reidemeister torsion, and Chebyshev polynomials. We also verify a certain common tangent property, which yields a result on $L$-functions, that is, the orders of the knot modules associated to the universal deformations. Secondly, we prove that a representation is on the line $x=y$ if and only if it factors through the $-3$-Dehn surgery, and is non-acyclic if and only if the image of a certain element is of order 3. Finally, we study absolutely irreducible non-acyclic representations $\overline{\rho }$ over a finite field with characteristic $p>2$, to concretely determine all non-trivial $L$-functions $L_{{\boldsymbol{\rho }}}$ of the universal deformations over complete discrete valuation rings. We show among other things that $L_{{\boldsymbol{\rho }}}$ $\dot{=}$ $k_n(x)^2$ holds for a certain series $k_n(x)$ of polynomials.

PENGEMBANGAN PERANGKAT PEMBELAJARAN MENGGUNAKAN PENDEKATAN SAINTIFIK BERBANTUAN GEOGEBRA PADA MATERI GARIS SINGGUNG PERSEKUTUAN DUA LINGKARAN UNTUK KELAS VIII SMP

The aims of this research is to describe the process and outcomes of the development of learning equipment using the GeoGebra-assisted with scientific approach for common tangent of to two circles on 8th grade junior high school which is valid, practical, and effective. The process of developing learning equipment in this research use the Plomp model (2010) consisting of preliminary research phase by analyzing students’ needs and material analyzing, the second phase is prototyping that arranging learning equipment based of the result from the previous anlysis and the last phase is assessment by testing the result of the development of learning equipment. The learning equipment developed are Syllabus, Lesson Plan and Student Worksheet. Based on the results of the validation, the learning equipment meets the validity criteria with is 3,23 then the Syllabus is valid, is 3,43 then the Lesson Plan is very valid and is 3,22 then Student Worksheet is valid. The learning equipment meets the practicality criteria based on observations implementation with average score on the first day is 3,78 and the second day is 3,92 which is included in the excellent category. The effectiveness criteria are meets based on the results of the students' responses in the positive category is 85,2% and the results of the student learning test with the percentage of students completing classical learning in the high category is 81,25%. Based on the results of the analysis of these data, the result of this research is that the learning equipment using the GeoGebra-assisted scientific approach for common tangent of to two circles on 8th grade junior high school fullfilled the criteria of valid, practical and effective.

Analyzing students’ abstraction in learning common tangent lines of two circles based on cognitive styles

[English]: This study was aimed to describe the abstraction process of students with different cognitive styles in learning common tangent lines of two circles using recognizing, building-with, and construction (RBC) model. This qualitative research collected data through questionnaires, written tests, and task-based interviews. Eight students with field-dependent and field-independent were involved as the subjects. The interview transcripts were analyzed and grouped into cognitive actions of the RBC model. Findings showed that to reach the stage of construction activities, field-dependent students tend to need guidance and more time in recognizing and constructing the concept of a common tangent of two circles using their prior knowledge. Meanwhile, field-independent students tend to directly recognize and construct the concept using their prior knowledge so that they successfully constructed the concept of common tangent lines of two circles. This study shows that (1) field-dependent students use their prior knowledge that relates to the concept of common tangent lines of two circles less than field-independent students who tend to be able to use most of their prior knowledge relevant to the concept of common tangent lines of two circles, and (2) students who has similar cognitive style may not show the same success in abstraction process. Keywords: Abstraction, Circles, Common tangent line, Cognitive style, RBC Model [Bahasa]: Penelitian kualitatif ini bertujuan untuk mendeskripsikan abstraksi siswa SMP dengan gaya kognitif berbeda dalam mempelajari garis singgung pada dua lingkaran yang dianalisis menggunakan model RBC (Recognizing, Building-with, Construction). Data penelitian dikumpulkan melalui angket, tes tertulis, dan wawancara berbasis tugas. Delapan siswa dengan gaya kognitif field-dependent dan field-independent dipilih sebagai subjek penelitian. Data penelitian dianalisis berdasarkan rekaman wawancara yang sudah ditranskrip dan dikelompokkan berdasarkan tindakan kognitif model RBC. Hasil penelitian menunjukkan bahwa siswa field-dependent cenderung memerlukan petunjuk dan waktu lebih lama untuk mengenali dan membangun konsep garis singgung pada dua lingkaran melalui pengetahuan terdahulu hingga sampai pada aktivitas konstruksi. Sementara siswa field-independent cenderung langsung mengenali dan membangun konsep garis singgung pada dua lingkaran melalui pengetahuan terdahulu sehingga berhasil mengkonstruksi konsep garis singgung pada dua lingkaran. Penelitian ini menunjukkan bahwa (1) siswa field-dependent lebih sedikit menggunakan pengetahuan terdahulu yang berkaitan dengan konsep garis singgung dua lingkaran daripada siswa field-independent yang cenderung dapat melihat sebagian besar pengetahuan lama yang relevan dengan konsep garis singgung dua lingkaran, (2) siswa dengan gaya kognitif yang sama belum tentu menunjukkan keberhasilan yang sama pada proses abstraksi. Kata kunci: Abstraksi, Dua lingkaran, Garis singgung, Gaya kognitif, Model RBC

ANALYSIS OF ENERGY PARAMETERS OF BINARY INTERACTIONS OF UNIQUAC AND NRTL MODELS ON THE SECOND DERIVATIVE ENERGY OF GIBBS OF MIXTURE FOR BINARY MIXTURES

Проведена оценка энергетических параметров бинарного взаимодействия моделей UNIQUAC и NRTL по второй производной энергии Гиббса смешения на примере смесей 1-пропанол–вода и вода–масляная кислота. Экспериментальные и расчетные данные согласуются с высокой точностью. Установлено, что известные энергетические параметры для смеси 1-пропанол–вода прогнозируют расслаивание смеси, так как некоторые из членов второй производной энергии Гиббса смешения при расчете фазового равновесия пар–жидкость являются отрицательными. Расслаивание подтверждено наличием двух точек с общей касательной кривой зависимости энергии Гиббса от концентрации x1. В литературе отсутствуют данные о расслаивании данной смеси. 1-Пропанол и вода смешиваются в любых соотношениях, и азеотроп является гомогенным. Анализ энергетических параметров бинарного взаимодействия смеси вода–масляная кислота также показал наличие отрицательных членов второй производной энергии Гиббса смешения, что не противоречит имеющимся данным, согласно которым азеотроп является гетерогенным. Таким образом, при поиске параметров бинарного взаимодействия моделей UNIQUAC и NRTL при обработке экспериментальных данных необходимо проводить их анализ по второй производной энергии Гиббса смешения. The energy parameters of the binary interaction of the UNIQUAC and NRTL models for the second derivative of the Gibbs energy mixing are estimated using the example of mixtures 1-propanol-water and water-butyric acid. The experimental and calculated data are consistent with high accuracy. It is established that the known energy parameters for the 1-propanol–water mixture predict the delamination of the mixture, since some of the terms of the second derivative of the Gibbs energy mixing in the vapor-liquid phase equilibrium calculation are negative. The delamination was confirmed by the presence of two points with a common tangent to the curve of the dependence of the Gibbs energy on the concentration x1. There is no data in the literature on the delamination of this mixture. 1-propanol and water are mixed in any ratio, and the azeotrope is homogeneous. The analysis of the energy parameters of the binary interaction of the water–butyric acid mixture also showed the presence of negative members of the second derivative of the Gibbs energy mixing, which does not contradict the literature data, according to which the azeotrope is heterogeneous. Thus, when searching for the parameters of the binary interaction of the UNIQUAC and NRTL models during the processing of the experimental data, it is necessary to analyze them using the second derivative of the Gibbs energy mixing.

Modeling of Liquid-Liquid Demixing Curve in Lead-Zinc Binary System

In this work we discussed the modeling of the demixing curve in the liquid state in the Lead – Zinc binary system. We are interested to recalculate the free energies relating on Pb-Zn alloys for several temperatures based on the thermodynamic data collected in the bibliography. This calculation allows us to trace the curve of phase separation from a program after obtaining the mole fractions corresponding to the common tangent to the curve of the free energy with two minima at different temperatures. To do this, we used the Matlab 7.1 as the programming language and the Redlich-Kister polynomial as a mathematical model of development. The results obtained are very satisfactory by comparing them with those of the bibliography.

System aksjologiczny muzułmanów — wyzwanie czy element wspólnej kultury Europy?

Niniejszy artykuł stara się w miarę możliwości odpowiedzieć na pytanie, czy sys­tem aksjologiczny reprezentowany przez wyznawców islamu stanowi wyzwanie dla kultury europejskiej, czy też może jest jej integralną częścią składową. Na drodze do rozwikłania tego złożonego zagadnienia artykuł prezentuje w pierwszej kolejności, obok pewnych uwag wstępnych i metodolo­gicznych, pewien zasób informacji historycznych stanowiących niezbędne tło do dalszych rozważań. W głównej części praca skupia się na ukazaniu interferencji europejskiej i muzułmańskiej kultury oraz prawa. Wskazuje na pewne elementy wspólne, styczne oraz rozłączne. Artykuł usiłuje zdefi­niować pewne — kluczowe dla zadanego pytania — pojęcia, sygnalizując trudności interpretacyjne i będącą konsekwencją tych nieścisłości niemożność jednoznacznej odpowiedzi na postawione w temacie artykułu pytanie. Axiological system of Muslims — achallenge or an element of the common culture of Europe? This paper attempts to answer the question whether the axiological system, repre­sented by Muslim believers, is a challenge for European culture, or is it an integral part of this culture. At first, the article presents some introductory and methodological thoughts as well as provides a ne­cessary historical background for further analysis. In its main part, the paper focuses on the interfer­ence of European and Muslim culture as well as legal systems. Some common, tangent and disjoint elements are pointed out. The article attempts to define some terms, essential to a given question. It highlights the difficulties of interpretation and, as a consequence, inability to give an unequivocal answer to the question raised in the subject of this article.

Radiographic assessment of the proximal tibial angles in dogs and cats with and without cranial cruciate ligament rupture

ABSTRACT: The influence of the proximal tibial angles in the cranial cruciate ligament (CCL) rupture in dogs is still controversial, and little is known regarding this topic in cats. The aim of this study was to evaluate and compare the angles of the proximal portion of the tibia in dogs and cats with and without CCL rupture. Retrospective and prospective radiographs of the stifle joints were obtained and divided into four groups. Group 1 was composed of 70 stifle joint images of dogs without orthopedic disorders (healthy dogs), group 2 had 70 stifle joint images of dogs with CCL rupture, group 3 had 50 stifle joint images of cats without orthopedic disorders (healthy cats) and group 4 had 25 stifle joint images of cats with CCL rupture. Radiographs were taken with the stifle joint in the mediolateral projection, positioned at the angle of hind limb support. Between the two groups of dogs evaluated, the dogs with CCL rupture had statistically greater tibial plateau angle (TPA) compared with healthy dogs. No difference was shown in relation to the TPA between healthy cats and cats with CCL rupture. In relation to the patellar ligament angle by tibial plateau method the values for the healthy dogs were significantly higher than those for the CCL ruptured dogs. Similarly, healthy cats had significantly higher mean values than cats with CCL rupture. In the patellar ligament angle by common tangent method there was no significantly difference between the two groups of dogs. Between the two groups of cats, animals with CCL rupture had statistically higher mean values than healthy cats. In general, the groups of dogs showed higher mean values than the groups of cats. For the patellar ligament insertion angle (PLIA) healthy dogs showed a significantly higher mean than dogs with CCL rupture. There was no significant difference between the groups of cats. In conclusion, the TPA and the PLIA possibly influence the etiology of CCL rupture in dogs but not in cats. The low patellar ligament angle measured by common tangent method may favorably influence the reduced incidence of CCL rupture in cats.

Steiner’s Porism in finite Miquelian Möbius planes

We investigate Steiner’s Porism in finite Miquelian Möbius planes constructed over the pair of finite fields GF(q) and GF(q2), for an odd prime powerq. Properties of common tangent circles for two given concentric circles are discussed and with that, a finite version of Steiner’s Porism for concentric circles is stated and proved. We formulate conditions on the length of a Steiner chain by using the quadratic residue theorem in GF(q). These results are then generalized to an arbitrary pair of non-intersecting circles by introducing the notion of capacitance, which turns out to be invariant under Möbius transformations. Finally, the results are compared with the situation in the classical Euclidean plane.