Pythagorean Theorem Research Articles

Cooperative learning and group learning: The impact on high order thinking skills in the pythagorean theorem material

This study aims to improve students High Order Thinking Skills through the application of the Group to Group Exchange learning model. The research method used is a quasi-experimental model with a Pretest-Posttest Control Group research design and a sampling technique using Cluster Random Sampling. The results showed that based on the research results obtained during the study, the average N-Gain Score for the experimental group using the Group to Group Exchange learning model was 59% with a minimum N-Gain Score of 51% and a maximum of 67%. While the average N-Gain Score control group with the Direct Instruction learning model is 39% with a minimum N-Gain Score of 34% and a maximum of 45%. This means that the Group to Group Exchange (GTGE) learning model is quite effective compared to the Direct Instruction (DI) learning model to improve students High Order Thinking Skill (HOTS).

A NEW CONCEPT OF THE EXTENDED FORM OF PYTHAGORAS THEOREM

According to Pythagoras Theorem : In a right-angled triangle x2 + y2 = z2 , where, base = x, altitude = y, and hypotenuse = z. In the present paper, the author states that x2 + y2 = – z2 is the extended form of the Pythagoras Theorem.

Re-Reading The Humans Within The Context of The Theorem and Philosophy of Pythagoras

In The Humans, published in 2013, Matt Haig tells the story of a ‘commissioned’ alien sent to Earth from an extra-terrestrial planet. The extra-terrestrials have solved the mystery of prime numbers and have gone far beyond humanity in every sense. On the other hand, the humans living on Earth have just solved the secret about prime numbers that started with Pythagoras and continued for centuries. A professor named Andrew has reached the solution; with this solution, people will make significant progress in many fields, especially in areas related to technology. This transformation is seen as a danger to the world, and the extra-terrestrials try to prevent it. An alien lands on Earth and tries to eliminate Professor Andrew and the people who know this solution. At this point, the reader not only witnesses the struggle between an alien and humans, but is also confronted with an action-packed science fiction with traces of the famous philosopher and mathematician Pythagoras in the background. The author indirectly references Pythagoras’ mathematical theorem, calculations, philosophy, and thought in his narrative, which he tells as humor independent of all this intensity. This study aims to address Haig's work with Pythagoras in the background by making Pythagoras more visible. It aims to examine in detail the direct and indirect references to Pythagoras in his work, which is mathematical and philosophical.

Improve the stability of the rolling bridge by changing the shape of the internal mechanism

The London-designed Rolling Bridge inspired this study by Thomas Heatherwick to add stability to this bridge. This study aims to analyze what structures can increase the bridge's overall stability and determine the basic parameters. Finally, it revealed the structural type of this structure. This study uses force analysis, Pythagorean theorem and calculation of degrees of freedom to determine that the new structure is more stable than the original structure. In the study, the total length and number of segments were assumed to be constant to study the effect on geometry and static height during deployment. The study concluded that when the bridge's internal structure is triangular, the bridge is more stable than the original design in the folded state—the internal structure changes from triangular to trapezoidal when the bridge is extended to a horizontal position. When the bridge changes from the horizontal position to the folded state, the internal structure changes from trapezoidal to triangular. Meanwhile, hydraulic columns are mainly used to lift and bend bridges. Each structure has five nodes and five segments. Despite the increasing number and complexity of computations, the variable triangular structure is more stable than the fixed trapezoidal structure.

IMPLEMENTASI TEOREMA PHYTAGORAS DALAM PENYELESAIAN SOAL RANGKAIAN AC UNTUK MENINGKATKAN HASIL TES SISWA SMA

Alternating current circuits are one of the physics taught in senior high school. Alternating current (AC) circuits are material related to mathematical equations so that to study this material students must have good mathematical abilities. This research will discuss the improvement of test results for AC circuit material, especially in the RL series, RC series, and RLC series using an alternative method in the form of the Pythagorean theorem on the impedance and voltage equations. This is because the Pythagorean theorem has a mathematical equation that is identical to the impedance and voltage equations in AC circuits. This research was conducted at SMAN 2 Jember using two classes, namely XII MIPA 5 and XII MIPA 7 classes. Based on the research that has been done, the result is an increase in test results in class XII MIPA 5 of 0.54 in the medium category and an increase in test results in class XII MIPA 7 of 0.30 in the medium category. Therefore student responses indicate that the Pythagorean theorem can attract students' interest, provide motivation with positive student responses and students are satisfied in applying it in solving AC circuit problems.

ANALISIS KEMAMPUAN BERPIKIR KREATIF SISWA DALAM MENGERJAKAN SOAL MATERI TEOREMA PHYTAGORAS PADA SISWA SMP KELAS VIII

Abstract: This study aims to describe and analyze students' creative thinking abilities in the Pythagorean Theorem material. The ability to think creatively is the ability that students have to solve problems in problems in a different, unique way or have never been found by others. In this study the method used is a qualitative research method. The subjects in this study were 3 students of class VIII. The level of creative thinking ability is divided into 3 namely, creative, less creative, and not creative. Data collection was carried out by providing 4 questions on the Pythagorean theorem material which contained indicators for assessing creative thinking abilities, namely fluency, flexibility, originality, and detail. In this study, it was found that 1 student had the ability to think creatively, and 2 student had the ability to think less creatively.Keywords: Creative Thinking Ability, Phytagorean Theorem

Contour angle and peri-implant tissue height: Two interrelated features of the implant supracrestal complex.

Recent research has suggested the contour of the prosthesis and the vertical height of the peri-implant mucosa as important parameters thatcan influence the long term health and stability of the peri-implant tissue. In particular, overcontouring of the prosthesis has been correlated with an increased risk for peri-implantitis, while reduced soft tissue height has been associated with marginal bone loss, recession, and other soft tissue complications.Although these two parameters have been investigated as independent in the current literature, clinical experience points towarda close interrelation between transmucosal tissue height and prosthesis contour angle. It is often foundthat a reduced vertical height of the implant supracrestal complex is the main reason for overcontouring of the prosthesis. At the same time, achieving a favorable contour of 30o or less is not possible unless the clinician has ensured an adequate vertical height of the soft tissue. The purpose of this short communication is to establish the relation between tissue vertical height and prosthesis contour by utilizing a theoretical geometry equation based on the Pythagorean theorem. In doing so, one can use the dimensions of the implant as well as those of the prosthesis at the mucosal marginto calculate the essential vertical height for achieving a favorable prosthesis contour. As the treatment plan of the implant supracrestal complex is "top-down,"in case of deficient vertical height, subcrestal placement of the implant should be considered to achieve a proper prosthesis contour.

Experimental Geometry, Pythagorean Theorem and Montessori

Background: Some 19th and 20th-century geometry textbooks show methodological innovations in relation to the traditional books that followed Euclid's logical-deductive proposal. Objective: To analyse in the book Psico Geometria: el estúdio de la geometria basado en la psicologia infantil by Maria Montessori (1934) as the didactic approach of the Pythagorean theorem, proposed by her, fits into an experimental geometry perspective. Design: Using documentary analysis, we analysed the books of the following authors: Hoüel (1867), Méray (1874), Laisant (1898, 1906), Calkins (1861), Bert (1886), Prestes (1895), Lyra da Silva (1923), Wentworth and Hill (1901) and Montessori (1916, 1934) to understand the approach to teaching geometry.Environment and participants:The research sources collected in the National Library of France (BNF) and in the Universidade Federal de Santa Catarina (UFSC) Digital Repository refer to the geographic environment of authors from four countries Data collection and analysis: The selected and analysed documents can be found at BNF – Gallica in a digitized version, as well as at the UFSC Digital Repository. Based on the documentary analysis of these books, we found that the methodological proposals seek to escape from a deductive presentation of elementary geometry and include in their texts experiences for the introduction of concepts and visual demonstrations of elementary geometry. Results: The authors of the analysed works, from different countries, criticized the elementary teaching of geometry, especially the authors of textbooks, for the fact that they approach deductive geometry in the initial classes, favouring a deductive presentation of mathematics. Montessori's book shows an experimental geometry proposal for the Pythagorean theorem. Conclusion: We found that Montessori's proposal, besides presenting characteristics of an experimental geometry, also inserts some deductive reasoning.

Development of Adobe Flash as a media for learning Pythagoras Theorem in first State Junior High Schools

This development research aims to determine the results of the development of Adobe Flash as a medium for learning the Pythagorean theorem for class VIII SMP. The product resulting from this research is in the form of learning media on Pythagorean theorem material with several sub-discussions, namely using the Pythagorean theorem to calculate the length of one side of a triangle if the other two sides are known, calculating the ratio of sides in a right triangle with angles of 300 and 600, and calculating the ratio of the sides of a right triangle with an angle of 450. The development model used in this study refers to the model developed by Sivasailam Thiagarajan, Dorothy S. Semmel, and Melvyn I. Semmel in 1974, namely the 4D model. This model consists of four stages of development namely define, design, develop, and disseminate or abbreviated as 4D. The results of this development research were obtained as follows: First, the validation stage by 3 expert validators covering aspects of programming, content (material), and display obtained an average expert validation result of 4.19 indicating that learning media (products) are in the "valid" category. ”. Second, the trial phase is limited to students' responses to learning media and an average result of 89.167% is obtained which indicates that the learning media (product) is in the "very good" category. Third, the field test stage on average students gave a response of 87% indicating that the learning media (product) was in the "very good" category. The average pre-test result was 76.25 while the post-test average result was 86.27. There is a significant difference between the average results of the pre-test and post-test data. This result is reinforced by the results of the calculation of the related sample t-test with SPSS 16 software, the value of Sig. (2-tailed) = 0.000 < 0.05 = ????. Based on the results obtained from the stages that have been taken, it shows that the use of product development is "effective" in learning mathematics on the Pythagorean theorem material for class VIII students at SMPN 2 Labuapi

ANALYSIS OF CREATIVE THINKING SKILLS ON THE PHYTHAGOREAN THEOREM MATERIAL IN TERMS OF SELF-CONFIDENCE

The purpose of this study is to describe the ability of students' creative thinking processes on the Pythagorean theorem material which is reviewed based on self-confidence. The subjects of this study were Junior High School students at grade VIII in Jakarta, as many as 120 students. This study uses a qualitative method with a descriptive approach. The stages carried out are: filling out a self-confidence questionnaire, testing creative thinking skills with Pythagoras theorem questions, interviews, analyzing data, drawing conclusions. Based on the results obtained, the high self-confidence classification of students affects the students' high mathematical creative thinking skills as well. Classification of self-confidence is moderate, then the students' mathematical creative thinking ability is quite good. Conversely, if the classification of a student's self-confidence is low, then a student’s mathematical creative thinking skills is also low.
 Keywords: Creative Thingking Skill, Pythagorean Theorem, Self-Confidence

Deskripsi Kemampuan Representasi Matematis Siswa Kelas VIII SMP/MTs Ditinjau Dari Gaya Kognitif Visualizer Dan Verbalizer

Mathematical representation ability is one of the basic abilities that every student must have in examining, expressing, and exploring a mathematical idea in the form of a problem, information, definition, etc. to find an appropriate solution according to the results of the representation, whether in the form of pictures, words, tables, symbols, graphs, and patterns in mathematics. The biggest reason that hinders students' bright ideas from appearing is the weak ability of students' mathematical representations which hinders students in determining the completion of mathematical problems and even less careful in reading story problems, weak in problem analysis, inaccurate, and difficulty connecting between concepts. The subjects of this study were students of grade VIII in one of the MTs in the Angkona sub-district, which consisted of two students. The instrument used for this research is the Visualizer Verbalizer Questionnaire (VVQ). Mathematical representation ability test questions and interviews. This study used descriptive qualitative method. Based on the data analysis, it can be concluded that the students' representation abilities with the visualizer and verbalizer styles are quite good. There are several interesting things from the two research subjects, namely the Visualizer subject (SVi) in solving a problem prioritizing the visual aspect in examining each question and the information contained in the a simpler form in representing an image and illustration of a flat shape. Meanwhile, the subject verbalizer (SVe) is more likely to explore detailed and clear information in representing something related to the Pythagorean theorem.

Sums of the first n odd integers

There is a long tradition of mathematicians valuing collections of proofs, e.g. [1] is a famous recent collection. In the past, professional mathematicians have also written many different proofs of single important theorems, e.g. [2]. Proofs of the Pythagorean Theorem were collected by [3], and [4] discusses mathematical style through proofs of the irrationality of . The recent work of [5] is a discussion of mathematical style via a comparison of 99 different ‘proofs’ the following ‘theorem’.

Dissection-Like Proofs of the Law of Cosines

Summary Inspired by arguments illustrating the Pythagorean theorem, this paper gives six interrelated dissection-like proofs of the law of cosines. Each proof treats the acute- and obtuse-angle cases together, and uses a trigonometric double-angle formula. Some of the proofs assume the Pythagorean theorem.

Pengaruh Hubungankemampuan Komunikasi dan Penalaran Matematika Siswa Kelas VIII Terhadap Hasil Belajar Yang Diajar Dengan Model Pembelajaran Group Investigation (GI)

This study aims to determine whether there is a positive and significant effect of the Group Investigation type cooperative learning model on students' mathematical reasoning and communication skills in the Pythagorean Theorem sub-subject in class VIII SMP Negeri 1 Munte in the 2019/2020 Academic Year. The population in this study were all class VIII students of SMP Negeri 1Munte for the 2019/2020 Academic Year. While the sample in this study consisted of 2 classes of 38 students each in class VIII-1 as the experimental class and class VIII-3 as the control class. The experimental class uses the Group Investigation cooperative learning model consisting of 5 students per group, and the control class uses the Group Investigation type cooperative learning model consisting of 2 students per group. This type of research is an experiment. Prior to testing the hypothesis, the normality and homogeneity tests are tested first. Normality was tested using the Lilliefors technique and homogeneity using the F test. From the tests performed, it was found that both samples were normally distributed and homogeneous. There is a positive and significant influence of the Group Investigation cooperative learning model on the mathematical reasoning abilities of junior high school students. There is a positive and significant influence of the Group Investigation type of cooperative learning model on the mathematical communication skills of junior high school students because the average communication ability of students who are taught with the Group Investigation type cooperative learning model consisting of 5 people per group is higher than the average communication ability of students who are taught with the Group Investigation type cooperative learning model consisting of 2 people per group

Experimental Study of Robotic Polishing Process for Complex Violin Surface

This paper presents a robotic polishing process for complex violin surfaces to increase efficiency and minimize the cost and consumed time caused by using labor and traditional polishing machines. The polishing process is implemented based on modeling a smooth path, controlled contact force embedded with gravity compensation and material removal depth. A cubic Non-Uniform Rational Bases-Spline (NURBS) interpolation curve combined with an S-curve trajectory model is used to generate a smooth polishing path on a complex violin surface to achieve stable motion during the polishing process. An online admittance controller added to the fast gravity compensation algorithm maintains an accurate polishing force for equal removal depth on all polished surface areas. Then, based on Pythagorean theory, the removal depth model is calculated for the violin’s complex surface before and after polishing to estimate the accuracy of the polishing process. Experimental studies were conducted by polishing a wooden surface using the 6DOF robot manipulator to validate this methodology. The experimental results demonstrated that the robot had accurate polishing force based on the online admittance controller with gravity compensation. It also showed a precise proportional uniformity of removal depths at the different normal forces of 10, 15, and 20 N. The final results indicated that the proposed experimental polishing approach is accurate and polishes complex surfaces effectively.

The construction of $$\epsilon $$-splitting map

For a geodesic ball with non-negative Ricci curvature and almost maximal volume, without using compactness argument, we construct an $$\epsilon $$ -splitting map on a concentric geodesic ball with uniformly small radius. There are two new technical points in our proof. The first one is the way of finding n directional points by induction and stratified almost Gou–Gu Theorem. The other one is the error estimates of projections, which guarantee the n directional points we find really determine n different directions.

The Development of Mathematics Learning Media Using Google Sites Web Based on an Integrated Contextual Approach to Islamic Values for Junior High School Students in Riau, Indonesia

This article explains about the development of Google Sites web learning media based on a contextual approach integrated with Islamic values in mathematics material for junior high school or Islamic junior high school (MTs), including number patterns, circles, statistics, the Pythagorean theorem, and building flat-sided spaces, which can facilitate students’ learning. The product developed was tested in Islamic junior high schools or Islamic junior high school (MTs) in the Riau Province regencies, including Pekanbaru, Kampar and Indragiri Hilir, with the schools that have internet access. The research material for the Pekanbaru area is on Circles and Flat-sided Space Buildings, the Kampar area is on Statistics and the Pythagorean Theorem, and the Indragiri Hilir area is on Number Patterns. The data collection techniques used questionnaires and posttest questions with data types in the form of quantitative data and qualitative data. Based on data analysis from the learning media developed for the five materials above, it shows that the Google Sites web learning media based on a contextual approach integrated with Islamic values is in the valid, practical and effective category, where each material tested has an average posttest score for the experimental class which is higher than the average posttest score of the control class.

基于情境创设的初中数学深度学习教学设计研究——以“勾股定理”为例

基于情境创设的初中数学深度学习教学设计研究——以“勾股定理”为例

Analysis and Interpretation of Primary and Derived Data Sets in Cardiology

Investigators collect data and present them in a way that offers the best insight regarding the questions at hand. To facilitate understanding of certain aspects, it may occasionally be useful to rearrange primary data and formulate them as derived variables. For example, the travel distance divided by the invested time yields average velocity (as m/s). Problems may arise when interpreting ratios that fail to have a physical dimension. For example, current TV-sets have a fixed ratio for height and width, implying that we need an additional detail to define its size. Size then is determined by the diagonal, which can be calculated from the two sides using the Pythagorean theorem. Similarly, paired hemodynamic variables may be expressed as ratios. Again, a fixed ratio may refer to a variety of underlying primary data which require consideration if the ratio is unitless. In this survey, we evaluate several derived metrics commonly used in cardiovascular studies, and offer comprehensive analysis strategies.

A mathematical method to estimate angle and distance for percutaneous renal puncture based on computed tomography data: Description and validation.

Gaining access to the kidney is crucial step in percutaneous nephrolithotomy (PCNL); it has a steep learning curve. Describe the mathematical method to predict renal puncture angle and distance based on preoperative computed tomography (CT) measurements. Then evaluating how it correlates with measured values. The study was prospectively designed. After ethical committee approval, the study uses data from preoperative CT to construct a triangle so we can estimate puncture depth and angle. A triangle of three points, the first is point of entry to the pelvicalyceal system (PCS), the second is point on the skin perpendicular to it, and the third where the needle punctures the skin. The needle travel is estimated using the Pythagorean theorem and puncture angle using the inverse sine function. We evaluated 40 punctures in 36 PCNL procedures. After PCS puncture using fluoroscopy-guided triangulation, we measured the needle travel distance and angle to the horizontal plane. Then compared the results with mathematically estimated values. We targeted posterior lower calyx in 21 (70%) case. The correlation between measured and estimated needle travel distance with Rho coefficient of 0.76 with P < 0.001. The mean difference between the estimated and the measured needle travel was - 0.37 ± 1.2 cm (-2.6-1.6). Measured and estimated angle correlate with Rho coefficient of 0.77 and P < 0.001. The mean difference between the estimated and the measured angle was 2° ± 8° (-21°-16°). Mathematical estimation of needle depth and angle for gaining access to the kidney correlates well with measured values.