Pythagorean Theorem Research Articles

Pengembangan Bahan Ajar Berbasis Learning Cycle untuk Meningkatkan Hasil Belajar Matematika Siswa Kelas VIII SMP Kabupaten Tapanuli Utara

This study describes the development of learning cycle teaching materials that are valid, effective, and practical for improving students' mathematics learning outcomes in class VIII SMP Tapanuli Utara and improving student mathematics learning outcomes using teaching materials based on the learning cycle method developed in class VIII SMP Tapanuli District North. As subjects in this study were class VIII students of SMP Negeri 2 Parmonangan for the 2021/2022 Academic Year. As subjects in this study were class VIII students of SMP Negeri 2 Parmonangan for the 2021/2022 Academic Year. The object of this research is mathematics teaching materials which are developed based on the learning cycle learning method to improve mathematics learning outcomes in the Pythagorean Theorem material. The research model is development research with a modification of the Borg and Gall development procedure. Development research is generally divided into 3 (three) stages, namely the problem identification stage, the design stage, and the deployment stage. The results of the study stated that the teaching materials based on the learning cycle method developed were valid, effective, and practical to use to improve students' mathematics learning outcomes in class VIII of SMP Tapanuli Utara. Teaching materials based on the learning cycle method developed can improve student learning outcomes in class VIII of SMP Tapanuli Utara. Obtaining arithmetic results or an N-Gain value of 0.64 with the category of moderate or good learning improvement results.

Pengembangan Komik Digital Berbasis Cerita Parabel Untuk Meningkatkan Pemahaman Konsep Jenis Segitiga Berbantuan Teorema Phytagoras

The main objective of this research was to develop a digital comic based on a valid and effective parable story that can improve understanding of the concept of triangle types with the help of the Pythagorean theorem. The method used was research and development using the Borg and Gall development model. The subjects of this study were students of class VIII A MTs NU 01 Pecalungan Batang, totaling 30 students. Collecting data was done through expert validation questionnaires, product-related responses, and students' concept understanding tests. The results of this research and development were that learning media in the form of Digital Comics Based on Parable Stories were declared valid based on the validation results of material experts and media experts, as well as teacher and student response questionnaires. This study also showed an increase in students' pretest scores and post-test scores, so the media was also effective in increasing students' understanding of concepts. With this research and development, it is hoped that it can be used as an interest to develop other innovations that are effectively used in learning.

Development of a Pocket Book with Islamic Nuances Based on HOTS and Contextual Pythagorean Theorem

Development of a Pocket Book with Islamic Nuances Based on HOTS and Contextual Pythagorean Theorem

Analysis of Mathematical Communication Ability on Problem-Solving Pythagoras Theorem Viewed From Students' Cognitive Style

This research is motivated by the fact that students' mathematical communication skills still need to be improved. This study aims to describe students' written and oral mathematical communication abilities toward solving the Pythagorean theorem problem in terms of field-dependent and field-independent cognitive styles in class VIII-B at SMP Al-Islam Krian. This type of research is qualitative research with a descriptive method. Subjects in this study were taken using a purposive sampling technique after carrying out the GEFT test in class VIII-B of 2 students, each based on field-independent and field-dependent cognitive styles. The instruments prepared in this study were the GEFT test, a mathematical communication skills test, and an oral examination. Based on the analysis of the answer sheets for the mathematical communication ability test and the oral test, it was concluded that students with field-independent cognitive styles have good written or oral mathematical communication skills. This can be seen from students' ability to write down and convey information, solve problems coherently, systematically, and transparently, and draw conclusions correctly. Students with field-dependent cognitive styles need better mathematical communication skills. This can be seen from the ability of students who need help to correctly write down and convey information, problem-solving ideas coherently, systematically, and clearly, as well as conclusions

Representasi Matematis Siswa dalam Menyelesaikan Masalah Teorema Pythagoras berdasarkan Tahapan Polya Ditinjau dari Perbedaan Gender

Mathematical representations is the real product or result that represent mathematical ideas in various forms, such as diagrams, graphs and other concrete forms to help finding solutions to problems. Mathematical representation in problem solving is the main thing since, the use of right mathematical representation can help in solving the problem correctly. The purpose of this research is to describe the mathematical representation of masculine male students and feminine female students in solving Pythagorean Theorem problems based on Polya's stages. The research method used is descriptive qualitative. The research subjects were 3 masculine male students and 3 feminine female students at Junior High School 2 Gresik. Data is collected using BSRI questionnaire, mathematical ability test, problem solving test, and interviews. The results of problem solving test were showed that at the stage of understanding the problem, masculine male students presented known information using visual and symbolic representations while feminine female students used verbal and symbolic representations. To present what is being asked, masculine male students and feminine female students using verbal representations. At the planning stage, masculine male students and feminine female students explained solving strategies using verbal representations. At the stage of carrying out the plan, masculine male students and feminine female students solving the problems using visual, symbolic, and verbal representations, and presenting the results of the solution using verbal representations. At the re-examining stage, masculine male students and feminine female students using verbal representations to conclude the completion results and checking the completion results using symbolic representations.

Developing A Textbook of Alternating Current Circuit Completed by Solving Problems Using Pythagoras Theorem

One of the most difficult chapters in physics is alternating current circuits. This material is also one of the materials tested in the university test. This is because the material requires a fairly complicated mathematical approach. Additionally, the alternating current circuit textbooks that have been used so far still use too high language. Therefore, the researchers need a simple way that can facilitate students in solving alternating current circuit problems and be packaged in a textbook. A simple way to solve alternating current problems can be done using the Pythagorean theorem. This is because the two are identical. Therefore, the purpose of this research is to develop a textbook on alternating current circuit material accompanied by a solution using a simpler method, namely the Pythagorean theorem. This study uses a research and development model with the ADDIE (Analysis, Design, Development, Implementation, and Evaluation) stages. There were five research instruments used: (1) validation sheets; (2) teacher interview sheets; (3) teacher and student needs sheets; (4) test sheets; and (5) student response questionnaire sheets. The developed textbook has been validated by two experts and one user with a percentage value of 89.13%, so it is in the very valid category. In addition, based on the results of field tests on 34 class XII students of Senior High School in Jember, it is known that the developed textbook obtained an effectiveness percentage of 83.46% with an N-Gain value of 83.46. The textbook is in the high category and has a response questionnaire percentage of 80.3, so the developed textbook received a very positive response from students. By using this textbook, students can solve alternating current circuit problems more effectively and efficiently.

Developing a Colorimetric Equation and a Colorimetric Model to Create a Smartphone Application That Identifies the Ripening Stage of Lady Finger Bananas in Thailand.

This article develops a colorimetric equation and a colorimetric model to create a smartphone application that identifies the ripening stage of the lady finger banana (LFB) (Musa AA group 'Kluai Khai', กล้วยไข่ "gluay kai" in Thai). The mobile application photographs an LFB, automatically analyzes the color of the banana, and tells the user the number of days until the banana ripens and the number of days the banana will remain edible. The application is called the Automatic Banana Ripeness Indicator (ABRI, pronounced like "Aubrey"), and the rapid analysis that it provides is useful to anyone involved in the storage and distribution of bananas. The colorimetric equation interprets the skin color with the CIE L*a*b* color model in conjunction with the Pythagorean theorem. The colorimetric model has three parts. First, COCO-SSD object detection locates and identifies the banana in the image. Second, the Automatic Power-Law Transformation, developed here, adjusts the illumination to a standard derived from the average of a set of laboratory images. After removing the image background and converting the image to L*a*b*, the data are sent to the colorimetric equation to calculate the ripening stage. Results show that ABRI correctly detects a banana with 91.45% accuracy and the Automatic Power-Law Transformation correctly adjusts the image illumination with 95.72% accuracy. The colorimetric equation correctly identifies the ripening stage of all incoming images. ABRI is thus an accurate and robust tool that quickly, conveniently, and reliably provides the user with any LFB's ripening stage and the remaining days for consumption.

Space vector-based model predictive current controller for grid-connected converter under unbalanced and distorted grid without a phase-locked loop

This paper presents an improved current control strategy for a three-phase voltage source converter connected to distorted grid. The proposed controller can successfully compensate the induced harmonic currents, while suppressing possible active power ripple. To manage various objectives and deal with tough restrictions, model predictive control can offer a promising solution. However, a modified extended complex Kalman filter is introduced to estimate the positive and negative fundamental components of the grid voltages which are used with the real and reactive power references to generate pure sinusoidal reference currents without the need for a phase-locked loop (PLL), avoiding its challenges under abnormal grid conditions. An improved space vector-based model predictive control (SVM-MPC) is proposed to regulate the real and reactive power components. The main target of this controller is to maintain harmonic free grid currents, even in unbalanced and distorted grid conditions, with enhanced performance in terms of fast dynamic response and good steady-state behavior. The proposed SVM MPC uses Pythagoras theorem to determine duty factors, avoiding trigonometric functions, which improves the computational burden and implementation complexity. In addition, fixed switching frequency can be ensured. Simulation and experimental results are carried out to validate the effectiveness and the practical feasibility of the proposed controller under distorted grid conditions.

On Some Applications of the Method of Dimensional Analysis in the Course of Physics and Mathematics

Key words: problem, non-dimensional coefficient, quantity, exponent, dependence In the article, it was attempted to classify and represent the effective applications of the dimensional analysis method in the process of solving problems based on the principle of gradual complexity, which is the scientific and methodological novelty of the work, in order to highlight the role of the method in ensuring the informality and effectiveness of training. Particular attention is paid to the issues of the limits of the method’s applicability. In the first part of the work, the essence of the dimensional analysis method is briefly outlined, and then the simplest problems easily solved by its direct application are considered. The next section represents the cases when the desired physical expressions determined by this method can be uniquely determined with the accuracy of a constant dimensionless factor. As an example, the problem of determining the period of an oscillatory circuit is solved. The cycle of physical problems ends with a discussion of the problem of the Casimir phenomenon, for the solution of which, along with the method of dimensions, additional physical reasoning is used. When getting acquainted with the method of dimensional analysis, an initial erroneous impression may arise that the method is most applicable in physics, and is unlikely to have a possible effective application in mathematics. However, this is not true. No wonder the famous physicist, academician Migdal began his famous book on approximation and modeling of physical phenomena by proving the Pythagorean theorem using the dimensional analysis method. In the last section of the work, some tasks and test tasks of mathematics are considered, in the solution of which the dimensional analysis method is used.

Analysis of the Mathematical Comprehension Ability of Grade VIII Students on the Pythagorean Theorem

This study aims to describe students' mathematical understanding abilities, especially in circle material. This research was conducted at MTs Nurul Yaqin Pekanbaru to 10 grade VIII students. The method used in this study is a descriptive method using a qualitative approach to analyze student answers from the given instrument. The instrument used in this study was a written test of mathematical comprehension ability with two questions. Based on the results of data analysis, it can be seen that the mathematical understanding ability of class VIII students at MTs Nurul Yaqin Pekanbaru is still relatively low. Students cannot apply formulas in simple calculations, perform algorithmic calculations, and do not understand the questions given. During learning, only a few students actively asked and answered questions given by the teacher. Students who were less active in the learning process tended to listen and take notes delivered by the teacher. Students had difficulty understanding questions, were not challenged to solve non-routine math problems, were nervous about answering questions about poorly understood mathematic material, were doubtful about being able to learn difficult mathematic material on their own, and were unable to find new ways to do difficult math problems.

EVOLUTION OF TEMPLE ELEVATIONAL FORM WITH SQUARE CIRCLE METHOD: LAKSHMAN TEMPLE IN SIRPUR

One of the fundamental methods for shaping the constructional geometry of any building is the use of basic shapes: circles and squares. The circle represents vitality or energy, while the square represents strength. In world history, the concept of geometry traces its origins to construction in Egypt and Babylonia, where proportional systems were described through mathematical equations. They later became known as the Pythagorean Theorem, named after Pythagoras. In Ancient India, the concept of geometry starts with the construction of altars for Vedic sacrifices, as per the instructions of the Śulbasūtras. This involved creating circles and squares, converting squares to circles and vice versa, resulting in altars of various shapes and proportionate systems. The intersection of these basic shapes, the square and the circle, is the key to constructional building geometry. For instance, Vesica Piscis is a geometrical element derived from the circle-circle intersection. It has been applied by researchers to examine the geometry of both ancient and modern buildings. Similarly, the Square-Circle Sequence (SCS) is a method derived from the square-circle intersection. Gandotra (2011) used it to study the constructional geometry of the Hindu temples in North India (Nāgara temples). Meister (1985) also applied the square-circle intersection geometric constructional method to define the proportionate system of the Hindu temples in India. Finally, this study attempts to correlate these types of constructional geometry in the evolution of elevational form of Nāgara temples through Lakshman temple in Sirpur. It determines that the building’s elevational form may be derived from the basic shapes of the circle and the square.

Магический квадрат Лошу: регистр истины

The world’s oldest 3x3 magic square, discovered/invented in Ancient China and now known as Luoshu 洛書/ ‘Document [from the River] Luo’, was endowed by Chinese tradition with unprecedented dignity and placed at the very heart of Chinese thought. The bewitching geometric-numerical imagery of Luoshu, open to a great many different visions, when reading-interpretation becomes the final moment of the very act of perception, turns this Chinese mandala into a real eye trap. With its disturbing persistence, it resembles the magically attractive ‘Zahir’ from Borges’ short story of the same name. Among the most diverse ritual and ideological instrumentalizations of the Luoshu magic square (from the sacred emblem of cosmic harmony to the requisite of a geomancer), the mobilization of this esoteric figure for the arithmetization of the cornerstone of all Chinese philosophy, the fundamentally non-verbalizable Tao, is dominant. The coding of the dao by the number 15 is reinforced by its spatialization, so that the entire “Document [from the river] Lo” appears as a map of the various trajectories of the Tao within this nine-field square. Moreover, the coincidence (in number 15) of differently composed sums appears as an inscrutable variety of paths leading to the same goal - the final implementation of Tao. By virtue of the validity of the equality 15 =mod10 5 the magic sum of the Luoshu square (Const15) immutably, although covertly (in the form of a number 5), centers the entire Luoshu configuration. This secrecy of the magical constant (the latter is absent in the entire observable space of the “Document [from the river] Lo”) refers to the hidden “back-side” of Luoshu numbers, represented by the number 10 (in its role as a modulus of comparison in the arithmetic of residues modulo 10). Judging by the directly visible, so to speak, ‘front’ part of the magic square of order 3, it is allowed to count only up to nine in it. But the already absent-present magic sum (number 15), breaking the seemingly inescapable circle of arithmetic of residues, brings to light the comparison module (number 10) as Luosh’s hidden ‘truth’, which alone gives meaning to the entire nine-cell construction. Awareness of this truth is the first step in the transition to the ‘register of truth’ of this extraordinary gestalt. The subsequent connection to it of problems focused by the Pythagorean theorem radically expands Luoshu’s ‘register of truth’. The geometrized arithmetic of the Luoshu magic square, which is a unique spatial-numerical fixation of the seemingly fundamentally non-objectivable Tao (i.e., combining the apparently incompatible) marks the possibility of a paradoxical union of Heraclitus with Pythagoras, successfully realized by the Chinese tradition.

Kabes Pupphy Learning Media (Pythagorean Proving Puzzle) for Mathematics Learning Pythagorean Material

This study aims to describe learning media to facilitate students in constructing an understanding of the Pythagorean theorem. This study describes a learning media product in the form of a puzzle called Pupphy (Pythagorean Proving Puzzle). Pupphy is a puzzle proving the Pythagorean theorem on the Pythagorean theorem material for grade VIII students in junior high school. This media is different from the others because it is made from environmentally friendly materials that are easily found in the surrounding environment and can also be made by students themselves. This research uses a qualitative approach that uses narrative data and aims to describe a medium that can be used in learning mathematics using Pythagorean material as an innovative learning method. Pupphy is packaged in an interactive animation form that is equipped with an evaluation of the understanding of the Pythagorean theorem so that it allows students to carry out individual evaluations of competency achievements related to the Pythagorean theorem. The structure of the material in Pupphy consists of an explanation of the elements of a right triangle, an animation of the discovery of the Pythagorean theorem formula, and the application of this formula to right triangles. to find out the feasibility of a test conducted by media experts and material experts and also conducted on students.

Prediction of the Cervical Epidural Space Depth from the Skin Using Cervical X-Ray, During Cervical Epidural Block with Paramedian Approach.

The purpose of this study is to compare the actual needle depth measured during cervical epidural block (CEB) with the predicted needle depth measured through a cervical flexion x-ray image at the paramedian approach. The study was conducted based on the medical records of patients who underwent CEB at the pain clinic of Haeundae Paik Hospital. The actual needle distance (AD) was recorded after each successful CEB. The distance from the spinolaminar line to the skin, predicted median depth (PMD), was measured using lateral x-ray images. The medial to lateral distance (MLD), which is the distance from the midline of the spine to the needle insertion point, was measured using anteroposterior (AP) x-rays. The predicted paramedian depth (PPD) was calculated using the Pythagorean formula. The PMD represents the expected depth of the median approach, while the PPD represents the expected depth of the paramedian approach. The PMD, PPD, and AD were compared with each other. Concordance correlation coefficient (CCC) and Bland-Altman analysis were obtained for PMD and PPD. The CCC value of PMD was measured as 0.829, and the CCC value of PPD was measured as 0.830. In the Bland-Altman analysis, PPD was measured at -0.13 ± 8.37 mm, and PMD was measured at 1.29 ± 8.38 mm. When performing CEB through the paramedian approach, the depth can be predicted using a cervical flexion x-ray. At this time, the PMD can also be used to predict the depth during the paramedian approach.

How to estimate the sarcomere size based on oblique sections of skeletal muscle.

Ultrastructural analysis of muscular biopsy is based on images of longitudinal sections of the fibers. Sometimes, due to experimental limitations, the resulting sections are instead oblique, and no accurate morphological information can be extracted with standard analysis methods. Thus, the biopsy is performed again, but this is too invasive and time-consuming. In this study, we focused our attention on the sarcomere's shape and we investigated which is the structural information that can be obtained from oblique sections. A routine was written in MATLAB to allow the visualization of how a sarcomere's section appears in ultrastructural images obtained by Transmission Electron Microscopy (TEM) at different secant angles. The routine was used also to analyze the intersection between a cylinder and a plane to show how the Z-bands and M-line lengths vary at different secant angles. Moreover, we explored how to calculate sarcomere's radius and length as well as the secant angle from ultrastructural images, based only on geometrical considerations (Pythagorean theorem and trigonometric functions). The equations to calculate these parameters starting from ultrastructural image measurements were found. Noteworthy, to obtain the real sarcomere length in quasi-longitudinal sections, a small correction in the standard procedure is needed and highlighted in the text. In conclusion, even non-longitudinal sections of skeletal muscles can be used to extrapolate morphological information of sarcomeres, which are important parameters for diagnostic purposes.

Optic Nerve Head Changes After Intraocular Pressure-Lowering Glaucoma Surgeries Using Optical Coherence Tomography.

Optic nerve head (ONH) changes were detected with swept-source optical coherence tomography (SS-OCT) after intraocular pressure (IOP)-lowering glaucoma surgeries. The aim of this study was to detect changes in the ONH with SS-OCT after IOP-lowering procedures. Patients with progressing glaucoma who were referred for IOP-lowering procedures were included. The participants underwent a 24-2 visual field test and SS-OCT (DRI OCT Triton Plus; Topcon). IOP and SS-OCT scans were obtained during the preoperative period and up to 7 days and 30-90 days postoperatively. ONH parameters were measured with a B -scan at the center of the optic disc and an average of 5 central B -scans. The hypotenuse of the ONH cup (HOC) was calculated using the Pythagorean theorem: hypotenuse 2 = leg1 2 + leg2 2 , considering the length and depth of the cup as the legs of a right triangle. We also evaluated changes in Bruch membrane opening (BMO)-to-BMO diameter. Statistical analysis was performed using generalized estimating equations. A total of 15 eyes were included. The mean patient age was 70 (SD, 11.04) years. The mean circumpapillary retinal nerve fiber layer was 60.13 (SD, 23.21) µm and the visual field mean deviation was -13.29 (SD, 8.5) dB. The mean IOP at each visit was: 20.5 (SD, 4.99); 11 (SD, 4.95), and 15.7 (SD, 5.04), respectively. The mean HOC, the mean depth and length of the ONH cup, and the BMO-to-BMO diameter decreased significantly after the IOP-lowering procedures. The HOC evaluated with SS-OCT significantly decreased after IOP-lowering surgeries. This parameter was useful for evaluating short-term changes in the ONH.

Propagator-Oriented Programming Model Using Java

The aim of this work is to explore and analyze an unconventional style of programming based on a pro- pagator-oriented model of computation. The paradigm of propagation is characterized by networks of local, independent, stateless machines interconnected with stateful storage cells. This model allows for a highly modular design and multidirectional computation, enabling the creation of complex systems that can respond to changes and update their state accordingly. This work provides an overview of the propagator- oriented programming model, its motivations, and its advantages over other well-known alternative styles, using unsophisticated examples written in the Java programming language. We illustrate how propagator networks can be used to build flexible and efficient systems and present a basic framework for building such networks. The foun- dational components of the propagation model are imple- mented in Java as groundwork for the general-purpose framework. We demonstrate the power of propagator-oriented prog- ramming through an example of a Pythagorean Theorem implementation. The example shows how the model can be used to build complex systems of an arbitrary number of constraints and cells. We highlight the importance of information propagation over limited linear computation and the benefits of the multidirectional computation enabled by propagator networks.

It’s Off the Screen: Unearthing Megagons Through Technology

Mathematical action technology can foster equitable student discourse. Students engage in cycles of proof to create, test, and revise conjectures through dynamic exploration of the Pythagorean theorem.

Why and whence the Hilbert space in quantum theory?

We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum micro-events and from Hilbertian sum of squares $|\mathfrak{a}_1|^2+|\mathfrak{a}_2|^2+\cdots$. The latter leads (non-axiomatically) to the standard writing of the Born formula $\mathtt{f} = |\langle\psi|\varphi\rangle|^2$. As a corollary, the status of Pythagorean theorem, the concept of a length, and the 6-th Hilbert problem undergo a quantum `revision'. An issue of deriving the norm topology may no have a short-length solution (too many abstract math-axioms) but is likely solvable in the affirmative; the problem is reformulated as a mathematical one.

The Effect of the Use of Audio Visual Media on Student Learning Interest in the Concept of the Pythagorean Theorem

This study aims to determine whether there is an effect of using audio visual media on student interest in the subject matter of the Pythagorean Theorem in Class VIII of Timika Adventist Junior High School and how the effect is. The population in this study were all students of class VIII SMP Advent Timika with a total of 124 students. The results of the t-test statistic test using the Independent Sample Test technique to test the hypothesis "Is there any effect of using audio visual media on student interest in the subject matter of the Pythagorean Theorem for Class VIII of Timika Adventist Middle School." The test results show that the tcount value of audio-visual media is 2.327 and the tcount value of student learning interest is 3.327, with a Sig value of 0.000. This shows that the tcount value is greater than the ttable value of 1.671 while the Sig value is smaller than 0.05. Thus Ha is accepted and Ho is rejected, meaning there is a significant influence of the use of audio visual learning media on students' interest in learning the main material of the pythagorean theorem class VIII Timika Adventist Middle School.