Pyramidal Volume Research Articles

Students' Ontogenic and Epistemological Obstacles on the Topic of Pyramid Volume

The concept of pyramid volume has been studied at the starting of the elementary school (SD) level and studied more deeply in junior high school (SMP). However, many students make mistakes in solving problems related to the volume of pyramids. This study aims to identify the ontogenic and epistemological obstacles of students in understanding the concept of pyramid volume. This is a qualitative research using a Didactical Design Research (DDR). Sixteen students of grade IX in Bandung who had studied the concept of pyramid volume participated in the study. Data were obtained by analyzing respondents’ ability tests and interviews to solve problems related to the volume of pyramids. Characteristics of ontogenic and epistemological obstacles were found in students’ knowledge in solving problems related to the concept of pyramid volume. The results showed that students experienced several ontogenic and epistemological obstacles which resulted in errors in problem-solving. Keywords: epistemological obstacles, pyramid volume, students’ ontogenic

Glacier Retreat Leads to the Expansion of Alpine Lake Karakul Observed Via Remote Sensing Water Volume Time Series Reconstruction

Due to high altitudes, Central Asian alpine lakes can serve as indicators of localized climate change. This article monitored the water volume time series trends of the ungauged alpine Lake Karakul, which is typical because of the abundance of glaciers in the basin, from 1990 to 2020 via multiple source remote sensing data. The “Global-Local” multi-scale lake extraction method is used to delineate the boundary of Lake Karakul. Consistency analysis was performed on the altimetry data of CryoSat-2, ICESat-1 and ICESat-2, assuming that the lake surface was flat; a threshold value was set to remove gross error, and then 3σ was used to remove the surface elevation anomaly. Based on the pyramid volume model, the lake area and surface elevation information were used to reconstruct the water volume time series of Lake Karakul. The influencing factors of water volume temporal variation were discussed. The results show that Lake Karakul has been on an expansionary trend in recent years: The lake area increased from 394.9 km2 in 1988 to 411.4 km2 in 2020; the rate of increase is 0.74 m/year. The surface elevation increased from 3886.6 m in 2003 to 3888.6 m in 2020; the rate of increase is 0.11 km2/year. The lake water volume accumulated was 0.817 km3 in 2003–2020, with an accumulation rate of 0.059 km3/year. The Lake Karakul basin is developing towards dry heat, with a cumulative temperature variation rate of +0.38 °C/year; the average rate of variation in annual cumulative precipitation is −3.37 mm/year; the average evapotranspiration in the watershed is on a fluctuating increasing trend, with a rate of variation of +0.43 mm/year; glaciers in the lake basin have a retreating trend, with an average annual rate of variation of −0.22 km2/year from 1992 to 2020. Lake Karakul is more sensitive to temperature variations, and the runoff from retreating glaciers in the basin is an important contribution to the expansion of Lake Karakul.

Kepraktisan dan Keefektifan Penggunaan E-LKPD Konteks Sosial Budaya Berbantuan Workbook GeoGebra terhadap Kemampuan Numerasi Peserta Didik pada Materi Limas

Numeracy is a person's ability to implement mathematics in the home, work and community environments. This research aims to measure the practicality and effectiveness of using E-LKPD in a socio-cultural context assisted by GeoGebra workbooks in improving students' numeracy skills in pyramid material. The type of research used was a quasi-experiment (Quasi-experiment) with research subjects 21 class VIII students at SMPN 1 Kalisat Jember. The practicality of E-LKPD is assessed from the results of student response questionnaires, while the effectiveness of E-LKPD is assessed from the results of students' numeracy ability tests. The use of E-LKPD is said to be practical if the average percentage of students' questionnaire responses is at least in the practical category, and effective if students' numeracy skills are at least in the medium category. Based on the practicality analysis, the results of the student response questionnaire regarding the use of E-LKPD obtained a percentage of 81.67% or were in the practical category. In addition, the use of E-LKPD shows an increase in students' numeracy skills on all numeracy indicators. This can be seen based on the results of the numeracy ability test which obtained an N-Gain score of 0.51 or at a medium effectiveness level. Therefore, the use of E-LKPD in a socio-cultural context with the help of GeoGebra workbooks is practical and effective for improving students' numeracy skills, especially in learning surface area and volume of pyramids.

The Number and Size of Individual Kidney Medullary Pyramids is Associated with Clinical Characteristics, Kidney Biopsy Findings, and CKD Outcomes among Kidney Donors.

Segmentation of multiple structures in cross-sectional imaging is time-consuming and impractical to perform manually, especially if the end goal is clinical implementation. In this study, we developed, validated, and demonstrated the capability of a deep learning algorithm to segment individual medullary pyramids in a rapid, accurate, and reproducible manner. The results demonstrate that cortex volume, medullary volume, number of pyramids, and mean pyramid volume is associated with patient clinical characteristics and microstructural findings and provide insights into the mechanisms that may lead to CKD. The kidney is a lobulated organ, but little is known regarding the clinical importance of the number and size of individual kidney lobes. After applying a previously validated algorithm to segment the cortex and medulla, a deep-learning algorithm was developed and validated to segment and count individual medullary pyramids on contrast-enhanced computed tomography images of living kidney donors before donation. The association of cortex volume, medullary volume, number of pyramids, and mean pyramid volume with concurrent clinical characteristics (kidney function and CKD risk factors), kidney biopsy morphology (nephron number, glomerular volume, and nephrosclerosis), and short- and long-term GFR <60 or <45 ml/min per 1.73 m 2 was assessed. Among 2876 living kidney donors, 1132 had short-term follow-up at a median of 3.8 months and 638 had long-term follow-up at a median of 10.0 years. Larger cortex volume was associated with younger age, male sex, larger body size, higher GFR, albuminuria, more nephrons, larger glomeruli, less nephrosclerosis, and lower risk of low GFR at follow-up. Larger pyramids were associated with older age, female sex, larger body size, higher GFR, more nephrons, larger glomerular volume, more nephrosclerosis, and higher risk of low GFR at follow-up. More pyramids were associated with younger age, male sex, greater height, no hypertension, higher GFR, lower uric acid, more nephrons, less nephrosclerosis, and a lower risk of low GFR at follow-up. Cortex volume and medullary pyramid volume and count reflect underlying variation in nephron number and nephron size as well as merging of pyramids because of age-related nephrosclerosis, with loss of detectable cortical columns separating pyramids.

An unsupervised deep learning model for dense velocity field reconstruction in particle image velocimetry (PIV) measurements

Supervised deep learning methods reported recently have shown promising capability and efficiency in particle image velocimetry (PIV) processes compared to the traditional cross correlation and optical flow methods. However, the deep learning-based methods in previous reports require synthesized particle images and simulated flows for training prior to applications, conflicting with experimental scenarios. To address this crucial limitation, unsupervised deep learning methods have also been proposed for flow velocity reconstruction, but they are generally limited to rough flow reconstructions with low accuracy in velocity due to, for example, particle occlusion and out-of-boundary motions. This paper proposes a new unsupervised deep learning model named UnPWCNet-PIV (an unsupervised optical flow network using Pyramid, Warping, and Cost Volume). Such a pyramidical network with specific enhancements on flow reconstructions holds capabilities to manage particle occlusion and boundary motions. The new model showed comparable accuracy and robustness with the advanced supervised deep learning methods, which are based on synthesized images, together with superior performance on experimental images. This paper presents the details of the UnPWCNet-PIV architecture and the assessments of its accuracy and robustness on both synthesized and experimental images.

A Systematic Solution for Moving-Target Detection and Tracking While Only Using a Monocular Camera

This paper focuses on moving-target detection and tracking in a three-dimensional (3D) space, and proposes a visual target tracking system only using a two-dimensional (2D) camera. To quickly detect moving targets, an improved optical flow method with detailed modifications in the pyramid, warping, and cost volume network (PWC-Net) is applied. Meanwhile, a clustering algorithm is used to accurately extract the moving target from a noisy background. Then, the target position is estimated using a proposed geometrical pinhole imaging algorithm and cubature Kalman filter (CKF). Specifically, the camera’s installation position and inner parameters are applied to calculate the azimuth, elevation angles, and depth of the target while only using 2D measurements. The proposed geometrical solution has a simple structure and fast computational speed. Different simulations and experiments verify the effectiveness of the proposed method.

Penile length and circumference: are they related to nose size?

We investigated the relationship between the size of the penis and that of the nose. We retrospectively analyzed 1,160 patients whose nose and penis sizes were measured. These participants were selected from a subset of 1,531 patients who visited the Dr. JOMULJU Urology Clinic between March and October 2022. Patients aged <20 years and those who underwent surgery for the nose and penis were excluded. Nose size was determined by measuring the length, width, and height of the nose, which were used to calculate the volume of the triangular pyramid. Stretched penile length (SPL) and penile circumference before erection were measured. The participants' height, weight, foot size, and serum testosterone levels were measured. Testicular size was measured using ultrasonography. Predictors of penile length and circumference were assessed using linear regression analysis. The participants' average age was 35.5 years, mean SPL was 11.2 cm, and mean penile circumference was 6.8 cm. Univariate analysis revealed that body weight, body mass index (BMI), the serum testosterone level, and nose size were associated with SPL. Multivariable analysis revealed that BMI (P=0.001) and nose size (P=0.023) were significant predictors of SPL. Univariate analysis revealed that penile circumference was related to an individual's height, weight, BMI, nose size, and foot size. Multivariable analysis revealed that body weight (P=0.008) and testicular size (P=0.002) were significant predictors of penile circumference. Nose size was a significant predictor of penile size. The sizes of the penis and nose increased with a decrease in BMI. This interesting study confirms the truth of an erstwhile myth about penis size.

Another look at the two Egyptian pyramid volume ‘formulas’ of 1850 BCE

This paper provides some methodological, didactical, and historiographical reflections on Egyptian pyramid volume formulas, responding to suggestions by Paul Shutler from 2009. These suggestions partly reiterate a historically documented proof by the Chinese Liu Hui (third century CE), although Lui Hui’s contribution was apparently unknown to Shutler. The latter came forward, in addition, with intuitive arguments which might have been used by the Egyptians to convince themselves of the correctness of their formula for the volume of the full pyramid. In a broad sense, the reflections in this paper may contribute to the use of history in the mathematical classroom. As a cautionary note: The paper is an abridged version of a longer manuscript that contains detailed explanations and discussions of historical secondary sources. Since the paper is somewhat outside the usual canon of mathematics historiography, I have deposited the longer manuscript on <arXiv.org>.

Automatic myocardium strain quantification in MR synthetic images with Deep Leaning.

Accurate quantification of myocardium strain in magnetic resonance images is important to correctly diagnose and monitor cardiac diseases. Currently, available methods to estimate motion are based on tracking brightness pattern differences between images. In cine-MR images, the myocardium interior presents an inhered homogeneity, which reduces the accuracy in estimated motion, and consequently strain. Neural networks have recently been shown to be an important tool for a variety of applications, including motion estimation. In this work, we investigate the feasibility of quantifying myocardium strain in cardiac resonance synthetic images using motion generated by a compact and powerful network called Pyramid, Warping, and Cost Volume (PWC). Using the motion generated by the neural network, the radial myocardium strain obtained presents a mean average error of 12.30% +- 6.50%, and in the circumferential direction 1.20% +-0.61 %, better than the two classical methods evaluated. Clinical Relevance- This work demonstrates the feasibility of estimating myocardium strain using motion estimated by a convolutional neural network.

Unsupervised Convolutional Neural Network for Motion Estimation in Ultrasound Elastography.

High-quality motion estimation is essential for ultrasound elastography (USE). Traditional motion estimation algorithms based on speckle tracking such as normalized cross correlation (NCC) or regularization such as global ultrasound elastography (GLUE) are time-consuming. In order to reduce the computational cost and ensure the accuracy of motion estimation, many convolutional neural networks have been introduced into USE. Most of these networks such as radio-frequency modified pyramid, warping and cost volume network (RFMPWC-Net) are supervised and need many ground truths as labels in network training. However, the ground truths are laborious to collect for USE. In this study, we proposed a MaskFlownet-based unsupervised convolutional neural network (MF-UCNN) for fast and high-quality motion estimation in USE. The inputs to MF-UCNN are the concatenation of RF, envelope, and B-mode images before and after deformation, while the outputs are the axial and lateral displacement fields. The similarity between the predeformed image and the warped image (i.e., the postdeformed image compensated by the estimated displacement fields) and the smoothness of the estimated displacement fields were incorporated in the loss function. The network was compared with modified pyramid, warping and cost volume network (MPWC-Net)++, RFMPWC-Net, GLUE, and NCC. Results of simulations, breast phantom, and in vivo experiments show that MF-UCNN obtains higher signal-to-noise ratio (SNR) and higher contrast-to-noise ratio (CNR). MF-UCNN achieves high-quality motion estimation with significantly reduced computation time. It is unsupervised and does not need any ground truths as labels in the training, and, thus, has great potential for motion estimation in USE.

LKPD Berbasis Discovery-Learning Pada Materi Luas Permukaan dan Volume Prisma dan Limas

Mathematics learning has important and strategic roles in Indonesian education-system. One of mathematical subjects learnt at school is geometry. Many real-life contexts are related to concept of geometry, especially surface-area and volume. However, some previous studies show that many students have difficulties learning concepts of surface-area and volume of prisms and pyramids. This due to learning that only emphasizes on memorizing formulas makes the learning itself less meaningful for students, so students’ learning motivation is low. One alternative that can be done is the use of student worksheets (LKPD). This worksheet is based on a learning approach that facilitates students to build their understanding independently and present meaningful mathematical activities. Therefore, in this study, discovery-learning based worksheets were developed for surface-area and volume of prisms and pyramids. This study uses Research and Development method within ADDIE model. Result of this study shows that LKPD is valid. This is indicated by results of expert validation wich obtains 83.09% that meets valid criteria. Moreover, the assessment of experts on the aspect of "the suitability of LKPD with concept of discovery-learning" obtained 81.25% which indicates that the mathematical concept and activities used in the worksheets is in accordance with the concept of discovery-learning.

STUDENT'S ABILITY IN EXPLAINING THE CONCEPT OF SOLID FIGURE'S VOLUME REVIEWED FROM VISUALIZER VERBALIZER COGNITIVE STYLE

The purpose of this study was to describe student's ability to explain the concept of solid figure's volume reviewed from visualizer-verbalizer cognitive style using the Cognitive Style Test developed by Mendelson &amp; Thorson. This study used a qualitative approach and the data collection technique was carried out by giving tests about the concept of solid figure's volume and interviews. The indicators used to measure students' ability to explain the concept of solid figure's volume are, (1) Providing information in accordance with mathematical concepts (2) Information systematically organized with the aim of showing a mathematical relationship (3) using and selecting procedures or operations certain exactly. The results showed that both visualizer subjects (SV) and verbalizer subjects (SB) were only able to fulfill the first indicator in explaining the concept, both of them just can mention the formula of pyramid's volume. Meanwhile, to explain the concept of ball's volume, SV does not meet the third indicator, SV did not use the right mathematical procedures or operations. Both subjects showed characteristics that matched their cognitive style, namely SV was more flexible in providing explanations through pictures and SB preferred to make explanations in the form of descriptions.

Study of Virtual Reality Immersive Technology Enhanced Mathematics Geometry Learning.

Mathematics is an important foundation for the development of science education. In the past, when instructors taught mathematical concepts of geometry shapes, they usually used traditional textbooks and aids to conduct teaching activities, which resulted in students not being able to understand the principles completely. Nowadays, it has become a trend to integrate emerging technologies into mathematics courses and to use digital instructional aids. Emerging technologies can effectively enhance students’ sensory experience while strengthening their impressions and understandings of subject concepts. In this paper, we apply virtual reality immersive technologies to develop a “virtual reality immersive learning mathematics geometry system,” which is used to teach mathematical geometry concepts. Teachers use the system to develop three basic mathematical geometry learning materials: “Triangular pyramid volume = 1/3 prism volume,” “Cone volume calculation,” and “Triangle center of gravity derivation.” In the experimental activity, the teacher uses virtual reality teaching aids to guide students to learn mathematical geometry concepts in a fun way so that they can achieve the effectiveness of immersive learning. This study explores the impact of using the virtual reality immersive learning mathematics geometry system on students’ technology acceptance, learning motivations, and learning performance. The experimental result showed that using the virtual reality immersive learning mathematics geometry system can improve the learning motivation and learning performance of students. The findings indicated that the experimental group had better learning outcomes after completing the learning tasks of three geometric units. The experimental group used the virtual reality immersive learning mathematics geometry system which can lead to better learning outcomes. According to the ARCS questionnaire, students in the experimental group were confident to understand new subjects. At the same time, the mode of completing the game can effectively give students a sense of accomplishment. The use of emerging technologies in the classroom can be an attractive learning mode for students.

Efficient 3D Deep LiDAR Odometry.

An efficient 3D point cloud learning architecture, named EfficientLO-Net, for LiDAR odometry is first proposed in this article. In this architecture, the projection-aware representation of the 3D point cloud is proposed to organize the raw 3D point cloud into an ordered data form to achieve efficiency. The Pyramid, Warping, and Cost volume (PWC) structure for the LiDAR odometry task is built to estimate and refine the pose in a coarse-to-fine approach. A projection-aware attentive cost volume is built to directly associate two discrete point clouds and obtain embedding motion patterns. Then, a trainable embedding mask is proposed to weigh the local motion patterns to regress the overall pose and filter outlier points. The trainable pose warp-refinement module is iteratively used with embedding mask optimized hierarchically to make the pose estimation more robust for outliers. The entire architecture is holistically optimized end-to-end to achieve adaptive learning of cost volume and mask, and all operations involving point cloud sampling and grouping are accelerated by projection-aware 3D feature learning methods. The superior performance and effectiveness of our LiDAR odometry architecture are demonstrated on KITTI, M2DGR, and Argoverse datasets. Our method outperforms all recent learning-based methods and even the geometry-based approach, LOAM with mapping optimization, on most sequences of KITTI odometry dataset. We open sourced our codes at: https://github.com/IRMVLab/EfficientLO-Net.

Parallel multiscale context-based edge-preserving optical flow estimation with occlusion detection

Although convolutional neural network (CNN)-based optical flow approaches have exhibited good performance in terms of computational accuracy and efficiency in recent years, the issue of edge-blurring caused by motion occlusions remains. In this paper, we propose a parallel multiscale context-based edge-preserving optical flow estimation method with occlusion detection, named PMC-PWC. First, we exploit a parallel multiscale context (PMC) network for occlusion detection, in which the proposed PMC model is able to aggregate the multiscale context information to develop the performance of occlusion detection near motion boundaries. Second, we combine the PMC model with a context network to plan an occlusion estimation module and incorporate it into a pyramid, warping, and cost volume model to construct an edge-preserving optical flow computation network. Third, we design a novel loss function including an endpoint error (EPE)-based loss, a binary cross-entropy loss and an edge loss to supervise the proposed PMC-PWC network to produce optical flow and occlusion simultaneously. Finally, we run the proposed PMC-PWC method on the MPI-Sintel and KITTI datasets to conduct a comprehensive comparison with several state-of-the-art approaches. The experimental results indicate that the proposed PMC-PWC method performed well in terms of both accuracy and robustness, especially due to the significant benefits of edge preservation and occlusion handling.

PENGEMBANGAN VIDEO PEMBELAJARAN MATEMATIKA UNTUK MENINGKATKAN HASIL BELAJAR KOGNITIF SISWA

The purpose of this study is to produce a valid, practical, and effective learning video that can improve cognitive learning outcomes for grade VIII students of Public Junior High School 5 Malang on the Prism dan Pyramid Volume material. The development model used is ADDIE (analysis, design, development, implementation, and evaluation). The quality of the resulting learning video meets the following criteria: a) valid, with an averange score of 3,38 by material experts and media experts; b) practical, with an averange score of teacher response questionnaires and student response questionnaires of 3,50; c) effective, with an averange score of student learning test results of 83,75 and has met the Minimum Completeness Criteria (KKM) at Public Junior High School 5 Malang, namely 78. Thus, it can be conclude that the learning videos developed are valid, practical, and effective to improve cognitive learning outcomes of grade VIII Students of Public Junior High School 5 Malang on prism and pyramid volume material.

Ratio of In-Sphere Volume to Polyhedron Volume of the Great Pyramid Compared to Selected Convex Polyhedral Solids

The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result RV = π ⋅ φ5, where is the golden mean. It is important that the number φ5 is a fundamental constant of nature describing phase transition from microscopic to cosmic scale. In this contribution the relatively small volume ratio of the Great Pyramid was compared to that of selected convex polyhedral solids such as the Platonic solids respectively the face-rich truncated icosahedron (bucky ball) as one of Archimedes’ solids leading to effective filling of the polyhedron by its in-sphere and therefore the highest volume ratio of the selected examples. The smallest ratio was found for the Great Pyramid. A regression analysis delivers the highly reliable volume ratio relation , where nF represents the number of polyhedron faces and b approximates the silver mean. For less-symmetrical solids with a unique axis (tetragonal pyramids) the in-sphere can be replaced by a biaxial ellipsoid of maximum volume to adjust the RV relation more reliably.

Pengajaran Persiapan Ujian Nasional Mata Pelajaran Matematika di SMP Negeri 37 Samarinda

Community Service conducted at SMP 37 is teaching national math preparation tests for class IX. The method of community service in Samarinda 37 State Junior High School is by teaching using the junior high school national exam practice module. Activities carried out through the stage of providing material operations of fractions, value comparisons and reversals of values, ranks and roots, calculation of loan and savings interest rates, arithmetic sequences and sequences and geometry, linear and quadratic equations, sets, linear functions, line equations, line gradients, flat circumference and shape area, congruent and congruent triangles, circle angle, circle circumference, circle elements, prism and pyramid elements, volume and surface area of ​​prism and pyramid, statistics, sample space, and opportunity. After all the material has been submitted, it is continued with the prediction of the national mathematics exams in 2013, 2014, 2015, 2016, 2017, and 2018 with the development of the developed training modules. From the results of community service in Samarinda 37 Public Middle School, the level of student satisfaction found using modules was 41.52% very satisfied, 57.40% satisfied, 1.07% quite satisfied, and 0.00% dissatisfied. On the other hand, students also find it easier to understand learning if the teacher uses modules as teaching material in class

PENERAPAN MODEL PEMBELAJARAN KOOPERATIF TIPE INVESTIGATION DENGAN PENDEKATAN OPEN ENDED PROBLEM UNTUK MENINGKATKAN KEMAMPUAN REPRESENTASI MATEMATIS

The purpose of this research is to improve the ability of mathematical representation of Grade VIII2 students at SMP Negeri 3 Raha 2018/2019 Academic Year during mathematics learning activities with the application of cooperative learning model in the type group investigation with open ended problem approach. The type of research is classroom researh of two cycles based on teaching syllabus of the mathematics teacher in class VIII2. Each cycle is carried ot based on the competency standards to be achieved in learning. The cycle in this class action research through four stages, namely : planning of action; implementation of action; observation and evaluation; reflection. Based on the result of research conducted on the Grade VIII2 students at SMP Negeri 3 Raha 2018/2019 Academic Year on the competency standards: calculating area and volume of prism and pyramid using cooperative learning model in the type group investigation with open ended problem approach can improve the ability of mathematical representation, which are : respones and learning outcomes shown in cycle II are primly goodand the students scoreof mathematical representation test capability in each cycle has improve signivicantly, until 80% on the last cycle. Moreover, the results showed that there are only 4 students from total 20 students who obtain score 68 which is the minimum completeness criteria set by the school . Student activities and learning management by the teacher in the learning process also increased to cycle II reaching an average of 82% and 81%. Therefore, learning by applying cooperative learning model in the type group investigation with open ended problem approach can improve the ability of mathematical representation

Mathematical Reasoning in Mathematics Learning on Pyramid Volume Concepts

The purpose of this study was to describe the standard process of mathematical reasoning in learning on pyramid volume concepts. The study was a study with descriptive qualitative approach, carried out by peer teaching in the classroom. The subjects of this research were Class B Postgraduate 2018 (S2) students, State University of Malang. The standard process of this activity was to recognize reasoning and verification as a basic aspect in mathematics, to make and investigate mathematical conjecture, to find out how to develop and evaluate mathematical arguments and verification, to find out how to choose and use various types of reasoning and proof methods.