Penerapan Modifikasi Fraktal Segitiga Sierpinski pada Ragam Hias Geometris Tumpal

Sierpinski’s triangular fractal is a linear fractal that has self-similarity, which is identical until infinite iterations. This research aims to develop the Tumpal geometric ornaments with the implementation of modified Sierpinski’s triangular fractal. There are three algorithms that will be used. First, an algorithm to modify the Sierpinski triangle. The isosceles triangle is divided into nine congruent triangles. Then randomly selected several triangles to be left blank. Do the same way to the triangle that still exists until some iteration. Second, modeling the base frames. Third, fill the basic frame from the second algorithm with the modified Sierpinski's triangular fractal from the first algorithm into a motif. The results are various Tumpal geometric motifs with the implementation of modified Sierpinski’s triangular fractal. Keywords: linear fractal, Sierpinski’s triangular fractal, ornament, Tumpal geometric Abstrak Fraktal segitiga Sierpinski merupakan fraktal linier yang memiliki sifat self-similarity, yaitu identik sampai pada iterasi tak terhingga. Penelitian ini bertujuan untuk mengembangkan ragam hias geometris Tumpal dengan penerapan modifikasi fraktal segitiga Sierpinski. Ada tiga algoritma yang akan digunakan. Pertama, algoritma yang bertujuan untuk memodifikasi segitiga Sierpinski. Data awal berupa segitiga samakaki yang dibagi menjadi sembilan segitiga kongruen. Kemudian dipilih secara acak beberapa segitiga yang akan dikosongkan. Pada segitiga yang masih berisi dilakukan hal yang sama Kedua, modelisasi bingkai dasar. Ketiga, mengisi bingkai dasar hasil algoritma kedua dengan modifikasi segitiga Sierpinski hasil algoritma pertama sehingga menjadi sebuah motif. Hasil penelitian yang diperoleh adalah beragam motif geometris Tumpal dengan penerapan modifikasi segitiga Sierpinski. Kata Kunci: fraktal linier, segitiga Sierpinski, ragam hias, geometris Tumpal

Research on lubrication and friction characteristics of oil seal with isosceles triangle texture and micro concave lip

Purpose This paper aims to study the effect of isosceles triangle micro concave texture with different parameters on the performance of oil seal to obtain a reasonable combination of parameters. Design/methodology/approach Based on the theory of elastohydrodynamic lubrication, a numerical model is established by coupling the texture parameters of isosceles triangle with concave lip with the two-dimensional average Reynolds equation considering surface roughness. Findings The results show that there is an optimal combination of parameters to improve the performance of the oil seal. When hp = 5µm-6.5 µm, a = 110°−130°, O = 1.4, C = 1.6 mm-2.2 mm, the oil seal with isosceles triangle micro concave texture can show good lubrication characteristics, friction characteristics and sealing ability. Originality/value The model provides a new idea for the design of new oil seal products and provides a theoretical support for the application of surface texture technology in the sealing field in the future.

Effects of Texture Bottom Profile on Static and Dynamic Characteristics of Journal Bearings

The purpose of this paper is to numerically study the effect of texture bottom profile on static, dynamic, and stability performance parameters of hydrodynamic journal bearings. The different performance parameters of square textured journal bearings with different bottom profiles are numerically investigated and compared with those of smooth journal bearing. There are five bottom profiles of this square texture: flat, curved, isosceles triangle (T1), oblique triangle (T2), and oblique triangle (T3). The static and dynamic coefficients are calculated by solving the steady-state Reynolds equation and the perturbation equations with FDM numerical technique. The performance characteristics under different texture distribution, depth, and bottom profiles are studied, and the current numerical results show that the selection of texture parameters is crucial to improve the static, dynamic, and stability performances of hydrodynamic journal bearing. Meanwhile, it is also found that the square texture with a flat bottom profile has a higher improvement in the values of static performance parameters in comparison to those other bottom profiles. Moreover, the simulation results indicate that the dynamic and stability performances improvement of textured journal bearing is also significant, especially when the eccentricity ratio is smaller.

Examination of 4th Grade Students' Definitions for Square, Rectangle and Triangle Geometric Shapes

The aim of this study is to obtain information about students' definitions, mistakes, misconceptions, and van Hiele geometry thinking levels by using the definitions of 4th grade students for geometric shapes of rectangle, square, isosceles triangle, equilateral triangle, and scalene triangle. The study was carried out with 156 primary school 4th grade students. In the study, the case design, one of the qualitative methods, was used. Students were asked to describe geometric shapes. It was observed that most of the 4th grade students participating in the study were in the visualization stage of van Hiele. There are very few definitions of the hierarchical structure in the study. Most correct definitions are in the partitional form. In the study, misconceptions were detected in some of the students.

The ‘golden section’ on Kitawa Island

When one first looks at the lagimu and tabuya, the two multicoloured prowboards placed symmetrically, like mirror-images of one another, on the ceremonial canoe (masawa) used for the Kula Ring exchanges, one is struck by the delicate visual balance between the graphic signs carved in the surface of the wood. The concept of randomness, in the sense of lack of 'order', as absence of planning, must, one feels sure, have been foreign to the person who carved these two prowboards: his hand and his eye must have been guided by precise rules of composition. In what follows I shall try to identify some of the aesthetic principles which determine these rules of composition and the technique which realizes them on a lagimu and tabuya. My exposition is based, as far as the aesthetic principles are concerned, on a series of conversations with Towitara Buyoyu, regarded as one of the greatest woodcarvers in Milne Bay, and Tonori Kiririyei and Siyakwakwa Teitei. Of these last two the former is a young carver of multicoloured prowboards, and the latter a carver and builder of hulls for ceremonial canoes. The lagimu/tabuya, as a geometrical and abstract schema, is equivalent to an equiangular spiral inscribing a golden or isosceles triangle. It is no coincidence that in the past Kitawans used to build ceremonial canoes called goragora (Nautilus pompilius) and characterized by a lagimu in the form of a large, stylized, Nautilus shell.

Formation Control of Swarming Vessels Using a Virtual Matrix Approach and ISOT Guidance Algorithm

The formation control for the effective operation of multiple vessels is discussed. First, a virtual matrix approach is proposed to improve the formation robustness and transform performance during swarm operations, which is created based on the virtual leader vessel location, and agents composing the formation follow cells in the matrix to maintain formation. This approach is affected by the virtual leader vessel location. The virtual leader vessel location is defined by two cases: matrix center and geometric center; furthermore, robustness and efficiency comparison simulations are performed. The simulation results show that in most formations, the geometric center is better in terms of efficiency and robustness. Second, the isosceles triangle guidance algorithm is proposed to improve the “go-back behavior” of certain agents during excessive maneuvering. Through a waypoint-following simulation, the algorithm is confirmed to be superior to the line-of-sight guidance algorithm. The swarm simulation on the virtual map verifies the performance of the proposed formation n control and guidance algorithm.

Examination of 4th Grade Students' Definitions for Square, Rectangle and Triangle Geometric Shapes

The aim of this study is to obtain information about students' definitions, mistakes, misconceptions, and van Hiele geometry thinking levels by using the definitions of 4th grade students for geometric shapes of rectangle, square, isosceles triangle, equilateral triangle, and scalene triangle. The study was carried out with 156 primary school 4th grade students. In the study, the case design, one of the qualitative methods, was used. Students were asked to describe geometric shapes. It was observed that most of the 4th grade students participating in the study were in the visualization stage of van Hiele. There are very few definitions of the hierarchical structure in the study. Most correct definitions are in the partitional form. In the study, misconceptions were detected in some of the students.

In vitro comparison of cleaning efficacy and force of cylindric interdental brush versus an interdental rubber pick

Background Interdental brushes (IDB) are according to the actual evidence the first choice for cleaning interdental areas (IDR). Their size should be chosen individually according to the IDR morphology. However, interdental rubber picks (IRP) are appreciated better by the patients and are hence becoming more and more popular but the evidence regarding their efficacy is still limited. The aim of this in vitro study was to measure the experimental cleaning efficacy (ECE) and force (ECF) during the use of interdental brushes versus newer wireless types with rubber filaments (IRP), both fitted and non-fitted for different IDR. Methods The medium size of a conical IRP (regular, ISO 2) with elastomeric fingers versus four sizes (ISO 1, 2, 3, 4) of cylindric IDB with nylon filaments (all Sunstar Suisse SA, Etoy, Switzerland) were tested. Interdental tooth surfaces were reproduced by a 3D-printer (Form 2, Formlabs Sommerville, MA, USA) according to human teeth and matched to morphologically equivalent pairs (isosceles triangle, concave, convex) fitting to three different gap sizes (1.0 mm, 1.1 mm, 1.3 mm). The pre-/post brushing situations at IDR (standardized, computer aided ten cycles) were photographically recorded and quantified by digital image subtraction to calculate ECE [%]. ECF were registered with a load cell [N]. Results Overall, a higher ECE was recorded for IDB compared to IRP (58.3 ± 14.9% versus 18.4 ± 10.1%; p < 0.001). ECE significantly depended on the fitting of the IDB. ECE was significant higher in isosceles triangle compared to concave and convex IDR for both IDB and IRP (p ≤ 0.001). ECF was lower for IDB (0.6 ± 0.4N) compared to IRP (0.8 ± 0.5N; p ≤ 0.001). ECE in relation to ECF increases with smaller IDB. For IRP highest values of ECF were found in the smallest IDR. Conclusions Within the limitations of an in vitro study, size fitted IDB cleaned more effectively at lower forces compared to conical IRP.