MODELISASI KURSI DENGAN PENGGABUNGAN HASIL DEFORMASI BENDA-BENDA RUANG MENGGUNAKAN KURVA BEZIER

Chairs are needed by humans to do some work, especially students and office workers. The parts contained in the chair are the chair legs, chair legs eats and chair backs. The purpose of this study is to obtain variations in the shape of office chairs using Bezier curves and incorporate the results of deformation of space geometric objects. In modeling this chair, it is divided into several stages, namely first, building the chair leg components. This chair leg component consists of chair wheels, connecting two wheels with tube deformation, modeling the chair leg branch components and modeling chair leg supports. Second, namely the model of the chair leg seat. Chair leg seat consists of regular hexagon prism deformation and regular quadrangle prism deformation. The third is the modelization of the back of the chair by using a rectangular prism model. The result of combining several components of the chair using one modeling axis produces 36 chair models, with special provisions, namely that the seat support parts can only be joined using a tube.

Rationality in pier geometry of Kintaikyo Bridge from viewpoint of river engineering

The Kintaikyo Bridge, with its elegant wooden arches, has a unique pier shape and continues to be loved by residents and visitors alike. Although this bridge is an active footbridge and an important landscape element along with the Nishikigawa River and its river beach, the rationality or irrationality of the shape of its piers remains unknown. This paper is intended to clarify the river engineering characteristics of the piers for the first time by conducting 1/129 scale hydraulic model experiments. The shapes tested were a perfect spindle shape (which has been adopted as a common theory for many years) and a reconstructed current shape based on the spindle shape, and for comparison, an oval and a non-regular hexagon shape with the same width and area. The current shape, along with the spindle shape, suppressed the water level rise around the pier more than the others. As for the riverbed fluctuation, the current shape slightly increased the scour more than the others, but it also maximized the sedimentation around the scoured part. In other words, the current shape has the potential to facilitate the procurement of sediment for post-flood restoration. In addition, the current shape overwhelmingly reduced the statistical dispersion associated with the experiment, suggesting that it stabilizes the trend of riverbed fluctuation even during actual floods. Based on the results, the future conservation of the Kintaikyo Bridge was also discussed.

Banach–Mazur Distance from the Parallelogram to the Affine-Regular Hexagon and Other Affine-Regular Even-Gons

We show that the Banach–Mazur distance between the parallelogram and the affine-regular hexagon is $$\frac{3}{2}$$ 3 2 and we conclude that the diameter of the family of centrally-symmetric planar convex bodies is just $$\frac{3}{2}$$ 3 2 . A proof of this fact does not seem to be published earlier. Asplund announced this without a proof in his paper proving that the Banach–Mazur distance of any planar centrally-symmetric bodies is at most $$\frac{3}{2}$$ 3 2 . Analogously, we deal with the Banach–Mazur distances between the parallelogram and the remaining affine-regular even-gons.

High-precision GPS measurement method without geographical restrictions using crowd-sensing technology

In order to improve the flexibility of GPS measurement, a high-precision GPS measurement method that is not restricted by the geographical location under crowd-sensing technology was proposed. The performance of the crowdsensing network was improved through a regular hexagon-based crowd-smart big data sensing network deployment mechanism. The GPS /SINS/DR fast and high-precision combined measurement methods were used to achieve high-precision measurement without geographical restrictions. It has been verified that the proposed method in this paper has much better stability in the deployment strategy of a regular hexagon than that of the square. The proposed method can achieve fast acquisition of satellite signals and high-precision positioning, and its measurement accuracy in the low-latitude city and high-latitude city is higher than the online measurement method based on Google Earth, indicating that it has significant application value.

The Modified Helmholtz Equation on a Regular Hexagon—The Symmetric Dirichlet Problem

Using the unified transform, also known as the Fokas method, we analyse the modified Helmholtz equation in the regular hexagon with symmetric Dirichlet boundary conditions; namely, the boundary value problem where the trace of the solution is given by the same function on each side of the hexagon. We show that if this function is odd, then this problem can be solved in closed form; numerical verification is also provided.

Calibrations for minimal networks in a covering space setting

In this paper, we define a notion of calibration for an approach to the classical Steiner problem in a covering space setting and we give some explicit examples. Moreover, we introduce the notion of calibration in families: the idea is to divide the set of competitors in a suitable way, defining an appropriate (and weaker) notion of calibration. Then, calibrating the candidate minimizers in each family and comparing their perimeter, it is possible to find the minimizers of the minimization problem. Thanks to this procedure we prove the minimality of the Steiner configurations spanning the vertices of a regular hexagon and of a regular pentagon.

Hidden in Plane Sight: The Extraordinary Vision of Ernest Irving Freese

We assess selected geometric dissections associated with, or inspired by, Ernest Irving Freese’s 1957 manuscript and identify noteworthy features that lay beneath their surface. These include a dissection of a regular dodecagon to a regular hexagon, a hingeable dissection of a Greek Cross to an equilateral triangle, a hingeable dissection of an equilateral triangle to a regular hexagon, a hingeable dissection of ten regular pentagons to a decagonal ring, a translational dissection of two regular decagons to one, a translational dissection of a dodecagram and a co-dodecagram to a regular dodecagon, a translational dissection of ten regular pentagons to two 5-pointed pseudo-stars and a regular decagon, a translational dissection of ten regular heptagons to four 7-pointed pseudo-stars and a regular 14-gon, a translational dissection of three regular octagons to a larger octagon, a hingeable dissection of regular pentagons for (sin π/5)2 + (cos π/5)2 = 1, a translational dissection of squares of areas 1, 3, 5, 7, 9, and 11 to a large square, and a translational dissection of squares for 82 + 92 + 122 = 172. Unsubstantiated claims by Freese are also evaluated.

On Calculating the Packing Efficiency for Embedding Hexagonal and Dodecagonal Sensors in a Circular Container

In this paper, a problem of packing hexagonal and dodecagonal sensors in a circular container is considered. We concentrate on the sensor manufacturing application, where sensors need to be produced from a circular wafer with maximal silicon efficiency (SE) and minimal number of sensor cuts. Also, a specific application is considered when produced sensors need to cover the circular area of interest with the largest packing efficiency (PE). Even though packing problems are common in many fields of research, not many authors concentrate on packing polygons of known dimensions into a circular shape to optimize a certain objective. We revisit this problem by using some well-known formulations concerning regular hexagons. We provide mathematical expressions to formulate the difference in efficiency between regular and semiregular tessellations. It is well-known that semiregular tessellation will cause larger silicon waste, but it is important to formulate the ratio between the two, as it affects the sensor production cost. The reason why we have replaced the “perfect” regular tessellation with semiregular one is the need to provide spacings at the sensor vertices for placing mechanical apertures in the design of the new CMS detector. Archimedean {3,122} semiregular tessellation and its more flexible variants with irregular dodecagons can provide these triangular spacings but with larger number of sensor cuts. Hence, we construct an irregular convex hexagon that is semiregularly tessellating the targeted area. It enables the sensor to remain symmetric and hexagonal in shape, even though irregular, and produced with minimal number of cuts with respect to dodecagons. Efficiency remains satisfactory, as we show that, by producing the proposed irregular hexagon sensors from the same wafer as a regular hexagon, we can obtain almost the same SE.