Isoperimetric problems on n-sided prisms

Impaired Reproduction of Three-Dimensional Objects by Cocaine-Dependent Subjects

In two-dimensional figures, the isoperimetric problem is defined as finding two-dimensional figures that will produce the largest area among several two-dimensional figures with the same perimeter. In this research, the isoperimetric problem is extended to find the shape with the largest volume among the shapes that have the same surface area. The aim of this research is to solve isoperimetric problems in three-dimensional shapes obtained by comparing various shapes of three-dimensional shapes. The discussion in this research is limited to three-dimensional shapes in the form of prisms with regular n-sided bases, pyramids with regular n-sided bases, cylinders, cones, and spheres. This research method uses concepts from calculus, trigonometry and algebra to prove the isoperimetric theorem with a simple and elementary approach. The result of this research is that the order of the maximum volume of three-dimensional shapes if the surface area is the same from smallest to largest is a pyramid with an equilateral triangular base, a pyramid with a square base, a prism with an equilateral triangular base, a pyramid with a regular n-sided base (n≥5), cone, prism with square base, prism with regular n-sided base (n≥5), cylinder, and sphere.

If we consider that “creating architecture, as viewed from our area of interest, consists in the production of three-dimensional inhabitable figures” (Burgaleta 2019) and we center our teaching around that fact, we will eventually be in need of some sort of procedure to provide our apprentices with the tools to verify that the spaces they produce – said three dimensional figures – are inhabitable.

We propose a method for recognizing a subject from the image taken by a CCD camera and comparing with the CAD figure. The three-dimensional CAD figure is transformed into a two-dimensional figure in which some color is added inside the contour. The transformed figure is used as the input of image processing. The two-dimensional CAD figure and an image of the recognized subject from one camera are represented by characteristics, that is, the center of gravity, contour, the distance between them, and FFT. The figure of the subject is estimated from these characteristics by comparing with the database of CAD figure.

In this paper, several extensions of the isoperimetric problem in solid figures are explored, focusing on oblique and right prisms with rectangular, right-angled triangular, and regular hexagonal bases. The objective of this research is to find the prism with the largest volume while keeping the surface area constant. Through manipulations of algebra and simple trigonometry, evidence is obtained that a right prism provides a larger volume than an oblique prism if their surface areas are equal. By utilizing partial derivatives of a two-variable function and the Lagrange multiplier method, conditions for the side lengths are derived to obtain the prism with the maximum volume. The results show that a cube is the solution to the isoperimetric problem, meaning it has the largest volume among prisms with rectangular bases, while for the isoperimetric solution on prisms with right-angled triangular bases, the base of the prism must be an isosceles right-angled triangle. A regular hexagonal prism has a larger volume than prisms with rectangular and right-angled triangular bases if their surface areas are the same.

The purpose of this study is to develop the criteria for measuring the observation abilities of elementary school students. Object, viewpoint and mental demand constitute the evaluation criteria of observation abilities. Object domain was classified into two- and three-dimensional figures, while viewpoint was classified into constancy and variety of views. Mental demand covered 2 through 5. The assesment tool based on the threedimensional criteria was developed for the lower, middle and upper grades of 166 elementary school students. Results from this study were as follows. These students' scores were significantly different in the classification by each dimension and distinguishable between the grades. They scored high on two-dimensional figures, constancy of view and lower mental demand, and the upper grade students' scores were higher than the lower ones in all dimensions. Therefore, the evaluation criteria developed in this study can be used effectively for measuring the observation abilities of elementary school students. Implication for this study was determined to be the development of a valid and reliable test for observation abilities of elementary school students.

A cyclic quadrilateral is called a Brahmagupta quadrilateral if the lengths of its four sides and two diagonals, and the area are all given by integers. In this paper, we consider the hitherto unsolved problem of finding two Brahmagupta quadrilaterals with equal perimeters and equal areas. We obtain two parametric solutions of the problem — the first solution generates examples in which each quadrilateral has two equal sides while the second solution gives quadrilaterals all of whose sides are unequal. We also show how more parametric solutions of the problem may be obtained.

PurposeThe purpose of this paper is to investigate the performance of Passive Direct Methanol Fuel Cell (PDMFC) experimentally using various Membrane Electrode Assembly (MEA) shapes such as square, rectangle, rhombus, and circle with equal areas and equal perimeters. The variation in MEA shape/size is achieved by altering gasket openings in the dynamic regions.Design/methodology/approachIn the equal areas of MEA shapes, gasket opening areas of 1963.5 (+/−0.2) mm2 are used. Whereas in the equal perimeters of shapes, gasket opening perimeters of 157.1 (+/−0.2) mm are used. In this experimentation, Nickel-201 current collectors with 45.3% of circular openings are used on both the anode and cathode sides. The experiment is carried out at a 5 molar methanol concentration to find out the highest power density of the cell.FindingsIn the equal areas, among the shapes that are chosen for investigation, the square shape opening consisting of a perimeter of 177.2 mm has developed a maximum power density of 6.344 mWcm−2 and a maximum current density of 65.2 mAcm−2. Similarly, in equal perimeters, the rhombus shape opening with an area of 1400 mm2 has developed a maximum power density of 7.714 mWcm−2 and a maximum current density of 85.3 mAcm−2.Originality/valueThe novelty of this research work is instead of fabricating various shapes and sizes of highly expensive MEAs, the desired shapes and sizes of the MEA are achieved by altering gasket openings over dynamic regions to find out the highest power density of the cell.

BackgroundThere has been concern regarding risks from inhalation exposure to nanoparticles (NPs). The large number of particles requiring testing means that alternative approaches to animal testing are needed.ObjectivesWe set out to determine whether short-term in vitro assays that assess intrinsic oxidative stress potential and membrane-damaging potency of a panel of metal oxide NPs can be used to predict their inflammogenic potency.MethodsFor a panel of metal oxide NPs, we investigated intrinsic free radical generation, oxidative activity in an extracellular environment, cytotoxicity to lung epithelial cells, hemolysis, and inflammation potency in rat lungs. All exposures were carried out at equal surface area doses.ResultsOnly nickel oxide (NiO) and alumina 2 caused significant lung inflammation when instilled into rat lungs at equal surface area, suggesting that these two had extra surface reactivity. We observed significant free radical generation with 4 of 13 metal oxides, only one of which was inflammogenic. Only 3 of 13 were significantly hemolytic, two of which were inflammogenic.ConclusionsPotency in generating free radicals in vitro did not predict inflammation, whereas alumina 2 had no free radical activity but was inflammogenic. The hemolysis assay was correct in predicting the proinflammatory potential of 12 of 13 of the particles examined. Using a battery of simple in vitro tests, it is possible to predict the inflammogenicity of metal oxide NPs, although some false-positive results are likely. More research using a larger panel is needed to confirm the efficacy and generality of this approach for metal oxide NPs.

The present study focuses on maximum compressive force of honeycomb structures produced from polylactic acid (PLA) and acrylonitrile butadiene styrene filament using an Ultimaker hot plate 3D printer. A honeycomb structure with an equal surface area and three different cell sizes and wall thickness was designed. The samples were produced with a cell width (d) of 6 mm, 9 mm, 12 mm, a cell wall thickness (t) of 0.8 mm, 1.2 mm, 1.6 mm and a cell height (h) of 10 mm, 20 mm and 30 mm for each cell width, respectively. The produced samples were weighed in order to calculate their porosity percentages. During the compression test, the highest compressive force was obtained from the samples produced from PLA filament with a cell height of 10 mm, a width of 12 mm and a wall thickness of 1.6 mm. Similarly, a detailed finite elements analysis of three structures with different cell widths and thicknesses using ANSYS® software yielded results similar to the experimental study. ANSYS® results were reliable in the range of approximately 81–98%. Thus, although the cell width in honeycomb structures with an equal surface area was increased using both experimental and finite elements method, it was observed that the wall thickness was directly proportional to a higher maximum compressive force.

The development of the pupil's ability to visualize spatial relationships has for a long time been recognized as one of the problems confronting the teacher of Solid Geometry. In 1923, the National Committee on Mathematics Requirements wrote: “The aim of the work in Solid Geometry should be to exercise further the spatial imagination of the student and to give him both a knowledge of the fundamental relationships and the power to work with tbem.”1 In 1940, the Joint Commission of the Mathematical Association of America and the National Council of Teachers of Mathematics reported: “Much attention should be given to the visualization of spatial figmes and relations, to the representation of three dimensional figures on paper.…”2

Line drawings used by Weisstein and Harris (1974) are seen as box-like three-dimensional figures if the lines are arranged properly. A flat two-dimensional pattern is seen when these same lines are disarranged. A target line contained within the three-dimensional figure is identified more readily than is the same line contained within a two-dimensional figure. This finding was extended in the present experiments: The three-dimensional stimulus was detected more quickly than the two-dimensional stimulus, under conditions of visual backward masking. Three-dimensional stimuli were also classified more quickly than two-dimensional stimuli. Just as with the face-detection effect and the word-detection effect, object detection can be affected by the form of the visual stimulus.

Lateralized visual behavior in bottlenose dolphins (Tursiops truncatus) performing audio–visual tasks: The right visual field advantage

The Museum of Perjuangan Subkoss Garuda Sriwijaya is a museum that preserves the history of South Sumatra’s struglle against the Dutch and Japanese colonialists. This research aims to obtain the results of an ethnomathematics study from the Museum of Perjuangan Subkoss Garuda Sriwijaya regarding historical, philosophical, and mathematical aspects and implement it in the Merdeka Curriculum in mathematics for elementary schools. This research employs an ethnographic approach with a qualitative descriptive approach, utilizing observation, interviews, documentation, field notes, and data triangulation. The analysis techniques include data reduction, data presentation, verification, and conclusions drawings. The study involved three informants who had direct interaction with the Museum of Perjuangan Subkoss Garuda Sriwijaya. The results of this research shows that ethnomathematics studies offer several insights: the historical aspect introduces local history and culture through artifacts that supported the struggle during the physical revolution; the philosophical aspectteaches the values ​​of caring, cooperation, creativity, and diversity within society; and the mathematical concepts reveals the concept of geometry, including area, perimeter, volume of both two-dimensional figures and three-dimensional figures, and length measurement.

Mathematics and culture are not mutually exclusive. They work well together. It is because the help of ethnomathematics. Ethnomathematics is a learning approach of mathematics seeking a cultural approach in mathematical concepts. Â This study aims at exploring the shape of the crock (earthenware jar), ladle, and chopping board associated with learning materials of the two-dimensional and three-dimensional figure at the elementary school level. The research method used was descriptive qualitative, conducted adopting an ethnographic approach. The ethnographic approach consists of three stages: selection, writing and exploration. The study results found that the shape of the crock (earthenware jar), ladle, and chopping board contained mathematical elements, which are two-dimensional figure including circles and rectangles as well as three-dimensional figure including cuboid, cone and ball.