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A new monotypic genus of Geometridae, Mirlatia gen. nov. , and a new species, M. arcuata sp. nov. , are described from Croatia. Based on external and genitalia characters, the new genus is tentatively placed in the subfamily Larentiinae. However, the new genus takes a highly isolated position by having unique characters of the tympanum and showing an unusually long pectination of female antennae. Genetic analysis of a fragmented DNA barcode (mtDNA; cytochrome c oxidase 1) did not result in a clear assignation to any geometrid subfamily or tribe. Adults, male and female genitalia, and habitat photos of the type locality of the new species are illustrated.

In this paper, we describe an experience to test the predominant presence of Delaunay triangulations in the artwork of Okuda, a quite famous, young, contemporary Spanish artist. We addressed this task involving, as a citizen science activity in a STEAM (Science, Technology, Engineering, Art, Mathematics) education context, several hundreds of students (of different kinds: secondary education, university undergraduates, in particular, following teacher training degrees). Each student was asked to select an Okuda archive and, with the concourse of a dynamic geometry program provided with some computational geometry commands, to measure the ratio of coincident triangles in Delaunay's and artist's triangulations, over an ample region of the chosen artwork. The results show a very large percentage of coincidence ratios. We conclude with some reflections about how to interpret this fact, and about the potential role of future, enhanced, dynamic geometry systems to automatically address similar issues, concerning mathematical properties of figures from the real world.

The purpose of this paper is to develop the Islamic geometric patterns from planar coordinates to three or higher dimensions through their repeat units. We use historical plane methods, polygons in contact (PIC) and point-joined, in our deductive approaches. The mentioned approach makes use of a novel method of tessellation that generates 3D Islamic patterns called “interior polyhedral stellations”. The outputs showed that both the PIC and point-joined methods have strengths and weaknesses. Point-joined stellations are more efficient for regular repeat units and PIC is suitable for complex designs. These two methods can produce a large range of patterns and can be employed simultaneously. This study effectively answers the question regarding the gap between planar design from Muslim achievements and contemporary demands in modern art and architecture. We also propose techniques for constructing aperiodic three-dimension Islamic geometric patterns tessellation and two-point family.

This quasi-experimental study sought to investigate the effects of the motivational adaptive instruction on Malaysian students' motivation towards mathematics in a technology-enhanced learning classroom. Geometer's Sketchpad is used in the study to foster a technology-enhanced learning environment. The motivationally adaptive instructions were designed following the Attention, Relevance, Confidence, and Satisfaction (ARCS) motivational model. The study adopted a non-equivalent control group design with pre-and posttest with two weeks of treatments. Two intact Form Two classrooms were randomly assigned to an experimental group and a comparison group -- each with 20 students. The findings showed that Malaysian students had a slightly above-average level of motivation towards mathematics. The ANCOVA results showed that the intervention did not significantly improve the experimental group's students' motivation towards mathematics learning, despite having their motivation mean scores improve from Time 1 to Time 2. The results also showed that motivation and mathematics performance were not strongly correlated for this group of students. The weak relationship between motivation and mathematics performance among Malaysian students may be explained by the culture and value of East Asian towards education, which is discussed in this paper.

Rumî is both a decorative composition style and the name of the motif of this style. The first Rumî motifs are believed to have appeared as the figures of stylized shapes of the wings, legs, and bodies of animals and creatures, then turned into ornaments consisting of abstract geometric shapes, after the Seljuk’s conversion to Islam. Although having general design principles, this composition style and motif do not have a full geometric explanation. This study is an attempt to re-construct classical Rumî compositions with compass and straightedge. This is expected to refresh a discussion on Rumî through its geometric explanation. We believe this discussion will contribute to the survival of the Rumî composition and its transfer to the next generations.

Because of its unequal beauty and mathematical sophistication, Islamic art has received a great attention from several scientists. Hence, several works have been done to investigate its mathematical structure, and to discover its principle of construction. Up to now, no method of constructing new self-similar patterns were proposed. In this paper, we will present a method for constructing new self-similar patterns. The proposed method is based on successive subdivisions of the golden mean triangles.

I begin with a question: in Leonardo’s famous Adoration of the Magi at what distance is the observer from the temple in ruins? The main clue we have to find the answer is the preliminary sketch of the temple, but it is not the one he transferred to the painting. I believe that Leonardo most likely drew another sketch; a sketch that somehow has been lost without leaving a trace. Based on the painting, I have deconstructed the perspective of the temple to see what Leonardo’s missing sketch might have looked like. Recently, multispectral imaging studies have made visible many of the underlying lines of the sketch and painting. However, here we discuss some aspects of the preparatory sketch that have not been yet thoroughly analyzed. The knowledge of perspective was in the making at the time Leonardo drew the sketch, so the way I see the sketch’s flaws shows the way new rules of perspective were found in practice. We are also able to tell here at which distance and height one has to stand to best view the painting correctly.

This article reveals a mathematical bridge between compass-only geometric constructions and parametric curves. A set of construction algorithms are presented which are used to locate points on any Bézier curve or B-Spline by using an abstract compass. These constructions aim to translate the B-Spline definition of Paul de Casteljau into the modified versions of compass-only constructions explained by Aleksandr Kostovskii. Several computer scripts are developed and used to simulate these constructions while calculating and minimizing their computational complexities. The mathematical bridge explained in this article is expected to bring back to mind the synthetic and axiomatic roots of design geometries.

A range of entirely different pentagon approximations are known from textual and graphic sources related to the architecture of the Middle Ages. Analysis of the mathematical logic behind them highlights the scientific knowledge of master masons who directly calculated constructional methods according to their practical needs. From the examination of these pentagon approximations, their mathematical features, such as the initial data of the construction or precision of side lengths and angles, the range of architectural design problems they would have been able to solve can be determined. This paper provides an accurate comparison of mathematical and geometrical features of pentagon constructions from medieval sources, studying their applicability from an architectural aspect.