NOVELTY ARCHITECTURE AND MATHEMATICS IN AN IRANIAN MOSQUE

Islamic architecture, particularly mosques architecture, has mainly been the focus of many architectural exhibitions in Muslim-majority countries. Recently, it has been influenced by novelty architecture and has been evolved into elaborate structures. Quds mosque in Tehran, Iran, is a picturesque architecture feat of a modern outlook that came under a lot of criticism for abandoning the traditional symbols of Islamic architecture. This study observes the Quds mosque from a mathematical standpoint using fractals as the method. Fractals are geometric constructions that exhibit similar or identical characteristics by order of magnitude. Rescaling a prominent architectural pattern is also a noticeable subject that considers Quds mosque from this point of view. This study shows that the Quds mosque used fractal principles; self-similarity and congruency. Those are applied in the roof form by using a triangle form on each side.

The topology of shapes made with points

In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements formed with elements (i.e. points) of the algebra of shapes Ui, for i = 0. This paper examines the kind of topology that is applicable to such shapes. From a mathematical standpoint, any “shape made with points” is equivalent to a finite space, so that topology on a shape made with points is no different than topology on a finite space: the study of topological structure naturally coincides with the study of preorder relations on the points of the shape. After establishing this fact, some connections between the topology of shapes made with points and the topology of “point-free” pictorial shapes (when i > 0) are defined and the main differences between the two are summarized.

Physical-chemical properties studying of molecular structures via topological index calculating

It’s revealed from the earlier researches that many physical-chemical properties depend heavily on the structure of corresponding moleculars. This fact provides us an approach to measure the physical-chemical characteristics of substances and materials. In our article, we report the eccentricity related indices of certain important molecular structures from mathematical standpoint. The eccentricity version indices of nanostar dendrimers are determined and the reverse eccentric connectivity index for V-phenylenic nanotorus is discussed. The conclusions we obtained mainly use the trick of distance computation and mathematical derivation, and the results can be applied in physics engineering.

Connections: Catch the monkey

Mazes are probably familiar to your students. Perhaps they have run through one at school or have visited a corn maze in the fall. In this rich investigation to connect experimental and theoretical probability, students use principles of probability to analyze a maze from a mathematical standpoint. They connect geometry to probability through the use of an area model and work together to communicate their ideas and use their intuitions whenever it seems reasonable.

Torsion of beams of L-cross-section

The torsion of beams of L-cross-section was studied for the first time, from a mathematical standpoint, by Kotter [1]. He solved the problem in the case of an L-section both arms of which are infinite. Some time later, Trefftz [2], in his work on the torsion of beams of polygonal cross-section, applied his method also to an infinite L-section. In 1934, Seth [3] solved the case of a beam of an L-section with only one infinite arm. In 1949, Arutyanyan [4] solved the torsion problem of an L-section that has both arms finite, but of equal length, reducing the problem to that of solving an infinite system of equations.