eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-06-01
4
1
1
10
10.22052/mir.2019.189803.1148
88764
Architecture, City and Mathematics: The Lost Connection
Almantas Samalavicius
almantsam@yahoo.com
1
Department of Architectural Fundamentals, Theory and Arts, Faculty of Architecture, Vilnius Gediminas Technical University, Vilnius LT-1132, Traku st. 1, Lithuania
The connection between architecture and science and sound based on mathematical relations has continued to develop[ since the rise of the Western classical civilization that originated in Ancient Greece. The mysterious Pythagorean cosmology pursued as secret esoteric knowledge was related to the search of rhythm, proportionality and harmony. Even somewhat earlier, Greek mysteries were based on a concord of music and form. This line of reasoning can be raced as early as when the doctrines of Orphism emerged in early Greece to be followed by the concepts of Pythagoras and his followers and eventually the philosophical school of Neo-Platonists. Early medieval thinkers like St. Aurelius Augustine and Boethius revived and continued this ancient tradition; they sustained and developed further the ideas of dependence between architecture and music (as well as mathematics). Their ideas were further elaborated by later Christian thinkers. Architectural principles practiced by architects belonging to the Western tradition were passed further on. The Pythagorean tradition was still alive during the Renaissance and even baroque. This tradition was gradually marginalized and forgotten with the rise of scientific mentality developed in post-Renaissance era. However, the roots of the application of mathematics and geometry to the design of urban settlements have survived. Such principles can be still observed while studying the early patterns of western as well as non-Western civilizations, and thus one can speak about the universal mathematical geometric character of early urban design.
http://mir.kashanu.ac.ir/article_88764_40dc35ae8718491e20e7309ad55f79e2.pdf
Architecture
urbanism, harmony
mathematical numbers
Pythagoreanism
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-06-01
4
1
11
19
10.22052/mir.2019.167225.1110
88765
An Overview of Mathematical Contributions of Ghiyath al-Din Jamshid Al-Kashi [Kashani]
Mohammad K. Azarian
azarian@evansville.edu
1
University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722 USA
In this paper, we study Ghiyath al-Din Jamshid al-Kashi's (1380-1429 A.D.) main mathematical achievements. We discuss his al-Risala al-muhitiyya ("The Treatise on the Circumference"), Risala al-watar wa'l-jaib ("The Treatise on the Chord and Sine"), and Miftah al-hisab ("The Key of Arithmetic"). In particular, we look at al-Kashi's fundamental theorem, his calculation of pi, and his calculation of sin1<sup>°</sup>.
http://mir.kashanu.ac.ir/article_88765_f17cdd08b35b70ad827078a7c1a8262a.pdf
Ghiyath al-Dın Jamshıd al-Kashı
Jamshıd Kashanı
al-Risala al-muhıtıyya
Miftah al-hisab
Risala al-watar wa’l-jaib
al-Kashı’s fundamental theorem
Euclid’s Elements
Lambert identity
Ptolemy’s theorem
Pythagorean theorem
Pascal triangle
Ruffini-Horner’s method
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-06-01
4
1
21
35
10.22052/mir.2019.187704.1140
92002
The Role of Geometry of Yard in the Formation of the Historical Houses of Kashan
Ahmad Danaeinia
danaeinia@kashanu.ac.ir
1
Mostafa Azad
azad@gmail.com
2
Asma Khamehchian
asama.k1404@gmail.com
3
Department of Architecture, Faculty of Architecture and Art, University of Kashan
Department of Architecture, Faculty of Architecture and Art, University of Kashan
Department of Architecture, Faculty of Architecture and Art, University of Kashan
Geometry is a base tool for establishing unity in Iranian architecture and is always considered by architects due to the discipline and rule that gives architecture to architecture. The architecture of the house in terms of its specific functional role, sought to adapt the geometrical principles to the best possible shape and achieve the proper understanding of the proportions and proportions of a harmonious geometry. In shaping the architecture of the Iranian house, the geometrical and functional role of the courtyard is important. This study is conducted through field study of 20 historical houses in Kashan to discover how geometry is used in the architectural design of Kashan historical houses. In this regard, the proportions of the arena and the court in these cells have been compared. The result shows that the yard follows the golden ratio as the house design basis. The 1.414 and 1.618 ratios have the highest frequency in the study samples. In addition, in terms of the level of occupation, the courtyard has occupied 20 to 40 percent of the building.
http://mir.kashanu.ac.ir/article_92002_2167c3ec1b00d6a9618c158b69e6afda.pdf
Geometry
ratio
Proportion
geometry of the area
geometry of the yard
traditional homes of Kashan
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-06-01
4
1
37
49
10.22052/mir.2019.176359.1124
92166
Calculations of Dihedral Groups Using Circular Indexation
Reza Dianat
dianat@pgu.ac.ir
1
Mojgan Mogharrab
mmogarab@gmail.com
2
Department of Electrical Engineering, Persian Gulf University
Department of Pure Mathematics, Persian Gulf University
In this work, a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$. Each element of the sequence represents a vertex of the polygon. Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis. Here each symmetry is considered as a system that takes an input circular sequence and generates a processed circular output sequence. The system can be described by a permutation function. Permutation functions can be written in a simple form using circular indexation. The operation between the symmetries of the polygon is reduced to the composition of permutation functions, which in turn is easily implemented using periodic sequences. It is also shown that each symmetry is effectively a pure rotation or a pure flip. It is also explained how to synthesize each symmetry using two generating symmetries: time-reversal (flipping around a fixed symmetry axis) and unit-delay (rotation around the center-point by $2pi /n$ radians clockwise). The group of the symmetries of a polygon is called a dihedral group and it has applications in different engineering fields including image processing, error correction codes in telecommunication engineering, remote sensing, and radar.
http://mir.kashanu.ac.ir/article_92166_1ddcfd25f7118154422f34d7fffe929c.pdf
The group of symmetries of a regular polygon (dihedral group)
Permutation
periodic (circular) sequences
the composition of functions
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-06-01
4
1
51
75
10.22052/mir.2019.187869.1143
93284
Reflection of the Role of Geometry in Design of the Aghabozorg School-Mosque in Kashan
Hamidreza Farshchi
farshchi46@kashanu.ac.ir
1
Maliheh Ansari
ansari71_m@yahoo.com
2
Vahid Askari Kashan
vahid_askari_kashan@yahoo.com
3
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Allameh Feiz Kashani University, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Aghabozorg Mosque with massive brick dome and the tiled minaret is one of the most magnificent Islamic buildings in Kashan in the Qajar period. The unique features of the architecture suggest the architects of this building, in terms of the nature of architecture in designing the form and architectural space, have considered principles that are based on geometric shapes and proportions between them. Regarding the importance of the issue, the authors, with the approach of geometric proportional analysis, seek to answer this question: what is the role of geometry and golden proportion in the construction and shaping of the elements of Aghabozorg School-Mosque? For this purpose, the descriptive-analytic research method has been used in this study. In order to retrieve geometric and proportional data, plan, elevations, and sections of the building were investigated and analyzed accurately. The results of this research indicate that the architects had the necessary knowledge about the systems of equations and geometric drawings and used golden proportions and circle divisions to design plan, elevations, and sections and also applied geometrical knowledge in the direction practical and qualitative for creating the building.<br />
http://mir.kashanu.ac.ir/article_93284_fcd4e4660085ad87f53144f3c7187e69.pdf
Geometry
traditional architecture
golden proportions
Aghabozorg School-Mosque
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-06-01
4
1
77
86
10.22052/mir.2019.169780.1112
93388
Independence Fractals of Graphs as Models in Architecture
Maryam Adl
adl.nastaran72@gmail.com
1
Saeid Alikhani
alikhani206@gmail.com
2
Vahid Shokri
shokri_vahid@yahoo.com
3
Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
Architectural science requires interdisciplinary science interconnection in order to improve this science. Graph theory and geometrical fractal are two examples of branches of mathematics which have applications in architecture and design. In architecture, the vertices are the rooms and the edges are the direct connections between each two rooms. The independence polynomial of a graph G is the polynomial I(G,x)=∑ i<sub>k</sub>x<sup>k</sup>, where i<sub>k</sub> denote the number of independent sets of cardinality k in G. The independence fractal of G is the set <em>I</em>(G)=lim<sub>k→∞</sub> Roots (I({G<sup>k</sup>},x)-1), where G<sup>k</sup>=G[G[...]], and G[H] is the lexicographic product for two graphs G and H. In this paper, we consider graphical presentation of a ground plane as a graph G and use the sequences of limit roots of independence polynomials of G<sup>k</sup> to present some animated structures for building.
http://mir.kashanu.ac.ir/article_93388_9dd7d4a7a9d3994d580a1edf2646098c.pdf
Independence fractal
structure
model
Architecture
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-06-01
4
1
87
106
10.22052/mir.2019.187587.1142
93466
Mathematics, Music and Architecture
Roghayyeh Rasulzade
rasulzade90@gmail.com
1
Javad Divandari
j.divandari@kashanu.ac.ir
2
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
In simple terms, architecture and music are two very different things, which is the product of one set of materials in the form of one building and the other product is a set of sounds in the form of a song and melody. In this sense, architecture and music are two separate issues that are not similar. But with a little care in the hidden layer of music and architecture we can find amazing similarities. Finding the structural, quantitative and qualitative similarities between architecture and music is the focus of this article. Achieving a qualitative and quantitative correlation between these two arts can be a way to aesthetically improve architecture and achieve its healing principles. Therefore, the main purpose of this study is the understanding of the immediate beauty of music in mind and the application of its aesthetic elements in architecture. The research method is descriptive-analytical study of library documents and case studies. In this article, first, the definitions and the general structure of music and architecture are presented, then the results of the studies are introduced in the form of qualitative and quantitative adaptive tables. Finally, by analyzing data, the common structure of music and architecture is determined.
http://mir.kashanu.ac.ir/article_93466_c1283ee6d0d7e3757a3bfc517cbbca57.pdf
Music
architecture
harmonic proportions
geometry
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-06-01
4
1
107
127
10.22052/mir.2019.195272.1157
93467
Golden Section in the Persian-Islamic Architecture; Case Study: Hasht Behesht Palace, Isfahan, Iran
Rouhollah Mojtahedzadeh
r.mojtahed@scu.ac.ir
1
Zahra Namavar
namavar.nam@gmail.com
2
Architecture Department, Shahid Chamran University of Ahvaz, Ahvaz, Iran
College of Architecture and Planning, University of Colorado, Denver, Colorado, USA
The subject of proportion used in architecture -and on a larger scale in any art work- is a debate having a special status in analytical studies on the history of art. “Golden Section” is known as one of the major topics of such debates. It has been given different names during the history of art, and it is generally defined under the ancient and Renaissance art in West. <br /> <br /> The present paper studies the status of this specific kind of proportion in Islamic civilization. The authors also demonstrate their findings about the manifestation of this proportion in Hasht Behesht Palace, Isfahan. Moreover, they attempt to indicate the roots of familiarity with the usage of respective proportion in Muslim world by referring to some first-hand references of Islamic civilization in the fields of mathematics and geometry. <br /> <br /> The findings of this paper show that the application of Golden Section in Islamic civilization was independent of the developments of Western Renaissance and Golden Section had practical theorems in Islamic civilization since 10th and 11th centuries AD.
http://mir.kashanu.ac.ir/article_93467_5dcb85342c9f56c6de80e5c23d6cf302.pdf
Proportion
golden section
Nisbit Dhat Vasat Tarafein
Hasht Behesht Palace
Persian-Islamic architecture