ORIGINAL_ARTICLE
Architecture, City and Mathematics: The Lost Connection
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
2019-06-01T11:23:20
2020-07-11T11:23:20
1
10
10.22052/mir.2019.189803.1148
Architecture
urbanism, harmony
mathematical numbers
Pythagoreanism
Almantas
Samalavicius
almantsam@yahoo.com
true
1
Department of Architectural Fundamentals, Theory and Arts,
Faculty of Architecture,
Vilnius Gediminas Technical University,
Vilnius LT-1132, Traku st. 1, Lithuania
Department of Architectural Fundamentals, Theory and Arts,
Faculty of Architecture,
Vilnius Gediminas Technical University,
Vilnius LT-1132, Traku st. 1, Lithuania
Department of Architectural Fundamentals, Theory and Arts,
Faculty of Architecture,
Vilnius Gediminas Technical University,
Vilnius LT-1132, Traku st. 1, Lithuania
LEAD_AUTHOR
[1] L. B. Alberti, On the Art of Building in Ten Books, Translated by J. Rykwert,
1
N. Leach and R. Tavernor, Cambridge: MIT Press, 1997.
2
[2] U. Eco, Art and Beauty in the Middle Ages, Translated by H. Bredin, Yale
3
University Press, New Haven, 1986.
4
[3] G. L. Hersey, Architecture and Geometry in the Age of Baroque, University
5
of Chicago Press, Chicago, 2000.
6
[4] L. Mumford, The City in History: Its Origins, Its Transformations, and Its
7
Prospects, New York, Harcourt, 1961.
8
[5] J. Rykwert, The Idea of a Town: The Anthropology of Urban Form in Rome,
9
Italy and the Ancient World (Faber Finds), Faber and Faber, London, 2010.
10
[6] N. Salingaros, Architecture, patterns and mathematics, Nexus Netw. J. 1(1-2)
11
(1999) 75 - 86.
12
[7] A. Samalavicius, Ideas and Structures: Essays in Architectural History, Eugene,
13
Oregon: Resource Publications/An Imprint of Wipf and Stock Publishers,
14
2011, 130 p.
15
[8] K. Williams and M. J. Ostwald, Architecture and Mathematics from Antiquity
16
to the Future, Volume I: Antiquity to the 1500s, Birkhäuser Basel, 2015.
17
[9] R. Wittkower, Architectural Principles in the Age of Humanism, W. W. Norton
18
& Company, Inc., New York, London, 1973.
19
ORIGINAL_ARTICLE
An Overview of Mathematical Contributions of Ghiyath al-Din Jamshid Al-Kashi [Kashani]
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°.
http://mir.kashanu.ac.ir/article_88765_f17cdd08b35b70ad827078a7c1a8262a.pdf
2019-06-01T11:23:20
2020-07-11T11:23:20
11
19
10.22052/mir.2019.167225.1110
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
Mohammad K.
Azarian
azarian@evansville.edu
true
1
University of Evansville,
1800 Lincoln Avenue, Evansville, IN 47722 USA
University of Evansville,
1800 Lincoln Avenue, Evansville, IN 47722 USA
University of Evansville,
1800 Lincoln Avenue, Evansville, IN 47722 USA
LEAD_AUTHOR
[1] M. K. Azarian, A study of Ris¯ala al-watar wa’l Jaib (“The treatise on the
1
chord and sine”), Forum Geom. 15 (2015) 229 - 242.
2
[2] M. K. Azarian, Al-Ris¯ala al-Muh¯ıt¯ıyya: A summary, Missouri J. Math. Sci.
3
22(2) (2010) 64 - 85.
4
[3] M. K. Azarian, The introduction of al-Ris¯ala al-Muh¯ıt¯ıyya: An english translation,
5
Int. J. Pure Appl. Math. 57(6) (2009) 903 - 914.
6
[4] M. K. Azarian, Al-K¯ash¯ı’s fundamental theorem, Int. J. Pure Appl. Math.
7
14(4) (2004) 499 - 509.
8
[5] M. K. Azarian, Meftah al-hesab [Mift¯ah al-his¯ab]: A summary, Missouri J.
9
Math. Sci. 12(2) (2000) 75 - 95.
10
[6] M. K. Azarian, A summary of mathematical works of Ghiy¯ath ud-D¯ın
11
Jamsh¯ıd K¯ash¯an¯ı, J. Recreat. Math. 29(1) (1998) 32 - 42.
12
[7] D. H. Bailey, J. M. Borwein, P. B. Borwein and S. Plouffe, The quest for Pi,
13
Math. Intelligencer 19(1) (1997) 50 - 57.
14
[8] Abu’l-Q¯asim Qurb¯an¯ı, K¯ash¯an¯ı n¯ameh [A monograph on Ghiy¯ath al-D¯ın
15
Jamsh¯ıd Mas’¯ud al-K¯ash¯ı], Tehran University Press, Tehran, Iran, 1971.
16
[9] P. Trueb, Digit statistics of the first 22.4 trillion decimal digits of Pi,
17
arXiv:1612.00489.
18
ORIGINAL_ARTICLE
The Role of Geometry of Yard in the Formation of the Historical Houses 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
2019-06-01T11:23:20
2020-07-11T11:23:20
21
35
10.22052/mir.2019.187704.1140
Geometry
ratio
Proportion
geometry of the area
geometry of the yard
traditional homes of Kashan
Ahmad
Danaeinia
danaeinia@kashanu.ac.ir
true
1
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
LEAD_AUTHOR
Mostafa
Azad
azad@gmail.com
true
2
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
AUTHOR
Asma
Khamehchian
asama.k1404@gmail.com
true
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
AUTHOR
[1] L. Aboalghasemi, The Norm of Formation in Islamic Architecture of Iran, in
1
the endeavor of Mohammad Y. Kiani, Samt Publication, 2005.
2
[2] A. Amirkhani, P. Baghaii and M. R. Bemanian, Investigating the metamor-
3
phism of the Timche symmetry in the Qajar period, Fine Arts 37 (2014)
4
[3] M. Ansari, H. Okhovat and A. A. Taghvaee, Investigating the historical pro-
5
cess of arithmetic arrangement systems with emphasis on practical consider-
6
ations and aesthetics, Ketab-e Mah-e Honar 151 (2011) 46 - 57.
7
[4] K. Attarian, K. Momeni and Z. Masoudi, Investigating the parameters of the
8
Yard of the mosques in the Safavid period of Isfahan, Motaleat-e Tatbighi-e
9
Honar 10 (2014) 67 - 81.
10
[5] M. R. Bemanian, H. Okhovat and P. Baghaii, Application of Geometry and
11
Proportions in Architecture, Tahan Publication, Tehran, 2010.
12
[6] M. R. Bemanian, Introduction to peymoon’s role and application in Iranian
13
architecture, Modares-e Honar 1 (2001) 1 - 10.
14
[7] A. Brooke, Geometric Patterns in Islamic Art, Translate: B. Zabihian, Maziar
15
Publication, Tehran, 2007.
16
[8] R. L. Brown, H. H. Richardson and the Golden Section Proportions in his
17
Architecture, Richard Brown Publication, New York, 2010.
18
[9] T. Chand, The Impact of Islam on Indian Culture, Translate: A. Pirnia and
19
A. Osmani, Pajang Publication, Tehran, 1994.
20
[10] A. Danaienia and M. Fattahpoure, The relationship between architecture and
21
symmetry in Persian architecture: A case study of Sheikh Lotfoll¯ah mosque
22
in Isfahan, Symmetry: Culture and Science 29 (2018) 423 - 439.
23
[11] M. T. Daneshpajoh and I. Afshar, Mojmal Al Hikmah, Institute of Humanities
24
and Cultural Studies Publication, Tehran, 1996.
25
[12] J. Efendi, Risale Memariye, Translate: M. Ghaiomi, Matn Publication,
26
Tehran, 2010.
27
[13] M. Falamaki, The Formation of Architecture in the Experiences of Iran and
28
the West, Faza Publication, Tehran, 1991.
29
[14] A. M. al-Farabi, Ihs¯a al-’ul¯um, Translated from the Arabic by Khady¯ujim,
30
Scientific and Cultural Publication, Tehran, 1969.
31
[15] M. Ghochani and M. Taji, Geometric Structure Analysis Karbandi and Compare
32
it with Geographic Fractal, International Conference on Modern Studies
33
in Civil Engineering, Architecture and Urban Planning, Mashhad, Sajjad Industrial
34
University, 2016.
35
[16] F. Mehdizade Seraj, F. Tehrani and N. Valibeyg, Applying normal triangles
36
in mathematical calculus and implement geometry in the construction and
37
implementation traditional Iranian architecture, Maremat & Memari-E Iran
38
1 (2010) 15 - 26.
39
[17] G. Najiboghlo, Geometry and Decoration in Islamic Architecture, Translate:
40
M. Ghaiomibidhendi, Rozane Publication, Tehran, 1999.
41
[18] A. Noghrekar, Theoretical Foundations of Architecture, Payamnoor University
42
Publication, Tehran, 2009.
43
[19] J. Peter Lu and J. Paul Steinhardt, Decagonal and quasi-crystalline tilings in
44
medieval Islamic architecture, Science 315 (2007) 1106 - 1110.
45
[20] A. Pourahmad and A. Vafaii, The effect of modernism on the physical-spatial
46
structure of the Iranian-Islamic city (case study: Kashan), Motaleat-e- Shahre-
47
Irani-Eslami 28 (2016) 63 - 76.
48
[21] M. Porahmadi, M. Yusefi and M. Sohrabi, The ratio of length to width in the
49
main spaces of traditional houses of Yazd: A test for Pirnia’s statement on
50
Iranian golden rectangle, Fine Arts 47 (2010) 69 - 77.
51
[22] P. Saltzman, Quasi-periodicity in Islamic geometric design, In: K. Williams
52
and M. Ostwald (eds) Architecture and Mathematics from Antiquity to the
53
Future, Birkhäuser, Cham, Springer, Switzerland, 1 (2015) pp. 585 - 602.
54
[23] A. Sharaf Al Din, Pleasant Geometry, Madrese Publication, Tehran, 2003.
55
ORIGINAL_ARTICLE
Calculations of Dihedral Groups Using Circular Indexation
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 $2\pi /n$ 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
2019-06-01T11:23:20
2020-07-11T11:23:20
37
49
10.22052/mir.2019.176359.1124
The group of symmetries of a regular polygon (dihedral group)
Permutation
periodic (circular) sequences
the composition of functions
Reza
Dianat
dianat@pgu.ac.ir
true
1
Department of Electrical Engineering, Persian Gulf University
Department of Electrical Engineering, Persian Gulf University
Department of Electrical Engineering, Persian Gulf University
LEAD_AUTHOR
Mojgan
Mogharrab
mmogarab@gmail.com
true
2
Department of Pure Mathematics, Persian Gulf University
Department of Pure Mathematics, Persian Gulf University
Department of Pure Mathematics, Persian Gulf University
AUTHOR
[1] N. S. Akbar, Mathematical model for blood flow through tapered arteries with
1
temperature dependent viscosity, J. Adv. Math. Appl. 3 (2014) 122 − 129.
2
[2] G. Arfken, Mathematical Methods for Physicists, 3rd Ed., Orlando: FL: Aca-
3
demic Press, New York-London, 1985.
4
[3] R. S. Caprari, Geometric symmetry in the quadratic Fisher discriminant op-
5
erating on image pixels, IEEE Trans. Inform. Theory 52 (2006) 1780−1788.
6
[4] T. L. Kunii, H. Nishida and M. Hilaga, Topological modeling for visualization,
7
J. Adv. Math. Appl. 1 (2012) 134 − 150.
8
[5] R. Lenz, Using representations of the dihedral groups in the design of early
9
vision filters, In: Proc. International Conference on Acoustics, Speech, and
10
Signal Processing, ICASSP-93, Minneapolis, MN, USA, 1993.
11
[6] G. Mayhew, Group property of the P4, K4, and NR16 error correction codes,
12
In: Proc. Aerospace Conference, 2017.
13
[7] A. V. Oppenheim, R. W. Schafer and J. R. Buck Discrete-Time Signal Processing
14
, 2nd ed, Prentice-Hall Signal Processing Series, Pearson, Upper Saddle
15
River, N. J., 1998.
16
[8] D. Saracino, Abstract Algebra: A First Course, Addison Wesley Longman
17
Publishing Co, USA, 1980.
18
[9] A. Thiele, E. Cadario, K. Schulz, U. Thoennessen and U. Soergel, Feature
19
extraction of gable-roofed buildings from multi-aspect high-resolution InSAR
20
data, In: Proc. International Geoscience and Remote Sensing Symposium,
21
(2007) 262 − 265.
22
[10] M. Thill and B. Hassibi, Frames from groups: Generalized bounds and di-
23
hedral groups, In: Proc. International Conference on Acoustics, Speech and
24
Signal Processing, (2013) 6043 − 6047.
25
[11] Y. Wang, W. Pedrycz, J. Lu and G. Luo, Denotational mathematical models
26
of an air traffic control system (ATCS-II): Process models of functions in
27
RTPA, J. Adv. Math. Appl. 2 (2013) 82 − 110.
28
ORIGINAL_ARTICLE
Reflection of the Role of Geometry in Design of the Aghabozorg School-Mosque in Kashan
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.
http://mir.kashanu.ac.ir/article_93284_fcd4e4660085ad87f53144f3c7187e69.pdf
2019-06-01T11:23:20
2020-07-11T11:23:20
51
75
10.22052/mir.2019.187869.1143
Geometry
traditional architecture
golden proportions
Aghabozorg School-Mosque
Hamidreza
Farshchi
farshchi46@kashanu.ac.ir
true
1
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
LEAD_AUTHOR
Maliheh
Ansari
ansari71_m@yahoo.com
true
2
Allameh Feiz Kashani University, Kashan, I. R. Iran
Allameh Feiz Kashani University, Kashan, I. R. Iran
Allameh Feiz Kashani University, Kashan, I. R. Iran
AUTHOR
Vahid
Askari Kashan
vahid_askari_kashan@yahoo.com
true
3
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
AUTHOR
[1] M. R. Bemanian, K. Momeni and H. Soltanzadeh, A comparative study of the
1
architectural feature’s designs: masjid- madreseh of Qajar and Safavid school (in Persian), Armanshahr Architecture & Urban Development 6(11) (2014)
2
[2] Z. Bozorgmehri, Geometry in Architecture, (in Persian), Editor: Jamshid
3
Mehrpouya, Cultural Heritage Organization of Iran, Tehran, Iran, 1992.
4
[3] A. Dahar and R. Alipour, Geometrical analysis of architecture of Sheik Lotfollah
5
Mosque to find the geometrical relations between its prayer hall and
6
the entrance, (in Persian) Bagh-e Nazar 10(26) (2013) 33 - 40.
7
[4] H. Hashemi Zarj Abad, M. H. Ziaee Nia and H. R. Ghorbani, Re-reading
8
the geometric basics and golden ratio of Showkateyeh school, (in Persian)
9
Pazhohesh-ha-ye Bashtanshenasi Iran 5(9) (2016) 207 - 222.
10
[5] M. Hejazi, Sacred geometry in nature and Persian architecture, (in Persian)
11
History of Science 6(2) (2009) 15 - 36.
12
[6] A. Helli, Knots and Arches in Islamic Architecture, (in Persian), A. Helli,
13
Kashan, 1986.
14
[7] Sh. Jarmoozi and S. Salehi, Beautiful ratios: the comparative analysis of
15
structural proportions in a marriage contract in the treasury of Astan Quds
16
Razavi and the common ratio structures in the west, (in Persian), Ganjine-ye
17
Asnad 23(2) (2013) 120 - 137.
18
[8] M. M. Karimnezhad and M. Abdi, Golden Proportions in Historical Architecture:
19
Case Study of Mosque of Aghabozorg in Kashan, (in Persian), In: The
20
First National Conference of Islamic Architecture & Urban Design & Definition
21
Sustainable Based on Islamic & Iranian Lose(Absent) Idendity, Zahedan,
22
Museum of South East, Iran, 2014.
23
[9] R. Lawlor, Sacred Geometry: Philosophy and Practice, Translation by
24
Hayedeh Moayeri, Ministry of Culture and Higher Education, Institute for
25
Cultural Studies and Research, 1989.
26
[10] M. Mehri and F. Zandi, A Study of the Pattern of Sustainable Architecture in
27
the Aghabozorg School-Mosque, (in Persian), In: 8th Symposium on Advances
28
in Science & Technology Commission-III: from Vernacular Architecture to
29
Sustainable City (VASCity), Mashhad, Iran, 2014.
30
[11] B. Molavi and M. Ghasemzadeh, A Study on the Application of Geometry
31
in the Past Iranian Architecture (Islamic Period), (in Persian), Building and
32
Housing Research Center, Tehran, Iran, 2002.
33
[12] N. Meshkouti, List of Historic Buildings and Ancient Places of Iran, (in Persian),
34
Iran National Antiquities Protection Organization, Tehran, Iran, 1970.
35
[13] M. Namnam and H. R. Saremi, Decoding of Geometry and Parameters in
36
Iranian Architecture, (in Persian), In: National Conference on Architecture,
37
Civil Engineering & Urban Modern Development, (2015) 16 pages.
38
[14] H. Naraghi, Social History of Kashan, (in Persian), Scientific and Cultural
39
Press of Tehran, Tehran, Iran, 1966.
40
[15] J. Neyestani, Drawing maps and applying geometry and arithmetic in Islamic
41
architecture (from the early Islamic centuries to the MID 9th century AH.),
42
(in Persian), Peyke Noor Journal 3(5) (2006) 42 - 49.
43
[16] M. Rezazadeh Ardebili and M. Sabetfard, Recognition of the application of
44
geometric principles in traditional architecture case study: Qasre Khorshid
45
and its hidden geometry (in Persian), Honar-ha-ye-Ziba Memari-va-Shahrsazi
46
18 (2013) 29 - 44.
47
[17] S. Silvaie, K. Daneshjou and S. Farmahin Farahani, Geometry in pre-Islamic
48
Iranian architecture and its manifestation in contemporary Iranian architecture
49
(in Persian), The Role of the World 3 (2013) 55 - 66.
50
[18] A. Sharbaf, Knot and Karbandi, Editor: Batul Ghanizadeh, Scientific and
51
Cultural Publishing, 1994.
52
ORIGINAL_ARTICLE
Independence Fractals of Graphs as Models in Architecture
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)=∑ ikxk, where ik denote the number of independent sets of cardinality k in G. The independence fractal of G is the set I(G)=limk→∞ Roots (I({Gk},x)-1), where Gk=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 Gk to present some animated structures for building.
http://mir.kashanu.ac.ir/article_93388_9dd7d4a7a9d3994d580a1edf2646098c.pdf
2019-06-01T11:23:20
2020-07-11T11:23:20
77
86
10.22052/mir.2019.169780.1112
Independence fractal
structure
model
Architecture
Maryam
Adl
adl.nastaran72@gmail.com
true
1
Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
AUTHOR
Saeid
Alikhani
alikhani206@gmail.com
true
2
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
LEAD_AUTHOR
Vahid
Shokri
shokri_vahid@yahoo.com
true
3
Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
Faculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, Iran
AUTHOR
[1] S. Alikhani and Y. H. Peng, Independence roots and independence fractals of
1
certain graphs, J. Appl. Math. Comput. 36(1 - 2) (2011) 89 - 100.
2
[2] M. F. Barnsley, Fractals Everywhere, Academic Press, Inc., Boston, MA, 1988.
3
[3] M. F. Blanco and M. Pisonero, An application of graphs in architecture, Available
4
at https://www.mi.sanu.ac.rs/vismath/proceedings/blanco.htm.
5
[4] J. I. Brown, K. Dilcher and R. J. Nowakowski, Roots of independence polynomials
6
of well covered graphs, J. Algebraic Combin. 11(3) (2000) 197-210.
7
[5] J. I. Brown, C. A. Hickman and R. J. Nowakowski, The independence fractal
8
of graph, J. Combin. Theory Ser. B 87(2) (2003) 209 - 230.
9
[6] C. A. Hickman, Roots of Chromatic and Independence Polynomials, Thesis
10
(Ph.D.) Dalhousie University (Canada), ProQuest LLC, Ann Arbor, MI, 2001.
11
[7] C. Hoede, and X. L. Li, Clique polynomials and independent set polynomials
12
of graphs, 13th British Combinatorial Conference (Guildford, 1991), Discrete
13
Math. 125(1-3) (1994) 219 - 228.
14
ORIGINAL_ARTICLE
Mathematics, Music and Architecture
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
2019-06-01T11:23:20
2020-07-11T11:23:20
87
106
10.22052/mir.2019.187587.1142
Music
architecture
harmonic proportions
geometry
Roghayyeh
Rasulzade
rasulzade90@gmail.com
true
1
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
AUTHOR
Javad
Divandari
j.divandari@kashanu.ac.ir
true
2
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
Department of Architecture, University of Kashan, Kashan, I. R. Iran
LEAD_AUTHOR
[1] L. B. Alberti, The Ten Books of Architecture, Dover Puplications, New York,
1
[2] M. R. Bemanian, H. Okhovvat and P. Baghaei, The Application of Geometry
2
and Conformity in Architecture (in Persian), Helleh & Tahaan, Tehran, 2015.
3
[3] J-Louis Cohen, Le Corbusier, Taschen GmbH, Cologne, 2015.
4
[4] F. Fakhruddini, Analyze and Explain the Music Row of Iran (in Persian),
5
Moin, third edition, Tehran, 2015.
6
[5] H. Hashemi Zarj Abadi, M. H. Ziaee Nia and H. R. Ghorbani, Re-reading
7
the geometric basics and golden ratio of Showkateyeh school (in Persian),
8
Pazhohesh-ha-ye Bashtanshenasi Iran 5(9) (2016) 207 - 222.
9
[6] M. Hejazi, Sacred geometry in nature and Persian architecture (in Persian),
10
History of Science 6(2) (2009) 15 - 36.
11
[7] R. Krier, Elements of Architecture, Translated by Mohammad Ahmadinejad,
12
3rd edition, Vol. 1, Khak, Isfahan, 2008.
13
[8] P. Mansouri, The Fundamental Theory of Music (in Persian), 20th edition,
14
Karnameh, Tehran, 1996.
15
[9] R. Mir Firoozi and D. Makhdoom Traveler, The eect of Iranian music on
16
architecture, In: Proc. National Conference on Structures, Roads and Archi-
17
tecture, February 22, 2011, Islamic Azad University, pp. 1 - 11.
18
[10] M. K. Portorab, Music Theory (in Persian), Cheshmeh, 65th edition, Tehran,
19
[11] R. Rasulzade Kande, J. Divandari, A. Shirmohammadzade and A. Es-
20
lamkhah, Comparative Study of Phonetic and Visual in Music and Architec-
21
ture (in Persian), Proc. of the International Conference on Architecture and
22
Mathematics, December 16-18, 2018, University of Kashan, pp. 162 - 173.
23
[12] K. Saian and M. R. Mohammadi, Condentiality in traditional architecture
24
(in Persian), Hoviat Shahr 1 (2006) 3 - 14.
25
[13] H. Seraj, Aestheticism is a natural step (in Persian), Honar-ha-ye-ziba:
26
Memari-va-shahrsazi 24 (2005) 105 - 111.
27
[14] H. Seraj, From Passing through to the Heart (in Persian), Neyestan, Tehran,
28
[15] M. Tabrizi, Property, Tabriz Music Tab (in Persian), MSc Thesis, Islamic
29
Azad University-Tabriz Branch, 2004.
30
[16] W. Kandinsky, Point and Line to Plane, Dover Publications, New York, 1979.
31
[17] I. Xenakis, Science and music, The Message of UNESCO 192 (1986) 34-39.
32
ORIGINAL_ARTICLE
Golden Section in the Persian-Islamic Architecture; Case Study: Hasht Behesht Palace, Isfahan, Iran
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. 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. 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
2019-06-01T11:23:20
2020-07-11T11:23:20
107
127
10.22052/mir.2019.195272.1157
Proportion
golden section
Nisbit Dhat Vasat Tarafein
Hasht Behesht Palace
Persian-Islamic architecture
Rouhollah
Mojtahedzadeh
r.mojtahed@scu.ac.ir
true
1
Architecture Department, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Architecture Department, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Architecture Department, Shahid Chamran University of Ahvaz, Ahvaz, Iran
LEAD_AUTHOR
Zahra
Namavar
namavar.nam@gmail.com
true
2
College of Architecture and Planning, University of Colorado, Denver, Colorado, USA
College of Architecture and Planning, University of Colorado, Denver, Colorado, USA
College of Architecture and Planning, University of Colorado, Denver, Colorado, USA
AUTHOR
[1] A. M. I. A. Al-B¯ır¯un¯ı, The Book of Instruction in the Elements of the Art of
1
Astrology, Written in Ghazneh 1029 A. D, Translation by R. Ramsay Wright,
2
M. A. Edin, LL. D. Tor. and Edin, Emeritus Professor of Biology University
3
of Toronto, London, LUZAC & CO, Published by Antioch Gate, 1934.
4
[2] Avicenna, The Healing, First Art of Total Assets of Mathematical Science
5
Engineering, Dr. Abraham Madkour, Dr. Abdhamid Sabra, Prof. Abdolhamid
6
Lotfi Mazhar, General Book Organization, Cairo, 1976.
7
[3] J. L. Bergiren, Parts of the Islamic Era Mathematics, Translated by Dr. Mohammad
8
Qasim Vahidi and Dr. Alireza Jamali (in Persian), Fatemi Publications,
9
Tehran, 1994.
10
[4] J. De Chardin, De Chardin Travelogues (Isfahan city section), Translated
11
by Arizi Hossein (in Persian), Negah Publications, Second Edition, Tehran,
12
[5] G. Doczi, The Power of Limits: Proportional Harmonies in Nature, Art &
13
Architecture), Translated by Hamidreza Karami with a preface of dr. Mohammad
14
Zeimaran (in Persian), Parchin Publications, First Edition, Tehran,
15
[6] A. Q. Ghorbani, Bozjani Nameh, Islamic Revolution Education and Publications
16
(in Persian), Tehran, 1992.
17
[7] A. Q. Ghorbani, Research in Abooreyhan Al-Biruni Mathematical Books (A
18
new written of Al-Biruni nameh) (in Persian), Samt Publications, Tehran,
19
[8] A. A. Halbi, Gozide-i-Rasa’el Ikhvan Alsafa, (in Persian), Asatir, Tehran,
20
[9] R. Hillenbrand, Islamic Architecture: Form, Function, and Meaning, Translated
21
by Dr. Baqer Ayatollahzadeh Shirazi (in Persian), Published by
22
Rozaneh, First Edition, Tehran, 2001.
23
[10] L. Honarfar, Esfahan eight heaven, (in Persian) Art and People Magazine
24
10(117) (1972) 2 - 16.
25
[11] R. Jafarian, The Safavids From Emergence to Deterioration (in Persian), The
26
Cultural Institute of Contemporary Science and Thought Publications, First
27
Edition, Tehran, 1999.
28
[12] M. S. A. Jenab, Al-Esfah¯an, Additions by Mohammad Reyaz¯ı (in Persian),
29
Iran’s Cultural Heritage Organization, Tehran, 1997.
30
[13] E. Kaempfer, Kaempfer Travelogues, Translated by Keykavousi Jahandar,
31
Kharazmi Publishing Company (in Persian), Third Edition, Tehran, 1985.
32
[14] R. Lawlor, Sacred Geometry: Philosophy & Practice (Art and Imagination),
33
(in Persian), Thomes & Hudson Ltd, First Edition, London, 1982.
34
[15] S. H. Nasr, Science and Civilization in Islam, Translated to Persian by Ahmad
35
Aram (in Persian), Elimi Farhangi Press, Tehran, 2009.
36
[16] G. Necipoglu, The Topkapi Scroll–Geometry and Ornament in Islamic Architecture,
37
Translated by Mehrdad Qayyummi Bidhendi (in Persian), Published
38
by Rozaneh, First Publish, Tehran, 2000.
39
[17] M. K. Pirnia, Persian Architecture, edited by Gholam Hossein Me’marian (in
40
Persian), Soroush-e-danesh Publications, First Edition, Tehran, 2008.
41
[18] B. Rafiee Sereshki, N. Rafi Zadeh and A. M. Ranjbar Kermani, Architectural
42
Culture of Iran, Building and Housing Research Center (in Persian), First
43
Edition, Tehran, 2003.
44