Geometric Proportional Schemas of Serbian Medieval Raška Churches Based on Štambuk’s Proportional Canon

  • Magdalena DragovićEmail author
  • Aleksandar Čučaković
  • Jelena Bogdanović
  • Marko Pejić
  • Milesa Srećković


In this paper, an analysis of three Serbian medieval Raška churches highlights the significance of the interaction of regular geometric shapes in the composition of their underlying proportional scheme. The complex geometry recognised in the layouts and cross-sections of these monastery churches points to the potential use of a unique triangular proportioning system. This proportional system is derived from the initial geometry of Štambuk’s proportional canon, which employs two circles constrained by an equilateral triangle in a specific setting. As the essence of religious medieval structures is often related to their interior, in this paper 3D “empty space moulds” are created by the parametric modelling of each element of the structure. This research shows how the variation of the two critical points of the church interior, the centres of the dome and of the main apse, along with the key triangles incorporated in the proportional scheme, affect the final 3D structural model.


Proportions Geometric scheme Orthodox church Raška style Parametric modelling 



The authors of the paper would like to thank the Serbian Orthodox Church-Eparchy of Žiča, for their blessing and permission for the research; the brotherhood of the monastery of Studenica for their hospitality and blessing; the David Lingle Fellowship at Iowa State University and the Serbian Ministry of Education, Science and Technological Development-project TR36008 for the financial support. Special thanks to the editor-in-chief of Nexus Network Journal, Michael Ostwald, and the anonymous reviewers for their time and constructive suggestions which shaped the final version of this paper.

Segments of this research were presented at the panel "Medieval Structures, Digital Tools and Architectural Knowledge", at the Conference of the Society of Architectural Historians, held in St. Paul, MN, April 2018. An earlier version of this paper was presented at the International Conference MoNGeometrija 2018, held in Novi Sad, Serbia, June 2018.

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  1. Banfi, Fabrizio. 2016. Building information modelling – a novel parametric modelling approach based on 3D surveys of historic architecture. In: Digital Heritage. Progress in Cultural Heritage: Documentation, Preservation, and Protection. Proceedings, Part I of the 6th International Conference EuroMed 2016, LNCS 10058 (Nicosia, October 31-November 2016), eds. M. Ioannides, E. Fink, A. Moropoulou, M. Hagedorn-Saupe, A. Fresa, G. Liestøl, V. Rajcic, P. Grussenmeyer, 116–127. Cham: Springer International Publishing AG.Google Scholar
  2. Bogdanović, Jelena. 2017. The Framing of Sacred Space: The Canopy and the Byzantine Church. New York: Oxford University Press.Google Scholar
  3. Bogdanović, Jelena. 2015. The Preservation of Architectural Heritage after World War One: Mihajlo Pupin and his book Serbian Orthodox Church. Matica Srpska Journal for Fine Arts 43: 195-210.Google Scholar
  4. Bogdanović, Jelena. 2011. The Architectural Design of the Church of St. George in Budimlja and Medieval Building Practices. In: Đurđevi Stupovi and the Eparchy of Budimlja, ed. Branislav Todić, 95-107. Berane and Belgrade: Bishopric of Budimlje and Nikšić, Institute of Art History Belgrade, and Museum of Polimlje.Google Scholar
  5. Bork, Robert. 2014. The Geometry of Bourges Cathedral. Architectural Histories 2(1), p.Art. 24: np. (accessed 14 February, 2018).
  6. Bošković, Đurđe and Branislav Vulović. 1956-1957. Iustiniana Prima-Kuršumlija-Studenica. Starinar VII-VIII: 173-180 (in Serbian).Google Scholar
  7. Cohen, Matthew A. 2014. Introduction: Two Kinds of Proportion. Architectural Histories 2(1), p.Art.21: np. (accessed 10 November, 2017).
  8. Corcuff, Marie-Pascale. 2012. Modularity and proportions in architecture and their relevance to a generative approach to architectural design. Nexus Network Journal 14(1): 53–73.Google Scholar
  9. Čanak-Medić, Milka and Đurđe Bošković. 1986. The monuments of the Serbian medieval architecture. Corpus of sacral buildings: Architecture of Nemanja’s time I. Belgrade: National Institute for Protection of Cultural Monuments of Serbia. (in Serbian).Google Scholar
  10. Čanak-Medić, Milka and Olivera Kandić. 1995. The monuments of the Serbian medieval architecture. Corpus of sacral buildings: Architecture of the first half of 13th century I. The Churches in Raška. Belgrade: National Institute for Protection of Cultural Monuments of Serbia. (in Serbian and French).Google Scholar
  11. Čanak-Medić, Milka. 1996. Design and construction procedures of ancient builders. In: Proceedings of the Scientific Symposium “Development of the Sciences in the Field of Civil Engineering and Geodesy in Serbia”, (Belgrade, Serbia, May 1996) eds. Miodrag Sekulović and Rastislav Mandić, 29-50. Belgrade: Građevinska knjiga. (in Serbian).Google Scholar
  12. Čanak-Medić, Milka. 2007. The Cathedral of St. Tryphon as Inspiration for Builders and Sculptors of Churches in Ras. Zbornik radova vizantološkog instituta 44(1): 245–251. (in Serbian).Google Scholar
  13. Čučaković, Aleksandar, Magdalena Dragović, Marko Pejić, Milesa Srećković and Jelena Pandžić. 2016. The possibilities of application of 3D digital models in cultural heritage object protection and reconstruction. In: Proceedings of the 5 th International Scientific Conference on Geometry and Graphics (MoNGeometrija 2016, Belgrade, Serbia, June 2016) eds. M. Obradović, B. Popkonstantinović, R. Obradović, 434-443. Belgrade: Serbian Society for Geometry and Graphics & Akademska misao.Google Scholar
  14. Ćurčić, Slobodan. 2010. Architecture in the Balkans. From Diocletian to Süleiman the Magnificent. New Haven: Yale University Press.Google Scholar
  15. Dabbour, Loai M. 2012. Geometric proportions: The underlying structure of design process for Islamic geometric patterns. Frontiers of Architectural Research 1(4): 380–391.Google Scholar
  16. Dragović, Magdalena, Aleksandar Čučaković and Milesa Srećković. 2015. Geometric approach to the revitalization process of medieval Serbian monasteries. In: Proceedings of the 13th International Conference on Engineering and Computer Graphics (BALTGRAF-13, Vilnius, Lithuania, June 2015) ed. E. Timinskas, 47-53. Vilnius: Vilnius Gediminas Technical University.Google Scholar
  17. Frings, Marcus. 2002. The Golden Section in Architectural Theory. Nexus Network Journal 4(1): 9–32.Google Scholar
  18. Heath, T. L. 1908. The thirteen books of Euclid’s elements (translated from the text of Heiberg with introduction and commentary of Heiberg T.L.). Cambridge: Cambridge University Press.Google Scholar
  19. Kandić, Olivera. 2005. Gradac. History and architecture of the monastery. Belgrade: National Institute for Protection of Cultural Monuments of Serbia.Google Scholar
  20. Kappraff, Jay. 1996. Linking the Musical Proportions of the Renaissance with the Modulor of Le Corbusier and the System of Roman Proportions. International Journal of Space Structures 11(1-2): 211-219.Google Scholar
  21. Kappraff, Jay. 1999. Systems of Proportion in Design and Architecture and their Relationship to Dynamical Systems Theory. In: Mathematical Connections in Art, Music and Science, Conference proceedings (Bridges 1999, Winfield, Kansas, USA, July-August 1999), ed. Reza Sarhangi, 27-40. Winfield: Bridges Conference.Google Scholar
  22. Kurtović-Folić, Nađa. 1996. Elementary forms of structural systems in Byzantine and medieval Serbia. In: Symposium on Development of the Sciences in the Field of Civil Engineering and Geodesy in Serbia, 85-103. Belgrade: Građevinska knjiga. (in Serbian).Google Scholar
  23. Lopez, Facundo Jose, Pedro M. Lorens, Jose Llamas, Jaime Gomey-Garcia-Bermejo and Eduardo Zalama. 2018. A review of Heritage Building Information Modelling. Multimodal Technologies and Interaction 2(2), 21: np. (accessed 5 August, 2018).
  24. Letić, Duško, Nenad Cakić, Branko Davidović and Katarina Živković. 2012. Phenomenology of golden section ϕ in the nature, art and science. Zrenjanin: Technical Faculty “Mihajlo Pupin”; Belgrade: Faculty of Electrical Enginering. (in Serbian).Google Scholar
  25. Murphy, Maurice, Eugene Mcgovern and Sara Pavia. 2011. Historic building information modelling–adding intelligence to laser and image based surveys. In: Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXVIII-5/W16, 4 th ISPRS International Workshop 3D-ARCH 2011: 3D Virtual Reconstruction and Visualization of Complex Architectures (Trento, Italy, March 2011) eds. F. Remondino and S. El-Hakim, 1-7. Hannover: ISPRS.Google Scholar
  26. Nenadović, Slobodan M. 1987. The architecture in Yugoslavia from IX to XVIII centuries (2nd ed.) Belgrade: Naučna knjiga. (in Serbian).Google Scholar
  27. Nenadović, Slobodan M. 2003. Building techniques in medieval Serbia. Belgrade: Prosveta. (in Serbian).Google Scholar
  28. Pejić, Svetlana. 2002. Pustinja Monastery. Belgrade: National Institute for Protection of Cultural Heritage of Serbia. (in Serbian).Google Scholar
  29. Petrović, Nevenka. 1956-1957. Proportions and dimensions of churches’ layouts in Iustiniana Prima. Starinar, VII-VIII: 165–171. (in Serbian).Google Scholar
  30. Potamianos, Iakovos, James Turner and Wassim Jabi. 1995. Exploring the proportions of middle Byzantine churches: a parametric approach. In: Proceedings of the 6 th International Conference on Computer Aided Architectural Design Futures, (Singapore, Malaysia, September 1995) eds. Milton Tan and Robert The, 483-493. Singapore: Centre for Advanced Studies in Architecture, National University of Singapore.Google Scholar
  31. Quatrini, Ramona, Paolo Clini, Romina Nespeca and Ludovico Ruggeri. 2016. Measurement and historical information building: Challenges and opportunities in the representation of semantically structured 3D content. DISEGNARECON 9(16): 14.1-14.11. (accessed 7 August, 2018).
  32. Quatrini, Ramona, Roberto Pierrdicca and Christian Morbidoni. 2017. Knowledge based data enrichment for HBIM: Exploring high-quality models using the semantic web. Journal of Cultural Heritage 28: 129–139.Google Scholar
  33. Roldan, Francisco. 2012. Method of modulation and sizing of historic architecture. Nexus Network Journal 14(3): 539–553.Google Scholar
  34. Stewart, Charles A. 2015. Modular design in the vaulting of the early Byzantine cisterns and reservoirs, In: Against Gravity:Building Practices in the Pre-Industrial World, eds. Robert Ousterhout, Dorian Borbonus and Elisha Dumser, Philadelphia: Center for Ancient Studies, University of Pennsylvania. (accessed 5 August, 2018).
  35. Suppes, Patrick. 1991. Rules of proportion in architecture. Midwest Studies in Philosophy 16(1): 352–358.Google Scholar
  36. Štambuk, Ivo. 2002. Forgotten proportions: The canon for building churches. Contributions to the History of the Island Hvar XI: 91–109 (in Croatian).Google Scholar
  37. Štambuk, Ivo. 2017. Forgotten proportions: The canon for building churches 2. Contributions to the History of the Island Hvar XIII: 97–123 (in Croatian).Google Scholar
  38. Štambuk, Ivo. 2014. Hvar belfries. Contributions to the History of the Island Hvar XII: 147–169 (in Croatian).Google Scholar
  39. Tomas, Ivana. 2011. St. Mary’s church in the island of Mljet and its links with Apulian Romanesque monuments, Prostor, 19 (2(42)): 296–309 (in Croatian).Google Scholar

Copyright information

© Kim Williams Books, Turin 2019

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringUniversity of BelgradeBelgradeSerbia
  2. 2.Architecture Department 158 College of DesignIowa State UniversityAmesUSA
  3. 3.Faculty of Electrical EngineeringUniversity of BelgradeBelgradeSerbia

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