Gavrić, Gordana

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  • Gavrić, Gordana (2)
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Orientation of medieval churches of Morava school

Tadić, Milutin; Gavrić, Gordana

(Beograd : Srpsko geografsko društvo, 2012)

TY  - JOUR
AU  - Tadić, Milutin
AU  - Gavrić, Gordana
PY  - 2012
UR  - https://gery.gef.bg.ac.rs/handle/123456789/531
AB  - In this paper we present the mathematical and topographic analysis of orientation of the most significant churches (11) of Morava school, the last style in architecture of medieval Serbia whose executors were chief architects. The deviation from equinox East of the main axis of each church and the dates when the Sun rises on the physical horizon, in the extension of the main axis, have been calculated. These were the dates when the church could have been oriented towards the rising Sun. This possibility has been ruled out for four churches. As for the other churches, the matching of the mentioned dates with the patron's days wasn't established. The churches in monasteries Ljubostinja and Kalenic are oriented with astronomical precision towards equinox East, an admirable fact considering the tools available to the builders. Rade Borovic, the only chief architect who put his signature on his work, was the chief architect of Ljubostinja.
AB  - U radu je izvršena matematičko-geografska i topografska analiza orijentacije najznačajnijih crkava (11) moravske škole, poslednjeg stila srpske srednjovekovne arhitekture čiji su nosioci srpski protomajstori. Izmerena su odstupanja ose svake crkve od ravnodnevačkog istoka i izračunati datumi u kojima sunce izlazi na fizičkom horizontu, u produžetku te ose. To su dani kada je crkva mogla biti orijentisana prema izlazećem suncu. Za četiri crkve isključena je takva mogućnost, a kod ostalih nije ustanovljeno poklapanje pomenutih datuma sa danima posvećenim njihovim patronima. Crkve manastira Ljubostinja i Kalenić orijentisane su astronomski tačno prema ravnodnevačkom istoku, što je vredno divljenja, s obzirom na jednostavnost pomagala sa kojima su tadašnji graditelji raspolagali. Protomajstor prve bio je Rade Borović, jedini srpski protomajstor za koga znamo da je potpisao svoj rad.
PB  - Beograd : Srpsko geografsko društvo
T2  - Glasnik Srpskog geografskog društva
T1  - Orientation of medieval churches of Morava school
T1  - Orijentacija srednjovekovnih srpskih crkava Moravske škole
VL  - 92
IS  - 1
SP  - 185
EP  - 202
UR  - https://hdl.handle.net/21.15107/rcub_gery_531
ER  - 
@article{
author = "Tadić, Milutin and Gavrić, Gordana",
year = "2012",
abstract = "In this paper we present the mathematical and topographic analysis of orientation of the most significant churches (11) of Morava school, the last style in architecture of medieval Serbia whose executors were chief architects. The deviation from equinox East of the main axis of each church and the dates when the Sun rises on the physical horizon, in the extension of the main axis, have been calculated. These were the dates when the church could have been oriented towards the rising Sun. This possibility has been ruled out for four churches. As for the other churches, the matching of the mentioned dates with the patron's days wasn't established. The churches in monasteries Ljubostinja and Kalenic are oriented with astronomical precision towards equinox East, an admirable fact considering the tools available to the builders. Rade Borovic, the only chief architect who put his signature on his work, was the chief architect of Ljubostinja., U radu je izvršena matematičko-geografska i topografska analiza orijentacije najznačajnijih crkava (11) moravske škole, poslednjeg stila srpske srednjovekovne arhitekture čiji su nosioci srpski protomajstori. Izmerena su odstupanja ose svake crkve od ravnodnevačkog istoka i izračunati datumi u kojima sunce izlazi na fizičkom horizontu, u produžetku te ose. To su dani kada je crkva mogla biti orijentisana prema izlazećem suncu. Za četiri crkve isključena je takva mogućnost, a kod ostalih nije ustanovljeno poklapanje pomenutih datuma sa danima posvećenim njihovim patronima. Crkve manastira Ljubostinja i Kalenić orijentisane su astronomski tačno prema ravnodnevačkom istoku, što je vredno divljenja, s obzirom na jednostavnost pomagala sa kojima su tadašnji graditelji raspolagali. Protomajstor prve bio je Rade Borović, jedini srpski protomajstor za koga znamo da je potpisao svoj rad.",
publisher = "Beograd : Srpsko geografsko društvo",
journal = "Glasnik Srpskog geografskog društva",
title = "Orientation of medieval churches of Morava school, Orijentacija srednjovekovnih srpskih crkava Moravske škole",
volume = "92",
number = "1",
pages = "185-202",
url = "https://hdl.handle.net/21.15107/rcub_gery_531"
}
Tadić, M.,& Gavrić, G.. (2012). Orientation of medieval churches of Morava school. in Glasnik Srpskog geografskog društva
Beograd : Srpsko geografsko društvo., 92(1), 185-202.
https://hdl.handle.net/21.15107/rcub_gery_531
Tadić M, Gavrić G. Orientation of medieval churches of Morava school. in Glasnik Srpskog geografskog društva. 2012;92(1):185-202.
https://hdl.handle.net/21.15107/rcub_gery_531 .
Tadić, Milutin, Gavrić, Gordana, "Orientation of medieval churches of Morava school" in Glasnik Srpskog geografskog društva, 92, no. 1 (2012):185-202,
https://hdl.handle.net/21.15107/rcub_gery_531 .

A mathematical and geographical analysis of the orientation of two early Christian churches in Serbia

Tadić, Milutin; Gavrić, Gordana

(Beograd : Univerzitet u Beogradu - Geografski fakultet, 2011)

TY  - JOUR
AU  - Tadić, Milutin
AU  - Gavrić, Gordana
PY  - 2011
UR  - https://gery.gef.bg.ac.rs/handle/123456789/404
AB  - Among many medieval sacral edifices there are numerous churches built in old cult sites. In such cases where the medieval churches were preceded by the early Christian churches it is interesting to observe the differences or similarities in their orientation. In order to approach this systematically, it is necessary to start with the analyses of the longitudinal axes of certain Christian basilicas. For this occasion, we have chosen two churches, one in the valley of the river Gradac near Valjevo (6th century) and the other just under the peak, of Kopaonik, in Nebeske Stolice (5th/6th century) on the Kopaonik. Thus, the subject of this paper is the exact analysis of the orientation of the cited edifices. The church located in the valley of the river Gradac has been pretty accurately oriented in the west-eastern direction, with the altar naturally facing the east. Since it is positioned atop a rocky cliff, with the eastern and western part of the horizon completely hidden, it is clear that the builder was unable to follow the sunrise or the sunset, during the laying of the foundation, the builder couldn't be guided by the sunrise or the sunset, but he had to be familiar with the exact methods of orientation. The longitudinal axis of the basilica in Nebeske Stolice, on Kopaonik, is positioned fairly accurately and faces sunset during the summer solstice. As the basilica is positioned on a plateau with an altitude of nearly 1793m, the eastern part of the horizon is completely exposed. This allowed the builder to lay the foundation of the church visually during the dawn of the summer solstice Other than this possibility, the builder had another, in case he didn't want or couldn't wait for that exact day, and that would be the possibility of determining the direction via the geometric method, using analemma.
AB  - Među mnogim sakralnim srednjovekovnim građevinama brojne su one koje su podignute na starim kultnim mestima. U slučajevima kada srednjovekovnim crkvama prethode ranohrišćanske, zanimljivo je pratiti razlike ili podudarnosti u njihovim orijentacijama. Da bi se takvim analizama pristupilo sistematično, neophodno je poći od analize orijentacija uzdužnih osa pojedinih ranohrišćanskih bazilika. Za ovu priliku izabrali smo dve, jednu u dolini reke Gradac kod Valjeva (6. vek) i drugu pod samim vrhom Kopaonika, na Nebeskim stolicama (5/6 vek). Predmet ovog rada je, dakle, egzaktna analiza orijentacija navedenih objekata. Crkva u dolini reke Gradac je sa dosta tačnosti orijentisana u pravcu zapad-istok, sa oltarom na istoku, naravno. Pošto je smeštena na kamenom grebenu, sa potpuno zaklonjenim istočnim i zapadnim delom horizonta, graditelj se prilikom postavljanja temelja nije mogao upravljati prema izlasku ili zalasku sunca, već je morao poznavati egzaktne metode orijentacije. Uzdužna osa bazilike na Nebeskim stolicama, na Kopoaniku, usmerena je dosta tačno ka tački izlaska sunca letnjeg solsticijuma. Pošto se nalazi na zaravnjenoj platformi na blizu 1 793 m nadmorske visine ima potpuno otrkiven istočni deo horizonta, što graditelju otvara mogućnost vizuelnog utemeljenja crkve u zoru letnjeg solsticijuma. Pored ove mogućnosti, graditelj je imao i drugu, u slučaju da nije želeo ili mogao da sačeka baš taj dan, a to je mogućnost određivanja pravca geometrijskom metodom, pomoću analeme.
PB  - Beograd : Univerzitet u Beogradu - Geografski fakultet
T2  - Zbornik radova - Geografski fakultet Univerziteta u Beogradu
T1  - A mathematical and geographical analysis of the orientation of two early Christian churches in Serbia
T1  - Matematičko-geografska analiza orijentacije dve ranohrišćanske crkve u Srbiji
IS  - 59
SP  - 223
EP  - 234
UR  - https://hdl.handle.net/21.15107/rcub_gery_404
ER  - 
@article{
author = "Tadić, Milutin and Gavrić, Gordana",
year = "2011",
abstract = "Among many medieval sacral edifices there are numerous churches built in old cult sites. In such cases where the medieval churches were preceded by the early Christian churches it is interesting to observe the differences or similarities in their orientation. In order to approach this systematically, it is necessary to start with the analyses of the longitudinal axes of certain Christian basilicas. For this occasion, we have chosen two churches, one in the valley of the river Gradac near Valjevo (6th century) and the other just under the peak, of Kopaonik, in Nebeske Stolice (5th/6th century) on the Kopaonik. Thus, the subject of this paper is the exact analysis of the orientation of the cited edifices. The church located in the valley of the river Gradac has been pretty accurately oriented in the west-eastern direction, with the altar naturally facing the east. Since it is positioned atop a rocky cliff, with the eastern and western part of the horizon completely hidden, it is clear that the builder was unable to follow the sunrise or the sunset, during the laying of the foundation, the builder couldn't be guided by the sunrise or the sunset, but he had to be familiar with the exact methods of orientation. The longitudinal axis of the basilica in Nebeske Stolice, on Kopaonik, is positioned fairly accurately and faces sunset during the summer solstice. As the basilica is positioned on a plateau with an altitude of nearly 1793m, the eastern part of the horizon is completely exposed. This allowed the builder to lay the foundation of the church visually during the dawn of the summer solstice Other than this possibility, the builder had another, in case he didn't want or couldn't wait for that exact day, and that would be the possibility of determining the direction via the geometric method, using analemma., Među mnogim sakralnim srednjovekovnim građevinama brojne su one koje su podignute na starim kultnim mestima. U slučajevima kada srednjovekovnim crkvama prethode ranohrišćanske, zanimljivo je pratiti razlike ili podudarnosti u njihovim orijentacijama. Da bi se takvim analizama pristupilo sistematično, neophodno je poći od analize orijentacija uzdužnih osa pojedinih ranohrišćanskih bazilika. Za ovu priliku izabrali smo dve, jednu u dolini reke Gradac kod Valjeva (6. vek) i drugu pod samim vrhom Kopaonika, na Nebeskim stolicama (5/6 vek). Predmet ovog rada je, dakle, egzaktna analiza orijentacija navedenih objekata. Crkva u dolini reke Gradac je sa dosta tačnosti orijentisana u pravcu zapad-istok, sa oltarom na istoku, naravno. Pošto je smeštena na kamenom grebenu, sa potpuno zaklonjenim istočnim i zapadnim delom horizonta, graditelj se prilikom postavljanja temelja nije mogao upravljati prema izlasku ili zalasku sunca, već je morao poznavati egzaktne metode orijentacije. Uzdužna osa bazilike na Nebeskim stolicama, na Kopoaniku, usmerena je dosta tačno ka tački izlaska sunca letnjeg solsticijuma. Pošto se nalazi na zaravnjenoj platformi na blizu 1 793 m nadmorske visine ima potpuno otrkiven istočni deo horizonta, što graditelju otvara mogućnost vizuelnog utemeljenja crkve u zoru letnjeg solsticijuma. Pored ove mogućnosti, graditelj je imao i drugu, u slučaju da nije želeo ili mogao da sačeka baš taj dan, a to je mogućnost određivanja pravca geometrijskom metodom, pomoću analeme.",
publisher = "Beograd : Univerzitet u Beogradu - Geografski fakultet",
journal = "Zbornik radova - Geografski fakultet Univerziteta u Beogradu",
title = "A mathematical and geographical analysis of the orientation of two early Christian churches in Serbia, Matematičko-geografska analiza orijentacije dve ranohrišćanske crkve u Srbiji",
number = "59",
pages = "223-234",
url = "https://hdl.handle.net/21.15107/rcub_gery_404"
}
Tadić, M.,& Gavrić, G.. (2011). A mathematical and geographical analysis of the orientation of two early Christian churches in Serbia. in Zbornik radova - Geografski fakultet Univerziteta u Beogradu
Beograd : Univerzitet u Beogradu - Geografski fakultet.(59), 223-234.
https://hdl.handle.net/21.15107/rcub_gery_404
Tadić M, Gavrić G. A mathematical and geographical analysis of the orientation of two early Christian churches in Serbia. in Zbornik radova - Geografski fakultet Univerziteta u Beogradu. 2011;(59):223-234.
https://hdl.handle.net/21.15107/rcub_gery_404 .
Tadić, Milutin, Gavrić, Gordana, "A mathematical and geographical analysis of the orientation of two early Christian churches in Serbia" in Zbornik radova - Geografski fakultet Univerziteta u Beogradu, no. 59 (2011):223-234,
https://hdl.handle.net/21.15107/rcub_gery_404 .