Mathematical-geographical analysis of the orientation of St John’s church of the Studenica monastery

Considering the fact that ecclesiastical rules do not precisely say that a church must be directed “to the East” or “to sunrise”, it should always be checked if there is a connection between the orientation of a church and geometry of the Sun. In this paper, such examination is performed on the example of the church of St. John (the 13th century), one of four churches of the Studenica monastery, in the following way: 1) using gnomon method, the azimuth of the main longitudinal axis of the church is measured; 2) the altitude above the horizon of the point in which the extended axis of the church touches the true horizon is determined by cartometry; 3) the most probable dates when the Sun rises at that point are determined: May 7th according to Gregorian calendar, or April 30th according to Julian calendar, in the 13th century. The applied method is described in details and it can be applied for the analysis of the orientation of any other medieval church. This method can determine the time when the church was founded, as well as the fact if the church is original, or possibly erected on the foundations of some older sacral object

Solstice orientation of the St Nicholas' Church monastery Studenica, Serbia

St Nicholas’ Church of the Serbian monastery Studenica was erected in 13th century, before 1230. This is a modest one-nave building with an entrance on the west and the apse on the east side. In order to explain a large deviation of the longitudinal axis of the church from the southeast direction, the following has been done: 1) deviation of the longitudinal axis of the church from the east direction (24o to the NE) was accurately measured; 2) a corresponding sector of true horizon of the church was constructed in the orthographic transverse map projection; 3) the position of the point where ends the line of observation in the vertical axis of the church and the position of the point of actual Sunrise of Summer Solstice were determined topographically on the true horizon. Since the distance between these points is about 1.5o, it can be said that the protomaster probably founded the Church St Nicholas on the basis of Summer Solstice. A direct check made on 21st of June, 2011 confirmed the accuracy of the applied method

GNOMONIC TERMS IN THE SERBIAN LANGUAGE

In Serbia, as in many other European countries, there has been a widespread revival of interest in gnomonics in recent decades. An increasing number of sundials and a growing number of publications on gnomonics demonstrate the popularity of sundialling. Accordingly, it is interesting to find out which gnomonic terms are used, when they appeared and how they developed. In Serbia (and the countries formed after the disintegration of the former Yugoslavia), societies of gnomonics enthusiasts do not exist and therefore it is not reasonable to expect any concern intended to preserve gnomonic heritage or the existence of the gnomonic terminological system. This assumption has been confirmed by the analysis of publications in the field of gnomonics published in the Serbian language. Due to unfavorable historical circumstances in the Balkans, Serbian scientific terminology began to form rather late (19th century) and the first gnomonic terms appeared at the beginning of the 20th century. They were introduced in the articles of the Serbian astronomers, professors Milan Nedeljković (1902) and Vojislav V. Mišković (1930; 1932). However, most of these terms have not been preserved. Contemporary gnomonic terminology is multidisciplinary, and when the terms belonging to neighboring sciences are removed, a small number of gnomonic terms remains. Among them, the following four are the key ones: gnomon, gnomonic projection, sundial and gnomonics. In this paper, a modified definition of the most important term — gnomon has been proposed as well as the definitions of all other key gnomonic terms related to it

Solstice orientation of the St Nicholas' Church monastery Studenica, Serbia

St Nicholas’ Church of the Serbian monastery Studenica was erected in 13th century, before 1230. This is a modest one-nave building with an entrance on the west and the apse on the east side. In order to explain a large deviation of the longitudinal axis of the church from the southeast direction, the following has been done: 1) deviation of the longitudinal axis of the church from the east direction (24o to the NE) was accurately measured; 2) a corresponding sector of true horizon of the church was constructed in the orthographic transverse map projection; 3) the position of the point where ends the line of observation in the vertical axis of the church and the position of the point of actual Sunrise of Summer Solstice were determined topographically on the true horizon. Since the distance between these points is about 1.5o, it can be said that the protomaster probably founded the Church St Nicholas on the basis of Summer Solstice. A direct check made on 21st of June, 2011 confirmed the accuracy of the applied method

A THEORETICAL EXPLORATION OF A SUNDIAL OF THE FRANCISCAN FRIARY IN DUBROVNIK (CROATIA)

The Franciscan friary in Dubrovnik (Croatia) has two old wall sundials mounted in the small and large monastery cloisters. Both indicate equinoctial hours according to the apparent solar time. It is known for one who made it and the year it was made in — Paško Baletin in 1770, and for the other, there are no data. The second sundial has two scales; on the upper scale, the direction of the shadow indicates hours counted from midnight (Ore francese), whereas on the lower scale, the hours counted from the previous sunset are indicated by the tip of the shadow i.e. its “sunlet” (Ore italiche) as it has been believed so far. In order to check this, we calculated both scales, made drafts and compared them with the existing sundial scales: hour lines on the upper scale coincide, while on the lower scale all calculated hour lines deviate from the existing lines towards the west. However, when the calculations for the lower scale are done in accordance to the hours counted from the end of the civil twilight (Ore italiche da campanile) there is complete compatibility. This was confirmed by on-site observation of the sundial. It remains to search through Dubrovnik archives to discover when the two-scale sundial was made. The last-mentioned variant could have been brought to Dubrovnik in the second half of the 18th century, and since then there was a need to construct a two-scale sundial

Orientation of the fifteenth and sixteenth century mosques in the former Yugoslavia

The paper presents the analysis of the orientation of 60 mosques built in the XV and XVI centuries in the Balkans' region of former Yugoslavia. The mosques have been selected according to their architectural value - mostly the dome mosques that were built by the most renowned builders. Based on the geographic coordinates, the qiblas of all mosques were calculated and the azimuths of their axes measured on orthophotographs. Statistical analysis has shown that the axes of these mosques vary in the horizon sector that is five times wider than the calculated sector of the correct qibla, with a systematic deviation of -10 degrees 15' in relation to the correct qibla. Connections between deviations of the architectural design (dome mosques and other mosques), location and elevation have not been identified. However, a connection between deviations and the time of construction has been identified: deviations from the qibla are smaller in mosques built at a later date. The paper has laid the groundwork for future analysis of the causes of the aforementioned deviations: in the XV and XVI centuries there were no accurate geographic coordinates of locations and the builders were not able to calculate (take over, measure) the exact qibla direction, regardless of the method they applied

Sunčani časovnik utvrđenja Hrusija (srpski manastir Hilandar, Sveta Gora)

The paper analyses a 1993 photograph of marble slab taken in front of the entrance to the harbour of the mediaeval fortification Hrusia which dates from 1302, the property of the Serbian monastery Chilandar on Mt. Athos. The slab is now dug under a pile of broken rocks from parts of a demolished wall, and it is inaccessible to direct verification of the assumption that it is 'a kind of sundial'. Based on the analysis it is highly likely that it is an old Greek sundial, which is today in its secondary position. The finding is of importance as it is the first old Greek or Byzantine sundial discovered on the Holy Mountain.U radu je analizirana fotografija iz 1993. godine snimljena ispred ulaza u pristanište srednjovekovnog utvrđenja Hrusija iz 1302. godine, koje pripada srpskom manastiru Hilandar na Svetoj Gori. Ploča je danas zatrpana kamenjem dela obrušenog zida i nedostupna za direktnu proveru pretpostavke da se radi o 'nekoj vrsti sunčanog časovnika'. Nakon posredne analize sa dosta verovatnoće može se pretpostaviti da se radi o starogrčkom sunčanom časovniku koji je danas u sekundarnom položaju. Nalaz je značajan zbog toga što je to prvi starogrčki ili vizantijski sunčani časovnik pronađen na Svetoj Gori

Kartografske projekcije u astronomiji

The article explains specifics of choice of map projections for charts used in astronomy - charts of celestial bodies and star charts. It says that map projections have appeared in the scope of astronomy, explains the differences between geographical and astronomical charts, analyzes the map projections which are most commonly used in today’s astronomy, and suggests projections which can be used.U radu se izlažu specifičnosti izbora kartografskih projekcija za kar-te koje se koriste u astronomiji - karte nebeskih tela i karte zvezdanog neba. Navedeno je da su kartografske projekcije nastale u okrilju astronomije, istaknute su razlike između geografskih i astronomskih karata, analizirane su kartografske projekcije koje se danas najčešće koriste u astronomiji i preporučene su projekcije koje bi se mogle koristiti

Crkve raške škole - monumentalni orijentiri (matematičko-geografski pogled na orijentaciju crkava raške škole)

The article presents the results of research on the direction of seventeen of the most notable churches of the Raška School on the territory of the Republic of Serbia, five of which are on UNESCO's World Heritage List. The azimuths of the main axis of each of these churches was measured and the dates were established when the sun rose in that direction on the physical horizon. With a single exception (the catholicon of Žiča Monastery), the main axes of all the churches lie in the eastern sector of the horizon. In nine churches the deviation of equinox East is ±60, while two of the churches (St. Achilles and the catholicon at Sopoćani Monastery), from a mathematical-geographical viewpoint, are ideally directed. No correlation was found between the direction of the churches and the points of sunrise on the days dedicated to the churches' patron saints.Članak prikazuje rezultate istraživanja orijentacije sedamnaest najpoznatijih crkava raške škole u Republici Srbiji, od kojih se pet nalazi na Uneskovoj listi Svetske baštine. Izmeren je azimut glavne ose svake od njih, i određeni datumi kada sunce izlazi u tom pravcu na fizičkom horizontu. Sa jednim izuzetkom (katolikon manastira Žiča), ose svih crkava leže u istočnom sektoru horizonta. Kod devet crkava odstupanje od ravnodnevačkog istoka kreće se u granicama ±6°, a dve crkve (Sv. Ahilej i katolikon Sopoćana), sa matematičkogeografskog stanovišta, idealno su orijentisane. Nije uočena veza između orijentacije crkava i tačaka izlaska sunca u dane koji su posvećeni njihovim patronima

Sunčani časovnik utvrđenja Hrusija (srpski manastir Hilandar, Sveta Gora)

The paper analyses a 1993 photograph of marble slab taken in front of the entrance to the harbour of the mediaeval fortification Hrusia which dates from 1302, the property of the Serbian monastery Chilandar on Mt. Athos. The slab is now dug under a pile of broken rocks from parts of a demolished wall, and it is inaccessible to direct verification of the assumption that it is 'a kind of sundial'. Based on the analysis it is highly likely that it is an old Greek sundial, which is today in its secondary position. The finding is of importance as it is the first old Greek or Byzantine sundial discovered on the Holy Mountain.U radu je analizirana fotografija iz 1993. godine snimljena ispred ulaza u pristanište srednjovekovnog utvrđenja Hrusija iz 1302. godine, koje pripada srpskom manastiru Hilandar na Svetoj Gori. Ploča je danas zatrpana kamenjem dela obrušenog zida i nedostupna za direktnu proveru pretpostavke da se radi o 'nekoj vrsti sunčanog časovnika'. Nakon posredne analize sa dosta verovatnoće može se pretpostaviti da se radi o starogrčkom sunčanom časovniku koji je danas u sekundarnom položaju. Nalaz je značajan zbog toga što je to prvi starogrčki ili vizantijski sunčani časovnik pronađen na Svetoj Gori