Anatolian Seljuk architecture was strongly influenced by a fusion of Islamic, Persian, and Byzantine cultures, complemented by the region’s unique historical, cultural, political, and religious context. The buildings from this era are remarkable, particularly due to their simple and introverted architectural designs. The buildings were constructed as plain and unembellished structures but were enhanced with elaborate entrances throughout the early Seljuk eras. The architectural features of the period are asymmetrical plans, courtyards and iwans, decorations, and buildings composed of more than one function. The Anatolian Seljuk Period is characterized by numerous examples of combined-function buildings. These examples may serve several functions, such as madrasah-mosque, mosque-tomb, mosque-mosque, and mosque-madrasah-tomb. Combined-function buildings hold a significant place in architectural history, as they are considered to represent the earliest examples of social complexes that influenced the development of similar structures in the following centuries. These buildings, which served multiple purposes, such as religious, educational, and social gathering places, laid the groundwork for the design and functionality of future social complexes. Their innovative approach to combining different functions within a single building highlighted an advanced understanding of architecture’s role in societal development and community life. In these multifunctional buildings, depending on the specific needs of the time or location, two or three distinct functions were integrated into a single building. Despite the combination of various functions, the relationship between them could either be unplanned, as observed in the Madrasah-Darüşşifa (educational institution-hospital) buildings, or it could evolve naturally, as seen with mosque-tomb complexes. This versatility in function and the varying degrees of integration between different spaces reflect the adaptive and innovative approaches to architecture during that period. Research efforts have focused on identifying the construction periods of combined-function buildings as well as establishing a typological classification for these buildings. Studies on geometric analysis, however, have typically concentrated on Seljuk patterns. A limited amount of research employs the geometric analysis method to examine buildings that provide several functions. The studies use the geometric analysis approach to examine the mass relationship between the hospital and the mosque in Divriği Grand Mosque and Hospital. These researches have indicated that particular guidelines might have been applied when combining various functions. Analyzing the mass relationship is crucial for understanding the history of architecture because no source indicates whether the mass combinations in Seljuk architecture are regular or irregular. This study’s research issue focuses on determining if the relationship among diverse functional masses, which together form combined functional buildings, adheres to specific geometric and proportional rules. The objective of conducting geometric analysis on the plans and sections of Anatolian Seljuk buildings, which serve multiple functions, was to identify the proportions and principles guiding the arrangement of various functional masses. 

The module system, special triangle analysis (3-4-5 triangle, 30-60-90 degree triangle, or equilateral triangle), and application of the golden ratio have been used to analyze combined-function Anatolian Seljuk buildings. 

Module: These are units with fixed dimensions where an element repeats, either increasing or decreasing, by itself or through its multiples. Previous researches have established that the Anatolian Seljuk Period did not have precise module measurements. Thus, only modularity was proportionately investigated in these researches.

Special Triangles: This kind of analysis investigates how equilateral and special (Pythagorean) triangles are used on drawings. The two triangle types most frequently employed in structural design are the right-angled isosceles triangle and the equilateral triangle, whose height is equal to the side of the square. The impact of special triangles on the forms or proportions of sections or facades will be examined in this study.

The golden ratio: The formula (x+y) /x = x/y expresses the golden ratio. The golden ratio is obtained by splitting a line segment into two pieces so that the ratio of the long segment (x) to the total component (x+y) equals the ratio of the short segment (y) to the long segment (x). The study’s goal is to identify the alignments defined by the golden rectangle, which was created using the golden ratio rule as a guide.

This study examined the plans and sections of seven combined-function buildings. This approach considers two sorts of functions when they come together: functions, such as mosque-tomb functions, and consciously created functions, such as Madrasah-Hospital functions. Within this framework, the emphasis lies on three instances of buildings that possess two primary functions that are interconnected, as well as four instances of buildings that have a tomb annexed to the main use. The designs and sections of the madrasah-tomb and mosque-tomb buildings were first studied in the analytical studies. Next, buildings that combine larger masses, like the madrasah-hospital and mosque-madrasah, were examined. Results of geometric analysis can thus be compared based on mass size, number, and function type. Çay Taş Madrasah, Beyşehir Eşrefoğlu Mosque, and Tomb, Amasya Burmalı Minare Mosque and Tomb, and Amasya Gök Medrese Mosque and Tomb were chosen for the first analysis group, where the tomb is integrated into the main purpose. The second analysis group buildings are the Divriği Grand Mosque and Hospital, the Kayseri Huand Hatun Social Complex, the Kayseri Gıyasiye Madrasah, and the Gevher Nesibe Hospital. Plans and sections of the buildings have been drawn using surveys of the buildings to illustrate their form and the interactions between the masses. Analyses were done on the drawings in the computer environment. It examined the usage of the modular system, special triangle, and golden ratio on the drawings. The investigations led to the determination of proportional and formal relationships between various functional masses, the golden ratio in plans, and corresponding triangles in sections. The dimensions of the portals and the positions and proportions of the tombs are determined by the golden rectangle in the plans of buildings where a tomb is connected to a main function, such as the mosque-tomb and madrasah-tomb. 

Golden rectangles on all façades have been noted to determine the exact positions and dimensions of the tombs in Amasya Gök Madrasah, Amasya Burmalı Minare Mosque, and Çay Taş Madrasah. Only the proportions of the northeastern façade of Beyşehir Eşrefoğlu Mosque’s tomb were accessible. The golden rectangle at Amasya Gök Madrasah determines the dimensions of the dome-covered naves within the building and the tower and portal located on the north façade.

The golden rectangle in Amasya Burmalı Minare Mosque exhibits identical dimensions for both the tomb’s interior space and the area in front of the mihrab. The dimensions and proportions of the tomb at Çay Taş Madrasah, including the size, position, wall thickness, and entrance width of the main iwan and the adjacent domed classrooms, were determined using the golden rectangle.

Golden rectangles establish the proportional connection between different masses on long façades in architectural plans that examine the two main functions (madrasah-mosque, şifahane-madrasah). The dimensions of the golden rectangles that determine the proportions of Kayseri Gıyasiye Madrasah, Gevher Nesibe Hospital, Divriği Ulu Mosque, and Hospital are the same. While the dimensions of the portals in both buildings are identified by the golden rectangles, no information is given about the sizes of the tombs.

The dimensions of the mosque portal and the proportional connection between the madrasah and mosque buildings were determined using the golden rectangle in the Kayseri Huand (Hunat) Hatun Complex. The analysis does not provide any details concerning the tomb situated within the mosque.

The findings demonstrate that the golden ratio had a crucial role in the design of multifunctional buildings in the Anatolian Seljuk Period. The golden rectangle on the plan indicates the position of a tomb combined with a main building. The study did not provide any information about the positions and sizes of the tombs that were combined with two main buildings. Modular systems, golden rectangles, and special triangles were used in the sections. Even though the golden square shows the inner sizes of the tomb and the naves of the Amasya Burmalı Minare Mosque, it does not how the tomb and mosque masses should be proportioned. A golden ratio can be used to show the relation between the height of the cone and the tomb wall, and the position of the dome springing line.

In Amasya Gök Madrasah, the golden ratio between the dome and the cone was found. The equal-length triangles identify the cone’s height and shape, as well as the proportions of the spaces of the harim. The 2:3 ratio was used for the tomb’s mass and the harim’s inner areas. Modules, special triangles, and golden rectangles were also seen in Taş Madrasah and Beyşehir Eşrefoğlu Mosque. It shows the dimensions of the tomb in Beyşehir Eşrefoğlu Mosque and the relation of the harim and the maksure dome. In the Kayseri Huand Hatun Social Complex, the proportions of the dome and the tomb cone were identified by golden squares that were all the same size. The same 5-12-13 triangle identifies the division of the mosque vaults and the dome in front of the mihrab. The madrasah’s iwan and the harim’s dome are the same size when measured by the equilateral triangle. 

The golden rectangle at the Divriği Grand Mosque and Hospital sets the right height for the Hospital and the tomb, as well as the dome’s measurements in front of the mihrab. Equal-sided triangles shape the cones on the roof. The 8-5-17 triangle shows how high the lantern is on the dome, and the 5-12-13 triangle shows how the naves are arranged next to each other. 

The study’s results were evaluated based on parameters such as number of functions and mass size. Based on the plan, the golden ratio was essential when designing combined-function buildings during the Anatolian Seljuk Period. The golden rectangle shows the ratios of the two main masses in a building with two primary functions and a tomb, but it fails to demonstrate a relationship with the tomb’s plan. This shows that Anatolian Seljuk builders and designers intentionally used the golden ratio in their plans. The golden rectangle established the ratios between the various masses in the architectural layout of each building. Nevertheless, the outcomes of the cross-sectional analysis varied for each building. The data on proportional relationships for the sections was obtained from the modular system or golden rectangles. Conversely, the information regarding the formal connections between the masses was derived from special triangles. When a building serves two main functions, one of which is as a mosque, it is possible to identify the relative relationships between different masses within the building. However, if a building served as both a madrasah and a hospital, 

there was no connection between the two masses. The modular system determines the internal dimensions of architectural components, such as roofs and vaults, rather than how the masses are interconnected. The ratio of 2:3 does not accurately represent the proportional relationship between masses. It can be used to indicate the relative size of the cone compared to the main building in specific examples, such as the Amasya Gök Madrasah, Divriği Ulu Mosque, and Hospital. Special triangles were primarily utilized to determine the shapes of structural components such as cones and domes. The sizes of the domes and cones of the Amasya Burmalı Minaret, the Amasya Gök Madrasah, and the Kayseri Huand Hatun Social Complex were determined using similar triangles in their sections. No existing research has examined the impact of special triangles on the architectural design of Anatolian Seljuk buildings. Geometric proportions and features are commonly used in buildings with structural elements such as cones to maintain formal and proportionate relationships. The study reveals that it is crucial to consider geometric and proportional relationships when designing contemporary additions for historically significant buildings or surroundings. The research contributes to the conservation of historic buildings and provides essential insights into using geometry in architectural design within architectural history. This study has made a significant theoretical and practical contribution to the combined function buildings of the Anatolian Seljuk Period. The results indicate that Seljuk architecture keenly understands aesthetics and design.

A constraint that extends the duration of the study is the difficulty in locating survey drawings of the buildings and then digitizing them. Therefore, the progress of these scientific inquiries relies on recording historical buildings and establishing and sharing a digital archive. Research will be done to analyze the social complexes and combined-function buildings built during and after the Anatolian Seljuk era. Periodic similarities and divergences in design choices can be identified using this approach.