هندسه

Proportion is a key feature of Iranian-Islamic architecture. It is essential for the cohesion and unity of different sections of a building, contributing to its stability, visual aesthetics, and harmony. The application of proportions in individual architectural elements is vital, and these proportions are often found across multiple buildings, even those with different functions. This study focuses on analyzing the proportional relationships between the length of courtyards, the height of minarets, the height of iwans (vaulted halls), and the height of surrounding chambers in mosques, schools, and mosque-schools of the Qajar period in Tehran. The central question of this research is: How do the geometric and proportional relationships of one building manifest in others, even with different functional purposes? The proportions of each type of building have been recorded and analyzed in separate tables, and the results show that mosque-school architecture incorporates proportions from both mosques and schools of the period. Moreover, the functions of mosques and schools are integrated within mosque-schools, demonstrating a consistent architectural harmony among their components.

The research results show that students face many challenges and difficulties in learning geometry, and many of these difficulties appear in solving geometric problems, especially problems that require the use of geometrical figures. To improve students' performance in solving geometric problems, it is necessary to study related theories. One of the theories presented to describe students' understanding of geometrical figures is the theory of figural apprehension. In this theory, the correct use of geometrical figures in solving problems requires perceptual, sequential, discursive, and operative apprehensions, whose strengthening improves geometry learning and fosters mathematical creativity. The current study aims to investigate the tenth grade mathematics students’ apprehensions of geometrical figures and also to examine the problems of the geometry textbook of this grade to compare the students' apprehensions with the content presented to them. Also, some of the students’ common mistakes in response to geometry problems are pointed out. Research Questions: How able are the 10th grade male and female mathematics students to solve geometric problems corresponding to each type of apprehension and what mistakes do they make while solving geometric problems? 2- To what extent do the 10th grade students' apprehension of geometrical figures correspond to the problems of the geometry textbook of this grade?

According to the research questions, the research process consists of two phases. In the first phase, the students' apprehensions of geometrical figures and their mistakes were investigated by survey method. The statistical population was male and female 10th grade mathematics students in Pakdasht city, and 235 of them were selected by cluster random method as the sample. To collect the data for this phase of the research, a descriptive test including eight problems was used. For its validation, face and content qualitative validity were examined. To check the reliability of the research test, first, the students' responses were assigned to three parts: correct, incomplete, and incorrect or no response, then scored and Cronbach's alpha coefficient was calculated. Descriptive statistics were used to analyze the data. In the second phase of the research, the content analysis method was used to examine the 10th grade geometry textbook. The statistical population was all the problems of the 10th grade geometry textbook published in 2023. The sample and the population size were considered the same. To analyze the textbook, first, all the problems were classified based on the four apprehensions. Content analysis forms were used, whose qualitative face and content validity were confirmed by several mathematics and geometry experts. To check the reliability of the data collection instrument to analyze the content of the book, one of the chapters of the 10th grade geometry textbook (the third chapter) was randomly selected and its problems were coded by two coders who were familiar with the research subject. Then the Holsti reliability coefficient was calculated and the value was 0.76.

According to the frequency of the students' responses to the test, the highest number of incorrect or no responses were related to discursive and operative problems, and there was no significant difference between the performance of girls and boys. Regarding the students' mistakes, the results show that many students are unable to recognize geometrical figures, draw them correctly by drawing instruments, make logical reasoning to justify geometric claims and make appropriate changes to the geometrical figures to find the solution to the problems. The results of the content analysis of the 10th grade geometry textbook also revealed that more than half of the problems in this book require discursive and operative apprehensions.

In the process of teaching and learning geometry, it is necessary to focus on all four apprehensions introduced in the theory of figural apprehension. In the present study, the 10th grade students' apprehensions and the geometry textbook have been investigated based on the theory of figural apprehension. The results of the present study indicated that in response to discursive and operative problems, the percentage of incorrect and no responses is more than the perceptual and sequential problems. On the other hand, the results of the content analysis of the 10th grade geometry textbook showed that solving more than half of the problems in this book requires discursive and operative apprehensions. Therefore, students' apprehension and the content presented to them in the textbook do not match. Also, the results of this research revealed some of the students' mistakes in response to geometric problems. The reason for these mistakes seems to be misunderstanding the concepts and characteristics of geometrical figures, relying on mere intuition, considering special situations in the process of proving, and sometimes considering geometrical claims as obvious without any need to be proved, etc. If teachers and professors get familiar with this theory, they can learn about the causes of the students’ common mistakes in solving geometric problems and its link to the four apprehensions. Also, they can organize teaching steps regarding the students’ weak points. The results of such research can also help textbook authors and educational planners to reform educational policies.

Globalization and the new world order is a complex process with ups and downs that has continued to evolve over time and has become the most common concepts of humanities in the focus of researchers in various fields today. The limitation of the world order to time and the formation of its different periods with a short history are caused by the lack of morality, the lack of global consensus on the concept of the new order, the lack of adherence to commitments, etc. So far, the new world order has often used war and military power in the path of evolution to achieve its goals, and it was successful in the economic dimension and international relations at first, but it is gradually trying to penetrate other dimensions by using information technology while expanding military power. to do The emergence of social networks as a key component with the capability of two-way communication and reality over time will take over the soft power of the new world order. In this period of history, the world order is ready to form a new structure based on evolution, dynamics and various components. Iran, after the Islamic revolution, by changing its symbols and strategies for the new world order, due to having outstanding characteristics such as intelligent and talented human resources, sensitive and privileged geographical location, high governmental and civilizational logic, etc., can occupy a prominent position. provide for himself in the new world order and stabilize it in the following periods.

Visual works are suitable platforms for the emergence of the most profound human thoughts, including mythological thoughts, and in every period and geography, its emergence can be traced in these works. Studying and reading these works, in a methodical way, can reveal the truths that are hidden behind the visual elements. Mounir Farmanfarmaian has presented a new expression and content by emphasizing the function of mirrors. The current research has analyzed five works of this artist that were created in a period of ten years, using the descriptive analytical method and the use of the myth analysis method. The findings show that the mirror as a work material and the use of sacred geometry with its architectural origin in the field of pop or conceptual art in the symbology stage, indicates unity while plurality, wisdom, and shapes such as labyrinth, square, hexagon and the like are a symbol of femininity. In the psychometric stage, the impressionability of the vague images in Shahcheragh mirrors as well as handwoven and other Iranian handicrafts and their integration with contemporary art is shown, and in the mythometric stage, the myth of Simorgh is the dominant myth in his works in such a way that the geometric reflection of the image In each work, a person has created a new knowledge of the concept of unity and plurality in the minds and presents the epistemological intuition of the "real me" to the audience.

The thoughts and ideas of artists and craftsmen, according to the way they perceive the manifestations of the world, are preserved in the form of works of visual arts, architecture and decorative crafts which are exhibited, as souvenirs of culture human. Aesthetics and art sciences introduce these works according to the change and transformation of human experiences, thus the precision and elegance “creativity” of artists throughout history, cultural value, dignity and validity of works of art are measured and determined. Today, given the new dimensions that have changed with technological progress and the production of new technical tools, the way of seeing the world and material effects has transformed and led to the creation of works of art more detailed and more complete. Paying more attention to (space) and creating new precise and comprehensive artistic dimensions is considered one of the modern achievements. The characteristics of design and creation of forms, which occupied the artist’s mind throughout the ages to see the world better and create better especially when he used “geometry”, he went through the exact terms of the world of senses and reason. Recently, some artists have paid special attention to the new common branch between mathematics, geometry and art called fractal geometry, which provides information about the common secret and harmony of the universe. Among them, modern architects and visual arts have created significant works in this regard.

Using different methods and techniques to achieve the best results and create synergies between them can be helpful in many issues. Educational data mining is one of the relatively new fields that can be used to solve educational problems, especially problems in the field of measurement. But before using these methods, it should be as familiar as possible and its problems, disadvantages and advantages should be examined. In this study, the aim is to investigate the technique of nonnegative matrix factorizations and how to determine the number of clusters before implementing the model. The research method is descriptive and the study population is all those present at the entrance exam for mathematics and technical sciences in 1398, of which 5,000 people were randomly selected by the country's assessment and education organization and provided to the researcher. The research tool is math questions and entrance exam geometry. The results of this analysis showed that there is a difference in estimating the number of clusters of math questions, but in the case of geometry questions, the results of all methods were the same. Due to the observed differences, it is suggested that in future research with the help of data simulation, this issue will be examined in more detail.

Input and its effects on the human psyche are among the topics of interest in the field of architectural research. Some of these studies refer to the subject of its geometric principles, which generally refer to mathematical proportions and relationships between components. But in this study, the aim is to consider the geometry and method of input form regulation from the perspective of environmental psychology and how it is perceived. In other words, the main question of this research is to address the components and principles that are considered in spatial geometry to achieve the desired goals in their design. For this purpose, according to the characteristics of traditional architecture and the capabilities that are generally mentioned for it, in the present study, a study was used on the entrance entrances of traditional houses in Mashhad.Based on this, first, by finding important characteristics in the effects of environmental geometry on the human psyche from the perspective of three theories in the field of environmental psychology, namely adaptive and exchange psychology, behavioral psychology and Gestalt psychology, the desired components in the study of samples Came. Then, by analyzing these cases, the results were discussed as a whole, which summarizes the results of the research. According to the findings of this study, privacy, avoidance of complexity, beauty away from many details and harmony with the surrounding texture are among the principles considered in the geometric design of the entrance of traditional houses in Mashhad.

The book “Symmetries of Islamic Geometric Patterns” written by Seyed Jan Abbas and Amer Shaker Salman has been translated into Persian by Amene Agharabi. Due to the authors' mastery of mathematics, the book has a different approach to other works in the field of Islamic patterns, which has made it attractive and useful for both researchers in the field of Islamic art and mathematical sciences, but its topics and points cannot be understood in its Persian translation. According to the main text of the book, it seems the lack of understanding of concepts is related to the quality of translation. Therefore, the present critique is about the Persian translation of this book. In order to evaluate this translation, the entire English text of the book was adapted to the translated text. Cases were criticized in 6 categories; 1) Incorrect translation, 2) Untranslated words and phrases, 3) Multiple translations for one word and multiple words with one translation, 4) Reverse translation, 5) Changes in the sentences and paragraphs of the original text, and 6) Selection of unfamiliar equivalent. The existence of serious and many problems in Persian translation has caused the text to be incomprehensible and as a result, the reader has been deprived of a different and valuable points of view of this book which are vital issues. Finally, the book needs serious revision in translation.

Scientific works constitute an important part of the collection of historical writings of Iran. Mathematical and arithmetic sciences have been among the sciences of interest to Iranian scientists. Examining mathematical manuscripts and arithmetic and geometry in terms of identifying the history of science, using their contents to establish new knowledge, as well as finding out the literary and linguistic features of the period in which it was written. Are of particular importance. Therefore, reviewing and correcting such manuscripts, even if they are not in the category of literary and scientific works, can be a priority for researchers and proofreaders active in this field. The treatise on arithmetic is one of the ninth and tenth century writings in the field of mathematics, arithmetic and geometry. The author of this work is Mir Mohammad Ghasem Asir Varamini (Isfahani). This book was written in Baghdad and the author is the same author. The date of its writing, according to the author and its scribe, dates back to 900 AH. This work consists of an introduction and a conclusion, as well as three articles, each of which is divided into different chapters. In this research, the most important features of the thesis book are written along with the introduction of its manuscript and finally the version is examined from a content point of view.

This study investigates the suburban caravanserais on the plateaus of Iran in terms of geometry and spatial structure in the three periods of Seljuk, Safavid and Qajar, which are the most active Islamic periods in the construction of such buildings. The present study also attempts to find the position of Khorasan plain caravanserais in this area. The process in this study includes the selection of caravanserais and characteristics, their classification and analysis, and achieving a conclusion. In this research, researchers, utilizing library studies and existing documents including specific sources and general histories, travelogues and recent research on caravanserais based on argument and using purposeful sampling method (non-probable), examined more than fifty samples of caravanserais. After reviewing the caravanserais and classifying them in terms of the historical period, geographical location, geometry and dimensions, the caravanserais were compared and analyzed. Examining the suburban caravanserais geometrically, it is clear that most of them have a square or rectangular plan, and some of them have taken on octagonal or circular shapes due to the provision of solutions. Meanwhile, Khorasan caravanserais such as Robat Sharaf, Robat Mahi and Robat Zafaranieh have often used quadrilateral geometries and four-porch patterns. The results demonstrated that the spatial structure of the caravanserais is sometimes mixed with non-service functions, and this issue can be clearly viewed in Robat Sharaf Khorasan, which has two prayer halls and two courtyards. The results also showed that over time and with the development of roads, caravanserais became more spacious, and in this regard, Sabzevar Zafaranieh Caravanserai, which had a reservoir on its southwest side, is an appropriate example.

Geometry is one of the most challenging math courses that has attracted the attention of many math educators from past to present. Understanding geometric figures plays a crucial role in understanding school geometry. Different geometric figures can be seen everywhere in geometry textbooks, and it can be said that recognizing and relating to geometric figures is an important part of the geometry learning process. But research results and teachers' experience show that students face many difficulties in understanding these figures and in understanding figural concepts in general, which is a major obstacle to their geometric reasoning. The purpose of this article, which is done in a library method, is to describe some of these difficulties based on valid research. Many students guess the name of geometric figures only according to their appearance and are not familiar with the main features of each of these figures and rely only on their previous intuitions and experiences in recognizing geometric figures and tend to ignore the definition. Discussions on such topics will raise teachers' awareness of students' learning difficulties, as well as review the process of teaching geometry and improve teaching methods.

The purpose of the present study was to study the level of learning of geometric reasoning in 9th grade students based on Van Hiele -theory in one of the topics of geometry, namely the topic of reasoning and proof in geometry and their properties. This study was conducted by survey method. The statistical population consisted of all 9th grade students of Babol public schools and the sample consisted of 470 people who were selected by random cluster sampling method. The measuring tool was a researcher-made test with 10 questions. The face and content validity of the test was confirmed by a number of mathematics and mathematics education professors as well as by some experienced junior school teachers. Descriptive and inferential statistics (T-test) were used for data analysis. The findings indicate that the dominant level of geometric thinking of the ninth grade students in the field of reasoning is at the first level. Also, boys performed better than girls in first level of Van Hiele. The results of t-test showed that this difference was statistically significant. The findings of this study can be used in reviewing the geometry education process by mathematics teachers, educational policy makers, and textbook authors.

In Islamic architecture, the architect must be face all the issues in architectural design. Create quantitative & qualitative issues by observing the principles & rules of the process. The architect must create the architectural structure with geometry through art & based on theoretical reason. Architecture has numerical & theoretical dimensions, because it is for the human being as a thinking being, it has qualitative dimensions. The architect must pay attention to the quantitative & qualitative dimensions in creating the architectural building. Traditional Iranian architecture has quality dimensions that include the wisdom of philosophers & Islamic thinkers of Iran. These topics are combined with the basics of other topics to work. Islamic architecture is called Islamic because it combines with the principles of Islamic wisdom & philosophy in uses it. In order to underst& Islamic architecture, wisdom must be examined in the process of creating an architectural building. The truth of the function of wisdom in the process of creating an architectural structure is an important issue. Wisdom in the science of architectural geometry can mean Coded truths that include the Coded structure of architecture. The Coded truths in Islamic philosophy are the same as the divine truths. God provides knowledge of divine truths to thoughtful & knowledgeable human beings who seek the truths of the universe. Thoughtful human beings become aware of the divine truths of God to the extent of the power of their intellect & perception. Islamic architecture in the l& of Iran has always used the principles & subjects of geometry in external & internal science. The use of geometry is superficial in maps & decorations & inwardly it is an architectural building in general form & body. The geometry used in the Islamic architecture of Iran has been done by Islamic thinkers, mathematicians & Scientists. Geometry in architecture increases the strength of the architecture & its beauty. Geometry has used wisdom in creating the beauty & function of an architectural building. An architectural structure is successful when human beings can meet their biological & spiritual needs through it. A skilled & professional architect can use all external & internal issues in creating an architectural building with wisdom. Geometry must also consider beauty in creating an architectural building through wisdom. Knowledge of geometry & wisdom is very important in creating an architectural building. Architecture as a traditional profession needs wisdom in geometry. In this article, the subject of geometry has been studied & analyzed from a scientific & artistic point of view. Also in this article, the subject of wisdom in geometry in creating an architectural building has been studied. Wisdom in this article is in the form of theoretical wisdom & practical wisdom. The point is, how does mathematics in geometry combine with artistic & aesthetic subjects? & How to create architecture using wisdom? In the present age there is no connection between the subjects of mathematics which are used rationally & the subject of wisdom. This is also seen in the science & art of architecture today. In the past architecture of Iran, there was a deep connection between mathematics & wisdom. In the past architecture of Iran, the connection between wisdom & mathematics in creating geometry has made the architecture of beautifuly & also its proper functionaly. In the science of wisdom, geometry has a meaning in the form of a code & this code has external & internal meanings & truths. The facts in the codes are not normally recognizable by human beings. The code of geometry is in the structure of the universe & has divine truth. Geometry in this world has a trend towards beauty. Wisdom in science belongs to Islamic philosophy. The meaning of wisdom in Islamic philosophy is knowledge & awareness that has been created through reasoning. Argument arises through deep thought in the human mind.

Methouds & Material:

In this research, the views of Islamic mathematicians in the form of mathematics & wisdom have been studied. Islamic mathematicians include the following.Mohamad Bouzajani; Abu Nasr Farabi; Ibn Sina, Akhavan Al-Safa & Jamshid Kashani. The subject of the research method is to obtain geometry & wisdom from the perspective of mathematics. How to transfer geometry from visual and numerical dimensions to the practical world has been analyzed in this method. The success of riddles in the past must be examined in terms of wisdom and geometry. The research method of writing in mathematics and numerical subjects is deductive. The Grounded theory method has also been used in dealing with historical situations.

In Islamic architecture, geometry has been associated with wisdom. Wisdom in geometry has created a beautiful and functional architectural space and decorations. Geometry in the wisdom of Islamic architecture has a sacred place & has hidden secrets. Wisdom & geometry in architectural building, in addition to creating decorative roles in a general & specific way, has led to the recognition of the divine truth in the hidden layers of architectural construction. Accordingly, geometry in Islamic architecture has caused the symbolic identification of the truth of existence and the display of the hidden world. The geometry inside the architectural building is like a code that must be known. In Iranian Islamic architecture, geometry has been used to be aware of divine knowledge as well as to reveal the hidden truths of the divine world in the external world. Geometry has used wisdom for this issue.

Geometry is hidden in Islamic architecture as a mystery & truth. Geometry in its process shows real tangible subjects along with hidden subjects. Geometry creates awareness of the external & internal codes contained in the architectural building. The geometry of the codes in creating the architectural building in which wisdom plays a role can be identified & informed. In addition to a few topics in Islamic architecture, geometry deals with many qualitative issues. Theoretical wisdom & practical wisdom in understanding the science of geometry can in fact distinguish the outer world and the inner world. Geometry causes the objects that exist in the world of imagination and mentality to become a visible world & human beings can see it with their physical eyes. Geometry creates a logical connection between the external world & the internal world. This logical connection creates a balance between the worlds. Using the balance of geometry, he can distinguish the facts of existence. Geometry in Islamic architecture makes quantities & qualities conscious to man externally & inwardly.

The present article entitled "the role of Khajeh Nasir al-Din Tusi in the development of mathematics and astronomy in the Islamic world" aimed to investigate Khajeh Nasir al-Din's influences on mathematics and astronomy. Maragheh observatory was once considered the most advanced scientific institution in the Eurasian world. His book al-Shakl al-qattā brought about a dramatic change in the field of mathematical sciences, especially geometry. By transforming three-dimensional into two-dimensional geometry, he was able to take fundamental steps in the field of mathematics. According to the findings, it can be said that the most important developments in astronomy before Copernicus was made by Khajeh Nasir. This study hypothesizes that Khajeh's serious criticisms of Greek mathematical and astronomical theories and therefore the emergence of new theories, became the basis for scientific developments in Europe.

Studies conducted in the domain of Iranian architecture are extensive as well as diverse. In these studies, different meanings of geometry are considered, and consequently, a wide variety of orders of Iranian architecture can be identifiable. Extensive studies are conducted on each of these geometrical orders of Iranian architecture. The importance of elaboration on these geometrical orders in comparison to each other is of great importance and considerable. Moreover, it would be able to prevent many of the errors that occurred. Taking into account the mentioned explanations, the underlying theme of this research is that what types of geometrical orders can be recognized among the votes of Iranian architectural research? This research is based on an assumption that geometrical orders of Iranian architecture have various types and levels which are elaborated till today. In this research, the qualitative content analysis method is applied to study the votes of the researcher. Choosing texts for this research and initial coding was based on the targeted selection among texts connected to the network of consistent concepts with geometry (basic concepts) in relation to Iranian architecture. Afterwards, selected texts were classified and named based on the similarities in fields (main topics), and again, these topics are secondly classified and named based on the similarities in fields. The results obtained from the geometrical orders of Iranian architecture include Geometrical orders of Human dimensions, climatic geometrical orders, geometrical orders of organization, aesthetic form geometrical orders and aesthetic arrays geometrical orders. It is noteworthy that these geometrical orders crystalize from the galaxy of Iranian geometrical architecture woven and impartible; therefore the primary goal of their identification is to gain cognition toward individually to shed light on them.

The present research aims to reach the monotheism origin of symbolic language of the patterns and geometric structures resulted from heaven and celestial traditions in the creativity resulted from the creation of Ka'bah [cube-like and sacred temple at Mecca] and the Islamic art and architecture works. The methodology is descriptive – analytic and the method of analysis is deductive by the approach of comparative. To explain Qur'an evidences of the example world and the shape features of drawings and the system of combination dominant on the presentations and volumes of the Islamic art and architecture works based on symbolic beauty dominant on the House of Ka'bah and its centricity in the universe. 1- Of the symbolic implications of Ka'bah is shape of Ka'bah, the best sample and an example of all holy places that has been built on the earth and driven from Bait al Mamoor pattern in the world of example and that pattern of the heaven in the world of celestial world. This points to Quran document of example world. 2-Of monotheism implication of Ka'bah geometry is the secret of square of Ka'bah and Bait al Mamoor and heaven based on fourfold principles of monotheism, purifying, praising God, glorification, eulogy. 3-Of the reasons of symbolic beauty in the Islamic art and architecture is personal motivations pallor, manifestation of inner of the sensitive world in the evident figure of example world and presence of coherent and style during continuous periods of Islamic world. 4-monotheism implications of geometry dominant on the arrays and the system of combination of the Islamic art and architecture, manifestation of  figures of geometry purifying in the geometry arrays and islimi and Khatayi drawings and making unity through presence of quality geometry based on the principle of centrality and general structure of the work considering necessary proportions and principles and regulations accompanied by adapted and supplemented elements and organizing the space centrism and bond between form and space by several ways of spatial axis, considering symmetry principle and make the space fluid by keeping the independence of several sections of the building.

In this article, understanding of Iranian architecture can be considered as art and mathematics, but unfortunately less to study architecture, the mathematical components of these elements have been analyzed in terms of art. Karbandy or Ribbed Vault consisting of curves with arches geometric rules specified under the original cover intersect and appear to pose is a covering structure. Another definition of Karbandy is a simple circular motion from the rafters in the form of a circle. In the 3rd century A.H., the Mosque of Shiraz (262 A.H.) in case we find that although the Karbandy no more corners of interpretation (which is to give the dome on it there) but its form, like complete “Karbandy”, and in fact, an introduction to the beginning Karbandy. Also, we can see a full example of Karbandy in dome of Nain Mosque in the 4rd century as well as an example of “Barber” and create of the main cover. Karbandy cases is named as Karbandy in bedchamber of the eastern dome of Nizam al-Mulk Mosque in the fifth century, after that in the 6rd century it is easily seen under the dome of the “Chehel Dokhtaran” building and dome of Sheikh Junaid at the Turan Posht village of Yazd. From the 7rd century hitherto now, Karbandy gradually was used in conjunction with the creation of architectural space as independent of sturcture. Unfortunately, the oldest written document about Karbandy being a draw on the scrolls belonged to the architecture texts of Akbar Mirza Qajar. The use of mathematics as an international language and understandable for everyone is the best way to reach a common cognition of the Karbandy. The studies show that regarding to the perfectly grammatical and legal nature of Karbandy, the mathematics can provide a complete base for reading it. This research can be considered as an objective and applied research that is done on studying the data collections gathered from written methods in the books, library-based manner and reviewing the cases that had not been registered. The research method is a descriptive, analytical and logical reasoning. Regarding to the several parameters of Karbandy, they can be separated into its components that a mathematical model was presented for each factor. After reviewing the material presented in the analysis, they show a mathematical model of simple Karbandy examined there and it was found that their formula replaces all types. This research shows that four factors is contributed to the formulate and model Karbandys. Their factors include N (sides Karbandy), D (distance connection), θ (vertical or non-vertical) and background factors (C1, C2, ..., Cm). There are other factors but these four factors are important that can help formulating and mathematical modeling th all of Simple Karbandys. Generally, we have two main methods for drawing Karbandy listed below: The Method of Pirnia and Manner of Sherbaf. In the method of Pirnia is shown that for drawing the circle, first, the circle should be divided, then it is splitted in connecting points, and finally it should be done on the the field. In the manner of Sherbaf, it is performed by drawing it on the access point. Therefore, on the base of every drawing, Karbandy is different and varied. Numerous examples of outlining the methods provided in the nodes and Karbandy to follow the outline of the presentation will be avoided in this abstract.