Re-Reading the Arithmetic and Geometric Features of the Inner Courtyard Facades of Historical Houses Attributed to The Last 4 Centuries of The Introverted City of Isfahan

Historic houses are among the valuable architectural monuments of Iran. One of the main problems in realizing the design of the historical houses is to identify the arithmetic features of the plan and their interior court-yard façade.  appearance, correctly by analyzing the geometric and arithmetic proportions, the arrangement of openings, entrances, axes, the transfer of the geometric system of the plan to the facade can reveal the characteristic features of historic houses. It is necessary to know the position of these two components, the interior plans of the historical houses of Isfahan. According to the mentioned goal, we try to address two general questions in this regard. Extensive research has been done in the field of geometry and interior design of houses, but the geometric arithmetic role of the article throughout history has been mentioned to a limited extent. This article tries to arithmetically identify the geometric components of house facades. Analysis of geometric systems in facade components is a topic for further research. The present article examined the general systems and structures in the formation of the Isfahan indexes, as well as the proportions and shapes that gave rise to these systems. The approach of the research is geometric and arithmetic analysis. The data collection is based on field studies and mainly impressions obtained by comparing the geometric features of these facades. In the study of the geometric system of the facades of houses, in the rhythm of the arrangement of the openings, there are numbers 3, 5, 7, which these repetitive arithmetic properties have affected the shape characteristics of the facade length. Mainly, the horizontal axes in these facades of various historical houses in Isfahan were four or more and the number of their vertical axes was four. The division system was mainly such that the input was on the right and left; In the middle, there was a sash frame and in houses whose vertical axis is more than four, the division system is mainly such that the sash is in the middle, the two sides of the sash are in; And next to the door; There is also a sash or several doors. In traditional houses, the greater the number of vertical axes, the number of entrance doors, several doors and the number of sash shafts. The data analysis revealed; Frames have the same number of divisions in each floor and the framing in the middle opening is larger than the other openings. The research results indicated that the facade geometric results from the proportions of the dimensions and surfaces of the openings, their locations affected by the geometric of the facade which have led to the information of meaningful repetitive ratios in the facade. Although these systems may have changed throughout the history of historical homes, they have persisted until recent decades and could be used by architects as a set of indicators to design similar items in the future.