A Study of GEOMETRY in Islamic Architecture by Professor Golroo Najibaaghlou is a valuable work in the field of Islamic architecture. This book has a detailed preface, a brief introduction, and five main sections. As it is known from the introduction of the book, this book was originally written for a non-Iranian audience. The first purpose of writing this book is to try to moderate public belief about GEOMETRY and the stages of compilation and discussion in Islamic architecture. Another purpose is to correct the negative view of the geometric documentation of Islamic architecture in the West, because such a view has created a kind of reluctance to equate the works of Islamic architecture with the great works of classical Western architecture. In addition, Najibaaghlou wants to reject and respond to Western criticism that reduces Islamic architecture to the level of an unedited work. In the final chapter of the book, Najibaaghlou looks at the compiled documents of Islamic architecture from a Western perspective and highlights some of the missed points of geometric sciences, including clarifying conceptualization, recording, and transferring architectural design in the Islamic world.

The main purpose of the article, as the topic itself shows, is defining an eternal GEOMETRY(as a basic foundation and unavoidable structure)for the Islamic architecture. Therefore, as an abstract of this article, (giving a short but conclusive definition of the main subject),and in order to avoid from some possible misunderstandings in the mentioned subjects and meanings in the article, the following points seems to be useful:A. The referring meaning of the word "GEOMETRY" (or its Arabic synonym "Hindiseh") by the author in this (article) is completely different from the common meaning of it in architecture (or the Euclidian GEOMETRY) and its closed and limitful field of rules of some mathematical meanings and physical shapes and forms. But by the phrase "Hindiseh Jaavidan" or "Eternal GEOMETRY" the author means the Unique, Wholistic and Comprehensive Truth, which according to the Quranic literature, is known by some Arabic terms such as "qadr", "taqdeer" and "muqaddir", "muqaddar", "qadeer", and so on. The meaning which points to the comprehensive and wholistic system of rules governing all various systems of measurement essential for the whole universe and its every individual parts's or thing's coming into existence (in their both physical being and meaningful identity).B. According to the above mentioned description, the referring meaning of the phrase "Natural GEOMETRY" (or "Hindisi-yi Tabee 'at" or "Taqdeer") by the author in this article can be imagined as a symbolic light through which everything in the universe become visible, readable and understandable for every other thing in the whole cosmos of varieties and multiplicities (in both qualitative and quantitative groups of limits and measures). The limits and measures without which everything's essential mutual relation and harmonic suitable cooperative sharing life with every other thing in the world seems to become impossible.C. Then, in a similar symbolic structure, the other important meaning of "GEOMETRY" or "Hindisih" to which the author is going to point to is "The Essential GEOMETRY" or "Hindisik-yt Dhaatee". According to the Holy Quran, for every possible matter of being in the physical world, there is a limitless, unchangeable, eternal specific and determined Truth in The Presence of God which, as same as all other Truthful Meanings in such a Sacred Presence is free from all limits essential for the material world such as: matter, physical shape and form, length, width, thickness, color and other similar limits.D. And at last, the author's purposed meaning of the subject of "Islamic Architecture" in this article, is an orderly and unitary structure which in its both whole and parts, and in its both physical structure and meaningful identity obey the One Divine System of Rules named Islam. And, at last, by the word of "Islam" means the universal governing order of both physical and spiritual worlds.

The GEOMETRY of imagination and thought are important tools to acquire knowledge. Human beings have always deployed these two significant tools to get an understanding of the macrocosm and microcosm. These two factors have been incorporated and well utilized to achieve a proper appreciation of these profound entities. This essay engages the strong links between knowledge and art by nature and struchire. There are samples of Hafiz poetry to the demonstrates the marriage of thoughts and the geometr-v of imagination as well to depict the mathematical relationship between their thought patterns.

In this paper, we considered cosmological constant as a variable and studied properties and the thermodynamics stability of BTZ black hole from a geometric perspective. Also, we examined the correspondence between thermodynamic curvature singularities and phase transitionpoints with different thermodynamic metrics. We found that theQuevedo metric cannot predict the phase transition points in two ensembles. This result is also valid for the kerr-de sitter spacetime.

Background: The aim of this study was to investigate vertebral GEOMETRY changes and determine cutoff value of vertebral height to predict fractures.Methods: In a cross-sectional study, 280 postmenopausal women recruited In all subjects bone mineral density and radiography of the lumbar spine performed. Lateral radiographs were evaluated for identification of vertebral fractures, using a validated semiquantitative method. T-score of vertebral height was calculated based on data extracted from Iranian Multicenter Osteoporosis Study. ROC curve used to determine cut off value of vertebral height T-score to predict fractures. Results: The mean of age and BMI were 55.34±8.7 years and 27.73±5 kg/m2, respectively. Among osteoporotic women, 59.8% had one or more vertebral fractures and 23.8% had at least 2 fractures. In fracture group the T-score of spine and femur BMD was lower than the others. The mean of vertebral height in women without fractures was 12.94±0.6 cm, and in the patient with 4 or more fractures was 12.3, thus every fracture accompany with 1.2% decreases in the height of vertebrae.The prevalence of vertebral fracture in osteoporotic patients was 71.4% and in healthy cases 39.5%. Better estimation of vertebral height T score in ROC curve was less than -0.7.The sensitivity and specificity of the cut off value were 81.3% and 52.9%, respectively.Conclusion: Vertebral fractures are common fractures in postmenopausal women. There was a correlation between vertebral height and fractures. Vertebral geometric parameters especially height T score can be used for fracture screening.

Let y"=f(x,y,y') be a 2nd order ODE. By Cartan equivalence method, we will study the local equivalence problem under the transformations group of time-fixed coordinates. We are going to solve this problem by an applicable method which has been recognized by R. Gardner, and classify them.