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In this article, Mehmet Vâsıf and his analytical geometry book, Hendese-i Halliyye-Musattaha and Kutû'-i Mahrûtiye were examined. Since this book is one of the first books written in its field in the Ottoman language, it has great importance for the Turkish history of mathematics and mathematics education. Mehmet Vâsıf taught mathematics at Mekteb-i Bahriyye between 1901-1908, and he taught geography at Tüccar Kaptan Mektebi Umûmî. He compiled many works in various fields and introduced them into the Ottoman language. In this article, information about Mehmet Vâsıf's life and works is given, and his book on analytical geometry and conic sections, Hendese-i Halliyye-i Musattaha and Kutû'-i Mahrûtiye is introduced. This study's scope includes the transliteration of the table of contents and the book's introduction. Mehmet Vâsıf didn't provide detailed information about his sources. Within the scope of this study, Mehmet Vâsıf's sources were also traced. [ABSTRACT FROM AUTHOR]

Classification of image groups has different applications in remote sensing, photogrammetry, digital painting catalogues and security related areas. Researchers from remote sensing, computer vision and photogrammetry have used different approaches based on image features (color, textures, object shapes) in order to develop robust classification methods. In this study, classification of viewpoint independent image groups is developed based on the principle of invariant properties of conic sections under projective transformation. At the beginning of this study a data set is created for testing the method. This dataset consists of nine categories of images, for each category ten images used that are taken from different viewpoints. Edge detection is applied on each image to detect boundary of objects in images. Detected edges are used for conic fitting so that each conic will be represented as a set of conic sections. Under projective transformation conic sections remain as conic section even if their shapes change. For each image in the dataset an invariant signature is computed using set of conic sections. It is assumed that there is similarity between invariant signatures of images belong to the same image category. These invariant signatures are used in histogram form for visual representation and computations. Since invariant signatures are high dimensional data, Support Vector Machines which is a stochastic pattern recognition algorithm is used instead of classical deterministic methods. Performance of classification is evaluated using ROC (Receiver Operating Characteristics) analysis. [ABSTRACT FROM AUTHOR]

The article discusses mathematician Archimedes' quadrature of the parabola. In the quadrature of the parabola he found the area of the region bounded by a parabola and a chord. Archimedes' method involved filling the region with infinitely many triangles each of whose area he could calculate and then to evaluate the infinite sum. A parabolic segment consists of the region bounded by a parabola and the line segment joining two of its points B' and B. The motion of a particle in a uniform gravitational field is used to study the properties of the parabolic curve. Archimedes' Theorem states that the area of a parabolic segment is 4/3 the area of its Archimedean triangle. It was assumed that the infinity of smaller and smaller triangles fill the parabolic segment.