It has long been recognized that learning content is very useful for developing the intellectual and creative abilities of children. Modern teaching requires dynamic, diverse teaching and its adaptability to the abilities of each individual student. This implies a skillful combination of modern teaching materials, methods, forms and the choice of teaching form in each lesson. In that context, motivational games in the class have a special function. It is common knowledge of every teacher that students in classes need to be encouraged towards full engagement of cognitive abilities. This is not always easy to achieve. In every class, psychological preparation (application) is necessary to mobilize students' attention in the shortest possible period of time, prepare them for cognitive activities, whether it is preparation for the processing of new teaching contents, doing exercises or repeating old material. In all this, well selected motivational games can play a significant role. With engagement of cognitive process in solving such tasks, students can find successful solutions in a short time, and success is the best motive for further work in class.

Abstract In this chapter, we present a new method of steganography using decomposition of Catalan numbers. The proposed steganographic method consists of two segments: the first segment refers to the process of embedding data and generation of a complex stego key, whereas the second segment refers to the process of extracting a hidden message based on the generated stego key. Both segments consist of several phases. The proposed method provides that the data carrier retains its original shape. At the end of the chapter, security testing and steganalysis of the proposed method are conducted. Implementation in Java programming language successfully proves the work of the proposed method.

: This paper presents the authentication method using the Delaunay triangulation incremental algorithm and the Catalan objects. The proposed method is a combination of computational geometry and cryptography. This method presents a new step towards encoding the triangle coordinates using the Catalan-key. We provided specific suggestions for the application of this method in the authentication for bank clients by the image encryption. Client authentication verification is performed by asking the client to enter the (x,y) coordinate values of randomly selected indices of an array. If the entered coordinates match the index values in the banking system array, then the transaction or other operation is approved. If the matching fails, it means that we have an unidentified person who has followed the whole process and wants to break into the banking system. There are many advantages arising from a scenario for the user authentication by the assigned Catalan object and the stack permutation method. Also, we provided concrete examples for the Delaunay encryption of image with an authentication scenario and experimental results for the proposed method.

Abstract This paper presents a new method of data hiding using Catalan numbers and Dyck words. The proposed steganographic solution belongs to the category of techniques based on the key generating process, rather than steganographic techniques such as injecting or substituting bits. The complex stego key consists of three sets of values that provide the technique of a hidden message generation completely. Hidden message is generated based on the data carrier and an adequate complex stego key. An important characteristic of the proposed method is that the data carrier retains its original shape, without supplements or modifications. Proposed method is explained in detail through the general scenario and through concrete examples. State of the art steganographic analysis of the proposed solution is presented in this paper, as well as possible suggestions for application in business information systems, authentication and distribution of secret cryptographic keys.

This study presents a practical view of dynamic programming, specifically in the context of the application of finding the optimal solutions for the polygon triangulation problem. The problem of the optimal triangulation of polygon is considered to be as a recursive substructure. The basic idea of the constructed method lies in finding to an adequate way for a rapid generation of optimal triangulations and storing - them in as small as possible memory space. The upgraded method is based on a memoization technique, and its emphasis is in storing the results of the calculated values and returning the cached result when the same values again occur. The significance of the method is in the generation of the optimal triangulation for a large number of n. All the calculated weights in the triangulation process are stored and performed in the same table. Results processing and implementation of the method was carried out in the Java environment and the experimental results were compared with the square matrix and Hurtado-Noy method.

This study presents a practical view of dynamic programming, specifically in the context of the application of finding the optimal solutions for the polygon triangulation problem. The problem of the optimal triangulation of polygon is considered to be as a recursive substructure. The basic idea of the constructed method lies in finding to an adequate way for a rapid generation of optimal triangulations and storing - them in as small as possible memory space. The upgraded method is based on a memoization technique, and its emphasis is in storing the results of the calculated values and returning the cached result when the same values again occur. The significance of the method is in the generation of the optimal triangulation for a large number of n. All the calculated weights in the triangulation process are stored and performed in the same table. Results processing and implementation of the method was carried out in the Java environment and the experimental results were compared with the square matrix and Hurtado-Noy method.

In this paper we implement Block method for convex polygon triangulation in web environment (PHP/MySQL). Our main aim is to show the advantages of usage of web technologies in performing complex algorithm from computer graphics. The basic assumption is that one obtained results we store in database and use it for other calculation. Databases are convenient and structured methods of sharing and retrieving data. We have performed a comparative analysis of developed program with respect to two criteria: CPU time in generating triangulation and CPU time in reading results from database.

This paper presents a new technique of generation of convex polygon triangulation based on planted trivalent binary tree and ballot notation. The properties of the Catalan numbers were examined and their decomposition and application in developing the hierarchy and triangulation trees were analyzed. The method of storage and processing of triangulation was constructed on the basis of movements through the polygon. This method was derived from vertices and leaves of the planted trivalent binary tree. The research subject of the paper is analysis and comparison of a constructed method for solving of convex polygon triangulation problem with other methods and generating graphical representation. The application code of the algorithms was done in the Java programming language.

Computational geometry is an integral part of mathematics and computer science deals with the algorithmic solution of geometry problems. From the beginning to today, computer geometry links different areas of science and techniques, such as the theory of algorithms, combinatorial and Euclidean geometry, but including data structures and optimization. Today, computational geometry has a great deal of application in computer graphics, geometric modeling, computer vision, and geodesic path, motion planning and parallel computing. The complex calculations and theories in the field of geometry are long time studied and developed, but from the aspect of application in modern information technologies they still are in the beginning. In this research is given the applications of computational geometry in polygon triangulation, manufacturing of objects with molds, point location, and robot motion planning.

In this paper is presented a procedure for the application of one computational geometry algorithm in the process of generating hidden cryptographic keys from one segment of the 3D image. The presented procedure consists of three phases. In the first phase, is done the separation of one segment from the 3D image and determination of triangulation of the separated polygon. In the second phase, is done a conversion from the obtained triangulation of the polygon in the record which represent the Catalan key. In the third phase, the Catalan-key is applied in encryption of text based on the balanced parentheses combinatorial problem.