The Metallic Ratio of Pulsating Fibonacci Sequences

The golden ratio and the Fibonacci sequence (Fn) are well known, as is the fact that the ratio Fn+1Fn converges to the golden ratio for sufficiently large n. In this paper, we investigate the metallic ratio—a generalized version of the golden ratio—of pulsating Fibonacci sequences in three forms. Two of these forms are considered in the sense of pulsating recurrence relations, and their diagrams can be represented by symmetry, which is one of their distinguishing characteristics. The third form is the Fibonacci sequence in bipolar quantum linear algebra (BQLA), which also pulsates

Hamiltonian Cycles in Cayley Graphs of Gyrogroups

In this study, we investigate Hamiltonian cycles in the right-Cayley graphs of gyrogroups. More specifically, we give a gyrogroup version of the factor group lemma and show that some right-Cayley graphs of certain gyrogroups are Hamiltonian

Teaching Fundamental Programming Using Augmented Reality

To learn a programming language, the students have to understand the logical flow of the commands as well as the syntax. The logical flow might be more difficult to understand when compared with a syntax which can detect easily. The primary flow of commands or the control structures includes the sequence, condition or selection, and iteration. The students construct the program flowchart by using these control structure. They also have to understand the result of each command execution, step by step. In this research, we propose the technique for developing the learning tool (AR flowchart) to simulate the result of the commands in program flowchart by using augmented reality (AR), so the learners can visualize the result. With this tool, the students can construct a program flowchart as a series of commands by using AR markers. The result of the execution of these commands can be displayed so the students can see whether the logic of the program is correct or not. The design of this tool aims at increasing student engagement and helping them to understand program logic better. The evaluation of the concept results by the group of university students supports our propose

Teaching Fundamental Programming Using Augmented Reality

To learn a programming language, the students have to understand the logical flow of the commands as well as the syntax. The logical flow might be more difficult to understand when compared with a syntax which can detect easily. The primary flow of commands or the control structures includes the sequence, condition or selection, and iteration. The students construct the program flowchart by using these control structure. They also have to understand the result of each command execution, step by step. In this research, we propose the technique for developing the learning tool (AR flowchart) to simulate the result of the commands in program flowchart by using augmented reality (AR), so the learners can visualize the result. With this tool, the students can construct a program flowchart as a series of commands by using AR markers. The result of the execution of these commands can be displayed so the students can see whether the logic of the program is correct or not. The design of this tool aims at increasing student engagement and helping them to understand program logic better. The evaluation of the concept results by the group of university students supports our propose