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In this research, we introduce an algorithm that produces what appears to be a new mathematical object as a consequence of projecting the \( n \)-dimensional \( Z \)-curve onto an \( n \)-dimensional sphere. The first part presents the algorithm that enables this transformation, and the second part focuses on studying its properties.

This paper describes a case study and the insights gained from prototyping an Intelligent Virtual Agent (IVA) for English vocabulary building for Spanish-speaking preschool children. After an initial exploration to evaluate the feasibility of developing an IVA, we followed a Human-Centered Design (HCD) approach to create a prototype. We report on the multidisciplinary process used that incorporated two well-known educative concepts: gamification and story-telling as the main components for engagement. Our results suggest that a multidisciplinary approach to developing an educational IVA is effective. We report on the relevant aspects of the ideation and design processes that informed the vision and mission of the project., Comment: Accepted in the IEEE Virtual Reality Conference 2022, Christchurch, New Zealand