Virtual Reality in Stereometry Training

*Penio Lebamovski*

### **Abstract**

A new stereoscopic system is presented in this chapter for training in stereometry. Virtual reality systems are two types: immersion and non-immersion. An example of a environments with immersion is the desktop computer in which the virtual world is displayed on a special stereoscopic monitor through 3D glasses. The HMD (Head Mounted Display) virtual helmet is an example of an immersion system. The new stereoscopic system can also implement both types of 3D technology. At the same time, the software can generate objects in the .obj file extension to print to a 3D printer or add to a virtual reality device. The 3D technology is one of the fastest-growing. Over the last decade, it has found application in almost all spheres of society, including education. In learning stereometry, a problem may arise in drawing the geometric figures, unlike planimetry, where the drawing 100% coincides with its original. The problem can be solved with the help of specialized 3D software.

**Keywords:** boundary method, extrude, stereometry, stereo system, virtual reality

#### **1. Introduction**

This chapter focuses on the application of 3D technology in teaching the discipline of stereometry. It is known that stereometry is a branch of Euclidean geometry, which mainly studies geometric figures in three-dimensional space. This course examines the properties, and determines the volumes and faces of the surfaces of geometric figures, such as cylinders, cones, truncated cone, sphere, prism and others. According to teachers and experts in mathematics, when studying this discipline, it is of particular importance for students to have a spatial imagination that allows the understanding of the studied geometric figures in three-dimensional space, i.e., in three dimensions: x, y, and z. What distinguishes 3D (volumetric) from 2D (flat) representation is that more information is acquired about geometric figures in three-dimensional space. Spatial thinking is an activity with the help of which it is possible to solve several practical and theoretical problems related to learning. With the use of 3D technology, the student can become part of the learning process, allowing him to actively participate in the study of geometric figures and discuss and discover new dependencies related to the studied material. The evolution of technology and the need to modernize teaching has led to the creation of specialized software applications to assist students in learning the discipline of stereometry. With the help of 3D simulations and

information technologies, such as virtual reality (Virtual reality-VR) and augmented reality (Augmented reality-AR), students' cognitive activities are developed, as well as their interest in geometry (stereometry) increases [1, 2]. 3D modeling software applications, including VR and AR, help visualize complex and abstract shapes that are difficult for students who lack spatial imagination to understand. In the teaching process of mathematics (stereometry), the main goals of the teacher are: To demonstrate the possibilities of modern technologies by using 3D specialized systems.


In the learning process, a problem may arise when drawing a stereometric figure, unlike planimetry, where the figures are 2D, and usually the drawing almost 100% matches its original. In the three-dimensional space, the figure transferred to a blackboard or white sheet does not match its real image, from where the problem that the teacher faces arises, namely that it is impossible to recreate the spatial figure completely. This problem can be solved using specialized 3D software to generate the geometric object (prism, pyramid, cube, etc.) and their corresponding sections and projections. Software with a suitable user interface can help the student "immerse" into virtual reality and absorb new knowledge of the studied discipline more easily.

The purpose is to perform an analysis of virtual reality systems and to present a new stereo system for stereometry training. The new system can be implemented by devices for VR with and without immersion.
