Abstract:

Computer technology is used ubiquitously in modern life. Mathematics and science education is not the exception. In our work, we investigate the possibilities of desktop publishing system LaTeX for application in the mentioned area. In our first paper in this direction [1], we have investigated the problem in general. In the second paper [2], we have considered our problem in application to plane geometry. Here we turn to the spatial geometry, namely, to the problems on the construction of plane sections of the spatial figures.

We begin with considering the problem of determining the notion of a section of a polyhedron. In the available literature, we have not found an exact definition of the concept. Having analyzed a sufficiently large number of cases where the term ‘section’ is used, we propose a definition covering all the cases examined. After that, we turn to the problems of constructing of the sections of polyhedra (we hope to consider the problems of construction of the sections of other spatial figures in our subsequent publications).

We find out that there is no generally accepted methodology teaching of solving such problems, and propose our own simple and natural methodology based on initial consideration of several simplest problems and subsequent systematic application these problems to solving more complicated problems. In the course of the process, we show how LaTeX naturally fits into the proposed methodology and allow getting easily beautiful and correct drawings. Unfortunately, the framework of Abstract does not permit to quote the relevant examples, to which we refer the reader to our full paper.

Thus, the purpose of our work is threefold:
1) to clarify the concept of the section of a spatial figure with a plane;
2) to propose a new methodology of teaching the solution of the problems about the construction of the sections of polyhedra based on the systematic application of solutions of several previously considered simple problems; and
3) to show how LaTeX naturally integrates into this methodology, and to give examples of LaTeX-codes for solving the problems under consideration, which will serve as samples for self-written analogous codes.

In conclusion, we note that these results could serve as a basis for a broader study. We hope that there will be the people willing to finance this promising research area.

References:
[1] "LaTeX as an ideal tool for integration of ICT and mathematics in science teaching", "New Perspectives in Science Education: 6th Edition": Proceedings of the International Conference (Florence, Italy, 16–17 March 2017). Florence: Pixel, 2017. — P. 181–187.
[2] “Computer support of teaching plane geometry by means of LaTeX”, EDULEARN17: 9th International Conference on Education and New Learning Technologies, — P. 3940–3945

Keywords:

Spatial geometry, Polyhedra, Sxtions, Computer support, LaTex.