Saransk, Saransk, Russian Federation
Saransk, Saransk, Russian Federation
Saransk, Saransk, Russian Federation
UDC 514
UDC 51
Recently our country has focused on the increasing role of mathematical knowledge in scientific and technological progress and strengthening Russia's sovereignty. In this regard the government demands an improvement in the quality of mathematics teaching in schools. Solving this problem requires a comprehensive methodological understanding. The relevance of the research topic is determined by the growing possibilities of digital educational platforms in the learning process and data visualization. The article is devoted to the use of computer animation as an element of a new digital learning technology in the study of geometry, the development of spatial and imaginative thinking of the learner. Experts and educators believe that using dynamic visualization of educational material is more effective than static, so math teachers face a rather difficult task – creating educational content that will allow them to visualize the solution of geometric problems. Computer animations, which have great capabilities at the current stage of information tech-nology development, can help solve this problem. The most popular tools for creating mathematical animations include the Manim library of the high-level Python programming language. The purpose of the article is to examine the features of creating and using computer animations in geometry teaching using the Manim library, and to identify its advantages and disadvantages. The paper presents program codes for creating geometric shapes, and illustrates the proof of the nine-point circumference theorem using the Manim library. The article will be useful for both beginners and experienced math teachers.
computer animation; Manim library; geometry training; animation drawing; geometric object; visualization; spatial thinking
1. Andreev O.D., Werner A.L., Lyaptsev K.A., Nikitin A.B., Tsikin I.A. Interactive Flash models in the school geometry course. Kompʹyuternye instrumenty v obrazovanii [Computer tools in education], 2006, no. 5, pp. 27-31. Available at: https://elibrary.ru/item.asp?id=12802841 (accessed 15 February 2026). (in Russian)
2. Bojkov A.A., Egiazaryan K.T., Efremov A.V., Kadykova N.S. Problems of geometric and graphic training of university students. Geometrija i grafika [Geometry and Graphics], 2023, V. 11, no. 1, pp. 4-22. DOI:https://doi.org/10.12737/2308-4898-2023-11-1-4-22. (in Russian)
3. Werner A.L., Nikitin A.B., Tsikin I.A. Digital educational resources in teaching mathematical disciplines. Nauchno-tekhnicheskie vedomosti SPbGPU. Informatika. Telekommunikatsii. Upravlenie. [Scientific and Technical Bulletin of St. Petersburg State Pedagogical University. Computer science. Telecommunications. Management], 2008, no. 3(60), pp. 250-256. Available at: https://elibrary.ru/item.asp?id=12802841 (accessed 15 February 2026). (in Russian)
4. Dubrovsky V.N. Stereometry with a computer. Kompʹyuternye instrumenty v obrazovanii [Computer tools in education], 2003, no. 6, pp. 3-11. Available at: https://rusneb.ru/catalog/000200_000018_RUNLR_Per_500345 (accessed 14 January 2026). (in Russian)
5. Elisova A.P., Firer A.V. Solving positional stereometric problems in the GeoGebra environment. Nauchno-pedagogicheskoe obozrenie. Pedagogical Review. [Scientific and pedagogical review. Pedagogical Review], 2020, no. 5(33), pp. 94-102. DOI:https://doi.org/10.23951/2307-6127-2020-5-94-102. (in Russian)
6. Zhivaya matematika [Live Mathematics]. Available at: https://zhm-edu.ru/ (accessed 16 January 2026). (in Russian)
7. Zimnyakova T.S., Larin S.V., Larina E.I. Features of using digital educational resources in teaching mathematics and physics. Vestnik KGPU im. V.P. Astafʹeva [Bulletin of the KSPU named after V.P. Astafiev], 2019, no. 2(48), pp. 26-32. DOI: https://doi.org/10.25146/1995-0861-2019-48-2-117. (in Russian)
8. Zinchenko V.P., Morgunov E.B. Chelovek razvivayushchijsya. Ocherki rossijskoj psikhologii [Is a developing person. Essays on Russian Psychology]. Moscow, Trivola Publ., 1994. 304 p. (in Russian)
9. Kompʹyuternaya animatsiya v obuchenii matematike v pedagogicheskom vuze [Computer animation in teaching mathematics at a pedagogical university] / V.V. Abdulkin, S.I. Kalacheva, S.V. Larin, V.R. Mayer. Krasnoyarsk, KSPU named after V.P. Astafiev, 2019. 164 p. Available at: http://elib.kspu.ru/document/33659 (accessed 10 January 2026). (in Russian)
10. Larin S.V. Metodika obucheniya matematike: kompʹyuternaya animatsiya v srede GeoGebra [Methodology teaching mathematics: computer animation in the GeoGebra environment]. Moscow, Izdatelʹstvo Yurajt Publ., 2024. 233 p. (in Russian)
11. Larin S.V., Mayer V.R., Kochetkova T.O., Karnaukhova O.A. Features of creation and use of computer animated drawings in teaching mathematics. Vestnik KGPU im. V.P. Astafʹeva [Bulletin of the KSPU named after V.P. Astafiev], 2020, V. 51, no. 1, pp. 6-14. DOI:https://doi.org/10.25146/1995-0861-2020-51-1-178. (in Russian)
12. Mayer V.R., Manchenkova E.O. Zhivaya matematika kak sredstvo povysheniya motivatsii k obucheniyu na urokakh geometrii v osnovnoj shkole [Live mathematics as a means of increasing motivation to learn geometry in primary school]. Informatsionnye tekhnologii v matematike i matematicheskom obrazovanii: materialy IV Vserossijskoj nauchno-metodicheskoj konferentsii s mezhdunarodnym uchastiem [Information technologies in mathematics and mathematical education: proceedings of the IV All-Russian Scientific and Methodological Conference with International participation, Krasnoyarsk, 18-19 November 2015]. Krasnoyarsk, KSPU named after V.P. Astafiev, 2015, pp. 71-73. Available at: http://elib.kspu.ru/document/15960 (accessed 14 January 2026). (in Russian)
13. Mayer V.R. Computer research and experiments in teaching geometry. Vestnik KGPU im. V.P. Astafʹeva [Bulletin of the KSPU named after V.P. Astafiev], 2012, no. 4, pp. 22-27. Available at: http://www.kspu.ru/page-4137.html (accessed 14 January 2026). (in Russian)
14. Matematicheskie etyudy [Mathematical studies]. Available at: https://etudes.ru/ (accessed 16 January 2026). (in Russian)
15. Nikitina T.A., Kokorin M.S., Knyazeva E.V. Classification of polyhedra in the course «Engineering Graphics» for students of technical and creative specialties. Geometrija i grafika [Geometry and Graphics], 2025, V. 13, no. 2, pp. 16-29. DOI:https://doi.org/10.12737/2308-4898-2025-13-2-16-29. (in Russian)
16. Palij N.V. Frame-by-frame animation in teaching descriptive geometry. Geometrija i grafika [Geometry and Graphics], 2023, V. 11, no. 3, pp. 39-47. DOI:https://doi.org/10.12737/2308-4898-2023-11-3-39-47. (in Russian)
17. Romanova V.A. Visualization of regular polyhedra in the process of their formation. Geometrija i grafika [Geometry and Graphics], 2019, V. 7, no. 1, pp. 55-67. DOI:https://doi.org/10.12737/article5c91ffd0916d52.90296375. (in Russian)
18. Savel'ev Yu.A., Babich E.V. Computer methodology for studying descriptive geometry. Technical specification. Geometrija i grafika [Geometry and Graphics], 2018, V. 6, no. 1, pp. 67-74. DOI:https://doi.org/10.12737/article5ad09d62e8a792.47611365. (in Russian)
19. Salʹkov N.A. Studying geometry as the most important way to develop heuristic thinking. Geometrija i grafika [Geometry and Graphics], 2024, V. 12, no. 1, pp. 22-31. DOI:https://doi.org/10.12737/2308-4898-2024-12-1-22-31. (in Russian)
20. Salʹkov N.A. The quality of geometric education with different approaches to teaching methods. Geometrija i grafika [Geometry and Graphics], 2020, V. 8, no. 4, pp. 47-60. DOI:https://doi.org/10.12737/2308-4898-2021-8-4-47-60. (in Russian)
21. Salʹkov N.A., Vyshnepolʹskij V.I. On the increasing role of geometry. Zhurnal estestvennonauchnykh issledovanij [Journal of Natural Science Research], 2017, V. 2, no. 2, pp. 53-61. Available at: https://naukaru.ru/ru/nauka/article/42405/view (accessed: 11 January 2026). (in Russian)
22. Salʹkov N.A., Kadykova N.S. About geometric science. Geometrija i grafika [Geometry and Graphics], 2025, V. 13, no. 3, pp. 45-54. DOI:https://doi.org/10.12737/2308-4898-2025-13-3-45-54. (in Russian)
23. Sanina E.I., Polyakov I.V. Teaching students how to solve planimetric problems using the coordinate method using GeoGebra. Continuum. Matematika. Informatika. Obrazovanie [Continuum. Mathematics. Computer science. Education], 2025, no. 1(37), pp. 15-28. DOI:https://doi.org/10.24888/2500-1957-2025-1-15-28. (in Russian)
24. Saryglar S.V. Computer animation in algebra lessons in grades 7 results of experimental work. Vestnik KGPU im. V.P. Astafʹeva [Bulletin of the KSPU named after V.P. Astafiev], 2021, no. 4(58), pp. 126-133. DOI:https://doi.org/10.25146/1995-0861-2021-58-4-310. (in Russian)
25. Smol'yanov A.G., Smol'yanova E.G., Kajmakova E.V. About an algorithm for constructing an ellipse using the chordal method. Geometrija i grafika [Geometry and Graphics], 2025, V. 13, no. 2, pp. 30-41. DOI:https://doi.org/10.12737/2308-4898-2025-13-2-30-41. (in Russian)
26. Tkachev V.V., Kuznetsova O.S. Primenenie biblioteki Manim dlya vizualizatsii uchebnogo materiala estestvenno-nauchnykh distsiplin [Application of the Manim library for visualization of educational material of natural science disciplines]. Materialy XV Vserossijskoj (s mezhdunarodnym uchastiem) nauchno-prakticheskoj konferentsii «Informatsionnye tekhnologii v obrazovanii» (ITO-Saratov-2023) [Proceedings of the XV All-Russian (with international participation) scientific and practical conference «Information Technologies in Education» (ITO-Saratov-2023), 2-3 November 2023, Saratov]. Saratov, Izd-vo Sarantovskogo un-ta Publ., 2023. V. 6, pp. 314-318. Available at: https://old.sgu.ru/sites/default/files/textdocsfiles/2023/12/13/ tkachev_v.v.pdf (accessed 11 January 2026). (in Russian)
27. Shakirova L.R. Galiaskarova K.R., Mukhamedvalieva S.R. Problems of visualization of mathematical knowledge in teaching geometry at school. Novye informatsionnye tekhnologii v obrazovanii i nauke [New information technologies in education and science], 2019, no. 2, pp. 80-86. Available at: https://www.elibrary.ru/ download/elibrary_41163776_40889108.pdf (accessed 11 January 2026). (in Russian)
28. Shekhovtsova D.N. Use of computer technologies for visualization of mathematical knowledge. Vestnik Tomskogo gosudarstvennogo pedagogicheskogo universiteta [Bulletin of Tomsk State Pedagogical University], 2010, no. 10(100), pp. 99-103. Available at: https://cyberleninka.ru/article/n/ispolzovanie-kompyuternyh-tehnologiy-dlya-vizualizatsii-matematicheskogo-znaniya (accessed 22 January 2026). (in Russian)
29. Yashchenko I.V., Vysotsky I.R., Samsonov P.I., Semenov A.V. Analytical report on the results of the Unified State Exam 2025 in mathematics. Pedagogicheskie izmereniya [Pedagogical measurements], 2025, no. 4, pp. 43-71. Available at: https://doc.fipi.ru/zhurnal-fipi/PI-2025-04.pdf (accessed 11 January 2026). (in Russian)
30. Yashchenko I.V., Vysotsky I.R., Semenov A.V. Metodicheskie rekomendatsii dlya uchitelej, podgotovlennye na osnove analiza tipichnykh oshibok uchastnikov EGE 2023 goda po matematike [Methodological recommendations for teachers, prepared on the basis of an analysis of typical mistakes of the participants of the Unified State Exam in 2023 in mathematics]. Moscow, Federalʹnaya sluzhba po nadzoru v sfere obrazovaniya i nauki FGBNU FIPI Publ., 2023. 43 p. Available at: https://doc.fipi.ru/ege/analiticheskie-i-metodicheskie-materialy/2023/ma_mr_2023.pdf (accessed 11 January 2026). (in Russian)
31. Manim Community Edition: Manim documentation. Available at: https://docs.manim.community/en/stable/ (accessed 05 May 2025).
32. Manim Community v0.17.3. Available at: https://www.manim.community (accessed 03 January 2026).
