Hyperbolic geometry

Scolastika Mariani; Abdurrobbil  Falaq Dwi  Anggoro; Wardono Wardono; Bambang Eko  Susilo

doi:10.20897/ejsteme/18043

Research Article

2026, 11(1), Article No: 12

Hyperbolic geometry "lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra

Scolastika Mariani ¹ ^* , Abdurrobbil Falaq Dwi Anggoro ¹, Wardono Wardono ¹, Bambang Eko Susilo ¹

¹ Universitas Negeri Semarang, INDONESIA
^* Corresponding Author

https://doi.org/10.20897/ejsteme/18043

Published in Volume 11 Issue 1: 05 Mar 2026

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Abstract

Lobachevsky geometry is an elective course that is difficult for students to learn. One of them is the concept of the number of angles in a triangle less than 180 degrees. The purpose of this study is to produce a design of a Triangle learning trajectory in Lobachevsky Geometry using the context of the Sumatran traditional snack "lupis cake". The subject of this study is a mathematics education student at one of the universities in Bengkulu province. The research approach used in this study is Design Research. This approach involves an iterative cycle consisting of three phases, namely the preparation phase, the experimental phase, and the retrospective analysis phase. The result of this study is that there are five activities in the learning trajectory of the Triangle in Lobachevsky Geometry using the context of Sumatran traditional snack "lupis cake". Using this context, students are able to find the concept of the number of angles on a triangle less than 180 degrees. The conclusion is that the design of the Triangle learning trajectory in Lobachevsky's Geometry in the context of the traditional Sumatran snack "lupis cake" is valid and practical for finding the number of angles in a triangle

Figure 1. Lupis cake (traditional snack in Sumatra) (Source: Authors' own elaboration)

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APA 7th edition

In-text citation: (Mariani et al., 2026)
Reference: Mariani, S., Anggoro, A. F. D., Wardono, W., & Susilo, B. E. (2026). Hyperbolic geometry "lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra. European Journal of STEM Education, 11(1), Article 12. https://doi.org/10.20897/ejsteme/18043

AMA 10th edition

In-text citation: (1), (2), (3), etc.
Reference: Mariani S, Anggoro AFD, Wardono W, Susilo BE. Hyperbolic geometry "lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra. European Journal of STEM Education. 2026;11(1), 12. https://doi.org/10.20897/ejsteme/18043

Chicago

In-text citation: (Mariani et al., 2026)
Reference: Mariani, Scolastika, Abdurrobbil Falaq Dwi Anggoro, Wardono Wardono, and Bambang Eko Susilo. "Hyperbolic geometry "lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra". European Journal of STEM Education 2026 11 no. 1 (2026): 12. https://doi.org/10.20897/ejsteme/18043

Harvard

In-text citation: (Mariani et al., 2026)
Reference: Mariani, S., Anggoro, A. F. D., Wardono, W., and Susilo, B. E. (2026). Hyperbolic geometry "lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra. European Journal of STEM Education, 11(1), 12. https://doi.org/10.20897/ejsteme/18043

MLA

In-text citation: (Mariani et al., 2026)
Reference: Mariani, Scolastika et al. "Hyperbolic geometry "lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra". European Journal of STEM Education, vol. 11, no. 1, 2026, 12. https://doi.org/10.20897/ejsteme/18043

Vancouver

In-text citation: (1), (2), (3), etc.
Reference: Mariani S, Anggoro AFD, Wardono W, Susilo BE. Hyperbolic geometry "lupis": Hypothetical learning trajectory of the triangle in the context of Sumatra. European Journal of STEM Education. 2026;11(1):12. https://doi.org/10.20897/ejsteme/18043

Keywords

hypothetical learning trajectory, triangle, Lobachevsky geometry, context of traditional Sumatran snacks, lupis cake

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