Geometric Transformations and Symmetry in the Panjunan Red Mosque, Cirebon: An Ethnomathematical Study for Culture-Based Geometry Learning

Abstract

Historic mosques in Indonesia embody mathematical ideas, yet studies of the Panjunan Red Mosque in Cirebon, built in 1480, have focused on its history and cultural acculturation rather than its mathematical structure. This study aims to identify and map the plane geometry, solid geometry, and geometric transformations embodied in the architecture of the mosque as a source of contextual mathematics learning. A qualitative descriptive design with an ethnographic approach was used. Data were collected through direct observation, a 45–60-minute semi-structured interview with the mosque caretaker, and photographic documentation of eight architectural elements: fence ornaments, roof, pillars, walls, ventilation openings, mihrab, gate, and wall reliefs. The data were analysed with the Miles–Huberman–Saldaña interactive model using inductive open and axial coding, and the transformations were modelled schematically in GeoGebra. The elements contain squares, rectangles, circles, triangles, trapezoids and rhombuses, as well as cylinders, cuboids, a square pyramid and a pyramid frustum. Four transformations were identified: translation in the ventilation openings, approximate reflection symmetry in the mihrab and the split gate, fourfold rotational symmetry in the wall relief (dihedral group D4), and dilation in the concentric square tiers of the gate pillars. The three isometries produce congruent repetition, whereas dilation produces similar figures of decreasing size. These regularities underpin the aesthetic balance of the building and are interwoven with its Javanese, Hindu-Buddhist, Chinese and Islamic meanings. The findings can inform culture-based geometry tasks; because the models are schematic, measured dimensions and classroom trials are needed in future work.