Geometric Transformations in the Lawang Sanga Gate of the Kasepuhan Palace, Cirebon: An Ethnomathematical Measurement Study

Studies of the Lawang Sanga Gate at the Kasepuhan Palace, Cirebon, have focused on its history and symbolism, whereas its geometric form has not been formally measured. This study examines how far translation, reflection, and dilation can be identified in the architectural elements of the gate. A descriptive qualitative design with an ethnomathematical perspective was used, combining field observation, tape measurements (precision ±0.5 cm) of doors, pillars, mouldings, and ornaments, photographic documentation, and an interview with a key informant. Patterns were coded as transformations, and their regularity was quantified with successive differences and ratios, left–right differences, and the coefficient of variation (CV). Reflection is the most consistent transformation: the three bays of the front façade (285, 180, and 285 cm) and the crown ornament are mirror-symmetric about the central axis, although corresponding pillars on the inner front wall differ in width by 18–23 cm. Translation is clearest in the spacing of the curved lines of the central arch (15.6, 15.8, and 16.6 cm; CV = 3.3%). In the central arch, blind arch, and rear door, successive mouldings change in width by ratios of 0.94–1.08, which approximates, but does not strictly satisfy, dilation, and the width-to-height ratio of the pillars is not constant (1:1.5 to 1:3.1). These findings indicate that the builders applied mirror symmetry and repetition deliberately at the level of layout and ornament, whereas sizes were scaled only approximately. The study provides baseline measurements for conservation and for ethnomathematics-based learning; higher-precision three-dimensional documentation is needed to confirm the proportions.