Riemann Integral In Minicraft Village Area Calculation With Geogebra - Muhammad Fahri Akmal; Nur Nabilah Yusuf Br Nasution; Fibri Rakhmawati (JTMT: Journal Tadris Matematika, 2026)
This study aims to model and estimate the area of a village in the game Minecraft through a Riemann-sum representation. The research employs a descriptive mathematical modeling approach focusing on a specific village area within the game environment. Spatial data were obtained by collecting the coordinates of boundary blocks, which were then mapped into a Cartesian coordinate system. The modeling and visualization process was carried out using GeoGebra to produce a two-dimensional representation of the analyzed region. The area calculation was performed through the summation of rectangular elements over partitioned intervals. Mathematically, for each fixed value of (y), the horizontal interval length is represented by (L(y)), while the area contribution at each partition is expressed as with ( ) representing the unit height of one block layer. The total area of the region is then approximated using the Riemann-sum formulation For each fixed value of (y), overlapping or adjacent (x)-intervals were first merged, and the interval lengths were multiplied by unit height to obtain the area contribution at each level. The resulting model produced an estimated village area of 232 square units ((m^2) equivalent). This study demonstrates how spatial data from block-based digital environments can be transformed into coordinate-based mathematical representations and analyzed systematically using mathematical modeling techniques. The findings also illustrate that discrete spatial structures in digital games can be interpreted through the concept of Riemann sums for area approximation. However, this study does not examine instructional effectiveness or student learning outcomes; therefore, any educational implications should be interpreted cautiously