Geometric Optimization of Under-Staircase Storage Using Trigonometric and Coordinate Methods: A Mathematical Framework for Efficient Space Utilization in Urban Dwellings

Authors

  • Aaditya Pandey Department of Mathematics, Mithila Institute of Technology, Nepal
  • Aadarsh Karn Department of Mathematics, Mithila Institute of Technology, Nepal
  • Deb Narayan Mandal Faculty of Science, Technology, and Engineering, Rajarshi Janak University, Nepal
  • Suresh Kumar Sahani Faculty of Science, Technology, and Engineering, Rajarshi Janak University, Nepal

DOI:

https://doi.org/10.52783/rev-alap.160

Keywords:

Under-staircase storage, geometric optimization, trigonometric modeling, coordinate geometry, space utilization, material efficiency, cost reduction, urban housing, mathematical design, accessible mathematics, DIY storage design, trapezoidal shelving, reach optimization, waste minimization, practical mathematics.

Abstract

This research presents a mathematical approach to optimize under-staircase storage using basic geometry and trigonometry. We apply triangular volume calculations, sine/cosine laws for partitioning, and coordinate methods for placement planning. Results show 40-60% capacity improvements, 90-95% space utilization (vs. 50-60% conventional), 10-15% less material waste, and 20-25% cost reduction. Python verification confirms mathematical models. The framework demonstrates that secondary-school mathematics effectively solves real-world spatial problems, enabling homeowners and designers to create efficient storage without advanced tools or expertise.

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Published

2025-12-26

Issue

Vol. 29 No. 1 (2025)

Section

Research Articles