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Explore the fascinating intersection of cartography and mathematics in this 27-minute conference talk that examines how mathematical principles underpin map-making and geographic representation. Discover the mathematical concepts that govern projection systems, coordinate transformations, and spatial relationships used in creating accurate maps. Learn about the geometric challenges involved in representing the three-dimensional Earth on two-dimensional surfaces and understand how mathematical solutions address distortions in area, distance, and direction. Examine various map projections through a mathematical lens, including their underlying formulas and the trade-offs between different types of accuracy. Gain insights into how mathematical modeling helps solve real-world cartographic problems and enhances our understanding of spatial data visualization. This presentation bridges the gap between abstract mathematical concepts and their practical applications in geography and navigation systems.