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Explore the mathematical limits of Eratosthenes' ancient shadow experiment through a comprehensive analysis that tests both spherical and flat Earth models. Examine the logical foundation behind the classical method for measuring Earth's circumference, then apply this technique across dozens of cities to determine which geometric model survives rigorous mathematical scrutiny. Discover how shadow measurements from multiple locations provide compelling evidence for Earth's true shape, while systematically demonstrating why alternative models fail under mathematical examination. Learn about the historical significance of this ancient Greek experiment and understand how modern data collection can validate or refute competing theories about our planet's geometry through empirical testing and mathematical analysis.