Geometry's Ancient Applications: Measuring Pyramids and Earth's Circumference

The word 'geometry' originates from Greek words meaning 'earth measurement,' reflecting its historical use in practical applications. Ancient mathematicians like Thales of Miletus utilized geometric principles to solve real-world problems, a prime example being the measurement of the Great Pyramid of Giza's height. Thales employed a simple stick and the concept of similar triangles, using the stick's height and shadow length to calculate the pyramid's dimensions without direct measurement. He ingeniously accounted for the pyramid's base by measuring the shadow's length to the edge and adding half the base's width, then applying the ratio of the stick's height to its shadow to the pyramid's corresponding measurements.

Centuries later, Eratosthenes of Cyrene, a scholar in ancient Alexandria, used geometry to estimate the Earth's circumference around 240 BCE. He observed that on the summer solstice, the sun was directly overhead in Syene (modern Aswan), casting no shadow at noon. However, in Alexandria, located 5,000 stadia north, a vertical stick still cast a shadow. By measuring the angle of this shadow (7.2 degrees) and knowing the distance between the cities, Eratosthenes applied geometric principles, specifically the concept of alternate interior angles and the Earth's spherical shape, to calculate its circumference. His estimate, approximately 250,000 stadia, translates to roughly 37,500 to 50,000 kilometers, remarkably close to the modern accepted value of 40,075 kilometers.