By: ZOE HAN

Geometry, one of the oldest branches of mathematics, is fundamental to humanity’s understanding of the Earth. The Greek words “geo” (earth) and “metron” (measure) indicate geometry’s purpose in measuring the world. Its origins can be traced to ancient peoples like the Egyptians and Babylonians, who used geometric principles for tasks, such as land surveying and architectural designs.

The official study of geometry began with the Greeks, particularly with Euclid. His work, “Elements,” laid the foundation for Euclidean geometry, and his systematic approach remained the definitive source for studying geometry for over two thousand years. This was until his fifth postulate, the parallel postulate, became a topic of debate, and led to the development of non-Euclidean geometries by mathematicians like Carl Friedrich Gauss, Nikolai Lobachevsky, and János Bolyai in the 19th century. These new geometries, such as hyperbolic and elliptic geometries, challenged the Euclidean structure and expanded the understanding of geometric principles.

During the Renaissance, projective geometry emerged from the work of artists and mathematicians who studied perspective. This branch deals with the relationships between geometric figures and the images, or mappings, that result from projecting the shapes onto another surface. Projective geometry was further developed by figures such as Girard Desargues, and later, Felix Klein. Both theorists demonstrated that non-Euclidean geometries could be derived from projective geometry.

In modern times, geometry has found its way into various fields. In computer science, computational geometry plays a critical role in creating realistic images and animations by modeling and manipulating complex shapes and surfaces. Similarly, robotics relies on geometric algorithms for navigation, object recognition, and motion planning, allowing robots to thrive in their environment.

Geometry continues to be a pivotal tool in solving modern problems, driving technological innovation, and maintaining its relevance and importance across diverse domains. As time goes on, this branch of mathematics will advance, and continue to prove its importance in our world.

Image Credit by Todd Trapani