Geometry is the study of points, lines, shapes, and surfaces. As one of the oldest branches of math, the history of geometry is rich and detailed, leading to the theories and processes that are studied in math class today. Below is a brief history of geometry and how it has evolved over time. 

Origins of Geometry

The study of geometry dates back to ancient times, where civilizations created rules for measuring, dividing, and combining different shapes for structures like temples and for setting roads. The Babylonians and Egyptians left records of their mastery of manipulating and working with shapes to build and create.

Around 300 BCE, Alexandria in Greece emerged as an important knowledge center and also the location of Euclid’s Elements of Mathematics. Using Aristotle’s principles of Greek logic and explaining theories, Euclid defined points, straight lines, shapes, axioms or postulates, and angles. In total, he created 23 definitions, five postulates, and five common notions as the basis. Necessary laws about right angles and lines came from his postulates, and are the basis for axioms still in use in today’s math classes.

The Shift Over Time

While Euclid’s work is a revered geometry text, one of his five postulates, the one regarding parallel lines, is controversial, which then led to an expansion of this branch of math. For centuries, mathematicians in various countries continued to study the postulate, leading to the discovery of theories such as the Pythagorean Theorem. This theory is still in use when discussing right-angle triangles in math class.

During the 17th century, two developments changed the face of geometry. One was the discovery of analytic geometry, which was comprised of coordinates and equations, and was an early version of calculus, by René Descartes and Pierre de Fermat. The second, created by Girard Desargues, was projective geometry that studied the points and their alignment without measurement.

In the 20th century, algebraic geometry took shape and expanded the study into curves and surfaces over finite fields. These finite concepts can be found in coding theory and cryptography today, leading to geometry and technology coming together to form in computational and digital geometry as well as algorithms.

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