October 8, 2023

Measuring Up

The History of Geometry as a Branch of Mathematics in Classical Antiquity

Math has been around longer than you think. Here’s a little inside scoop to the early stages of one of our most common math practices.

As we all know, many disciplines within Mathematics cater to particular scenarios, theories, and areas of quantitative knowledge. One of the more common and foundational disciplines aside from algebra would be geometry!

Like algebra, geometry is one of the oldest branches of mathematics still being utilized today! Merriam Webster’s formal definition of Geometry is articulated as “a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids”. Many of us initially learn the concept of geometry through shapes and graphs, but it seeps into so many more configurations! The purpose of geometry is to determine spatial relationships in our real-life scenarios and environments.

Where did geometry come from, you ask? Well, the term geometry originates from the two Greek phrases “gēo” (“Earth”) and “metron” (measurement). The Greek historian Herodotus (484-425 BC) was the one to credit Egypt with the subject’s origination. However, the Babylonian, Chinese and Hindu civilizations were the first to put it into practice; it was passed to the Greeks and Egyptians who popularized it through their obvious technological and cultural advancements. 

If you’re familiar with the Babylonians, they were the ones to utilize clay tablets as an early form of documentation. Some of the tables found on said tablets indicate the need for square roots, the area of various polygons, even reciprocals. Not only that but it is believed the Babylonians were also the first to calculate measurements of a circle, specifically the circumference. This instigated the long process of discovering the infamous, infinite number of pi (π). 

Unlike the Babylonians, the Egyptians kept records on papyrus scrolls. The Egyptians utilized geometry primarily for land surveying and construction; that’s how the Pyramids came into fruition! These groups of people were cognitively able to create and maintain streamlined systems of production! Geometry is such an elemental factor in the construction of our lives, it’s no wonder many ancient civilizations made great use of it as well.

The early Greeks were the ones to adopt geometry as a more rigid process. Greek philosopher Thales of Miletus (620-546 BC) was initially credited with bringing math from Egypt to Greece. After inhabiting the subject from their predecessors and neighboring communities, the early Greeks began prioritizing reasoning over results. Their emphasis on logic is incredibly representative in many influential works by early Greeks mathematicians.

One of the most infamous Greek documentations of math is known as Euclid’s Elements. It is a collection of 13 books the mathematician Euclid (appx. 300 B.C.) contrived. This series was intended to exemplify the functionality of many geometrical strategies. Plane geometry, geometric algebra, the geometry of a circle, elementary number theory, and proportions are just a few of the many subjects covered. 

Euclidian math clenched the reins on math education for many centuries, yet many other Greek mathematicians were eager to contribute newfound knowledge. Infamous figures such as Pythagoras and Archimedes were able to provide foundational parts of geometry we still use today!

Because geometry was a perfect strategy to determine the location and environmental factors, the Greeks incorporated it into other practices such as astronomy. They philosophized so much about the universe they orbited, therefore the Greeks felt compelled to calculate what we now recognize as our solar system. 

The most famous mind in early astronomy and classical antiquity is Ptolemy (circa 2nd century B.C.). Ptolemy was an Egyptian astronomer well known for his advancements in the model of our universe. He argued that our Earth was the center of the universe, thus formulated the geocentric solar system; this is what’s currently known as the Ptolemaic system. 

The application of geometry in astronomy consumed much of Greek thought. Their passion and prioritization of logic over result fueled much of their fire for many of their geocentric theories. Much later on, Greek cosmologists were the ones to apply the practicality of geometry to the Earth’s measurements and its orbital cycle in terms of time, location, even season. 

Many centuries passed before other civilizations throughout Asia and Europe were able to get their grip on geometry. Many geocentric Greek theories were debunked, and other communities took it upon themselves to study astronomy for results more than reason. Geometry has even gone on to evolve into different kinds, such as analytical geometry and progressive geometry. 

Universally applying these dimensional techniques was to not only grow humankind’s knowledge but the many empires. Without the study of these dimensional elements in our ever-growing reality, much of our structural and technological integrity would be lacking today.