July 23, 2023

Introducing… Euclid!

How the Contributions of One Alexandrian Mathematician Influenced the Course of Human Thought

What Started As A Thought…

Soon blossomed into an entire movement of thought and education.

We’ve all been taught about ancient Greece as well as their intellectually rich culture. They birthed and molded so many foundational leaders of thought in realms such as math, philosophy, religion, even art and architecture.

One of the most contributors to the evolution of math is Euclid. Euclid was known and referred to as the “father” or “founder” of Geometry. Geometry is a very distinct field within mathematics responsible for explaining the relationships of planes and objects. We all start to integrate geometrical knowledge when we learn the properties of shapes, points, lines, and the connection between them all!

Euclid is the namesake of Euclidean geometry, which is the basis of plane geometry like his published works allude to. But we’ll get into that later!

About Euclid

What we know of Euclid derives from a summary of famous mathematicians contrived by Greek philosopher Proclus (410-485 CE). Very little detail is actually known about Euclid’s life, however, has been hypothesized and framed by key events: his birth, death, and prominent mathematical contributions.

Euclid was born approximately 325 BCE and hails from the great Alexandria, a prominent civilization in Egypt. It is believed he passed there as well about 265 BC.

He taught in Alexandria at the time of Ptolemy I Soter (367/366-283/282 BC), the Macedonian ruler of Egypt.

In the summary procured by Proclus, it describes Euclid stating:

Not much younger than these [pupils of Plato] is Euclid, who put together the “Elements”… for Archimedes, who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry…

Euclid of Alexandria is typically mistook for Euclid of Megara, who lived 100 years before he was even born! And even though much of his existence remains in question, there is absolutely no doubt that he provided one of the most revolutionary pieces of work for math to evolve in the following 2000 years.

Euclid’s Contributions + Euclidean Geometry

What did Euclid ultimately contribute to math?

He wrote a collection of work known as the Elements. Euclid’s Elements is a compilation of postulates, proposals, and rules of geometry. There are five postulates introduced at the beginning of this collection, assuming the existence of points and lines and how they relate to one another.

The five postulates state:

– A straight line segment can be drawn to connect any two points.
– Any straight line segment can extend indefinitely in a straight line.
– Given any straight line segment, a circle can be drawn having the segment as a radius and one endpoint (of the segment) as the circle’s center.
– All right angles are congruent (equal).
– If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

The fifth postulate defines what’s known as a parallel postulate, and it has not been proven yet despite many attempts.

You’ll probably find many of these postulates as basic rules introduced to you when you learned what geometry was! Elements essentially highlights the fundamentals of Euclidean geometry, which is taught in secondary education.

There are thirteen books in total, highlighting definitions and propositions revolving around the theory of geometry, proportions, circles, number theory, geometric algebra, and solid figures. Euclid dives into great detail for each subject he accentuates with his writing to ensure the comprehension of how they all correlate to one another.
It’s one of the oldest surviving mathematical publications known to humankind, which is why it’s been carried into our prevalent education today.

Why Is It Important?

Subcategories of math such as geometry and number theory help us develop a wide array of applications. For instance, geometry helps us develop and understand spatial awareness as well as relationships. This helps us create modern structures that hold up, and it also helps us find shapes for functional inventions. Without the fundamental knowledge of circles, polygons, and solid shapes, we wouldn’t have half the stuff we use on a daily basis!