Who was Euclid?
Euclid was a Greek mathematician (based in Alexandria, Egypt) who was alive circa 300 B.C. (during the Hellenistic Empire) – he is often referred to as the “farther of geometry” due to his most famous text the “Elements”.
Plato’s students were based in Athens so it is deemed likely that Euclid was often based in Athens considering his familiarity with their work. Euclid also became a reputable teacher after establishing his own school in Alexandria – his students carried his legacy forward.
Aside from this however, not much is known about Euclid’s life in general, except for the written works he left behind. His most famous of which is his written work the “Elements” which was a standard and popular textbook on geometry used for the next 2000 years – this 13 volume textbook was outnumbered only by editions of the bible.
Euclidean geometry:
Geometry was an important and prominent area of study in Ancient Greece with lots of notable figures furthering the understanding of geometry such as Pythagoras and Plato. However, it can easily be stated that the singular most defining moment was Euclid’s assembly of the ‘Elements’ (a singular coherent source that contained all the known geometrical knowledge at the time (the Elements also covered other mathematical bases such as prime numbers, however geometry was its focal point)). The Elements begins with plane geometry and spans all the way too three plane dimensions.
However, it was not only the theorems in the Elements that were important but also Euclid’s approach to the understanding of said theorems. In Elements, Euclid is the first to build up a large body of knowledge from five fundamentals (referred to as Euclid’s postulates) – he began by assuming a set of axioms and then expanding on these assumptions by deducing more advanced theorems. Though many of these theorems were not proved by Euclid himself, he was the first to demonstrate how these theorems could fit into a wider, more logical system.
As a whole, Euclidean geometry unfolds on a flat two dimensional plane – on these planes, Euclid explored and investigated fundamental properties of circles, straight lines, distance, angle and area. In the Elements, Euclid also proved Pythagoras’ Theorem and the fundamental fact that is, all angles in a triangle will add up to 180 degrees. Some of his more advance theorems in regards to triangles were his thinking and results boarded on the threshold of what we now know as trigonometry. Euclid also investigated the qualities of parallel lines – proposing and then proving theorems such as the alternate angle theorem.
Another notable section of the Elements is that of what is referred to as ‘the golden section’ – renamed as such, in the renaissance by artists when considering its pleasing proportions. ‘The golden section’ covered construction and ration.
Euclid - Prime numbers:
Another of Euclid’s most notable achievements is also his work with prime numbers. In his lifetime, Euclid managed to proves two of the most fundamental facts in mathematics:
1. The list of prime numbers is infinite
2. That every number can be written as the product of prime numbers
Euclid’s breakthroughs in regards to prime numbers placed more focus on the study of prime numbers for future mathematicians (an interest that has remained ever since). Prime numbers are such a fundamental and integral part of math’s – we have entire teams dedicated to studying them and their patterns. For example Glenn Webb, in 2001, observed that certain species of cicada avoided similarities with the life-cycles of their predators by adopting 13 and 17 year life-cycles.
In book 9 of the Elements, Euclid had a section dedicated to number theory at the heart of which was the study of prime numbers.
References:
Wikipedia contributors. “Euclidean Geometry.” Wikipedia, 16 Dec. 2020, en.wikipedia.org/wiki/Euclidean_geometry#The_Elements.
Waerden, Bartel Leendert. “Euclid | Biography, Contributions, & Facts.” Encyclopedia Britannica, www.britannica.com/biography/Euclid-Greek-mathematician. Accessed 17 Dec. 2020.
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