# Ann Varela: Euclid and His Contributions

An Interview with Ann Varela: Euclid and His Contributions

Michael F. Shaughnessy –

1) Euclid is another name that is associated with the beginnings of math and numbers. Do we have any idea when and where he was born, and what his childhood was like, and how he got his early education?

Not much is known about Euclid’s early life except that he established a school and taught in Alexandria. Even the dates of his lifetime vary among sources, but most likely he lived from about 330 BC-260 BC. It is thought that he came from an affluent background and received his formal mathematical education from the students of Plato in Athens.

2) Now what would you say were his greatest contributions to math, arithmetic and numbers?

Euclid has been called the “Father of Geometry”. He wrote the *Elements of Geometry,* one of the most significant mathematical dissertations of all time, which was used as the primary textbook for teaching mathematics from its commencement until the early 20^{th} century. The *Elements* was a collection of all the known mathematics of his time and consisted of 13 books. Although a good portion of its contents was composed of earlier known philosophies and sources, Euclid was responsible for collating these individual works into a single composition based on a set of initial postulates, definitions, and axioms. He essentially created the first encyclopedia of mathematics by joining various manuscripts into one document.

3) How do his contributions impact us today?

Euclid’s endeavor was important because it permitted the dissemination of knowledge more easily and practically. Others could study mathematics from an extremely organized, coherent, and thorough transcript. Euclid’s *Elements* provides us with a good model of which to base our modern-day textbooks. His legacy includes Euclidean geometry, the Euclidean number, and the Euclidian algorithm.

In addition, the logical order and progression of thoughts from straightforward to most complex evident in the *Elements* was modeled in the structure and organization of the United States Declaration of Independence.

4) There are often stories about famous people that seem to linger- are there any anecdotes that you are aware of about Euclid- or the impact that he has had?

Apparently, Euclid motivated Abraham Lincoln, who used to carry the *Elements *with him everywhere he went and would occasionally quote Euclid in his speeches. Evidently, Lincoln mastered the first six books of *Elements* simply to aid in mental strength.

There is some speculation, yet not much confirmation, that Euclid was not, in fact, one man but a team of mathematicians who wrote the *Elements* manuscript and called themselves Euclid.

5) What have I neglected to ask about this famous mathematician?

It may be interesting to note that Euclid is known for having other mathematical achievements. He was the first to realize and prove that there are infinitely many prime numbers. Moreover, Euclid was the first to explain the Golden Ratio in terms of ratios and verified its presence within numerous geometric shapes.

Furthermore, Euclid defined a *perfect* number as a number which is the sum of its parts. In other words, its *proper* divisors. For example, the number 6 is perfect since its *proper* divisors are 1, 2, and 3. From here, we can see that 1 + 2 + 3 = 6. It remains unsolved as to whether or not there exists an endless number of *perfect* numbers and if odd perfect numbers indeed exist.