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# Euclid

Euclid was a Greek mathematician who came to be known as the “father of geometry.” While it is thought that he lived in Alexandria sometime between 300 to 200 BC, much about his life is a mystery. What we do know has mostly come from Proclus, a Greek Philosopher who lived in the 5th century. The following information discusses what is known about his life, his work in mathematics, what is speculated about the man, and his many contributions to the world of geometry.

## Euclid's Life

It is assumed that Euclid was born in Greece at approximately 325 B.C. and died in Egypt around the time 256 B.C. He studied in Athens, Greece at Plato's Academy. Only the wealthy were able to study here during this time. Euclid was believed to have taught mathematics at Alexandria, Egypt after being invited by Ptolemy I. He probably taught in the Alexandria library or museum. Some sources have claimed that he was born in Tyre and lived much of his life in Damascus. After Euclid died, the mathematicians he had been working with began to compile “The Complete Works of Euclid.” Even though little is known about him, Euclid is considered one of the greatest mathematics teachers of all time. His works have come to be known as Euclidean Geometry.

## The Elements

Euclid's greatest mathematical work is what is known as the Elements. The Elements are based on much of the work of earlier men. There is some disagreement as to whether Euclid came up with the work that is in the Elements himself or simply compiled and put together what he learned from others. Some of the works he used to form his own theorems belonged to Hippocrates of Chios. This Hippocrates was not the same as the famous physician Hippocrates. Euclid's work was also influenced by Aristotle, Thales, and Eudoxus. The Elements was first published in 1482 and consists of 13 books. Volumes 1 through 6 were about plane geometry. Volumes 7 through 9 were written about number theory. Volume 10 was the theory of the irrational number and Volumes 11 through 13 were about solid geometry. Some of his work culminated in what became known as the five regular solids. These are now called the Platonic Solids.

## Basic Teachings

An example of some of his basic teachings includes the unproved assumptions that he called postulates. They are sometimes called axioms. Postulates are not usually considered self evident as are axioms. Axioms are statements that are now accepted to be true. Euclid is also known for the Pythagorean Theorem. Some of his basic principles of geometry that are in use today include the following. Things equal to the same things are equal, all right angles are equal, and a straight line segment can go on indefinitely. Euclid's basic approach to mathematics was termed the synthetic approach. This meant his principles and theories were not based on methods of trial and error but rather from presenting facts from theory. Up until the 19th century his version of geometry was basically all that was known or taught. Modern mathematicians have since developed different theorems and have divided geometry into Euclidean and Non-Euclidean.

## Other Mathematical Works

Besides his most famous mathematical work, Euclid is known for other important works as well. He also contributed to developing principles regarding optics and perspective. In his work that is titled Optics, Euclid uses principles formed from Platonic traditions. Euclid puts forth dozens of propositions that relate to what size an object appears to be in relation to each of the objects distance from the eye. His work regarding spherical geometry was used for explaining planetary motions. This work is called Phaenomena. Euclid contributed to Catoptrics which involves mathematical concepts of mirrors. Euclid proved that it was impossible to find the largest prime number. His simple explanation was that adding 1 to the largest number would thus create a new largest number. He also worked with ratios and data. His other works have the same basic structure of logic as the Elements. They revolve around definitions and proved propositions.

## His Effect on Our Modern World

The elements were translated into Arabic and then into Latin. The first version in print appeared in 1482 in Venice. It wasn't until 1570 that mathematician John Dee translated Euclid's work into English, thus bringing his work on a large scale to Europe. Abraham Lincoln is said to have studied Euclid's work at the age of 40. Some of the logic and phrasing in Lincoln's speeches are attributed to what he read in Euclid. Much of Euclid's work provides the foundation of what we understand of modern geometry. His theorems and principles are studied by millions of students from elementary school through advanced college instruction. The first five of Euclid's ten axioms are referred to as Common Notions because they can be applied to all sciences, not just mathematics. These five are general statements and concepts that have been used for centuries now. One that was mentioned earlier is “Things that are equal to the same thing are also equal.” Another that is very well known is “The whole is greater than the part.”

Unfortunately, there are several of his works that have been lost or considered questionable as to whether he wrote them or not. Some of his lost works include Conics, Porisms, and Elements of Music. What is now considered Non-Euclidean Geometry was not accepted as another form of legitimate mathematics until the 19th century. Euclidean Geometry is still the basis of many aspects of our everyday life including what is done in surveying, electronics, and in the structure of buildings.