Euclid

In the history of geometry, Euclid of Alexandria is the main representative of this science. His contributions to humanity are invaluable and many of them remain today as universal premises. By many mathematicians and geometricians, he is known as the father of geometry . Euclid along with Archimedes and Apollonius of Perga is part of the triad of mathematicians of antiquity and is one of the most illustrious and best known mathematicians of all time. His most renowned work is “Elements”and it is composed of thirteen books that develop various themes of geometry and arithmetic and that have lasted without variations until the 19th century. This work has been as widespread as one of the most important written works of universal literature, as well as the Bible or Don Quixote.

Biography of Euclid

Little is known of Euclid’s life. He was born in 330 BC , he was the son of Naucrates. Some authors claim that he was born and lived in Alexandria , north of Egypt during the reign of Ptolemy I , while others claim that his birth was in the kingdom of Tire and lived in Damascus.

It is believed that his education began in Athens where he was able to acquire, in the school of Plato , great knowledge of geometry and mathematics. He was a teacher at his own school in Alexandria, founder of the Ptolemaic dynasty , in the reign of Ptolemy I – the first Greek pharaoh, who ruled Egypt from 305 BC. C. to 285 a. C.

In his life, he was able to develop several discoveries and collect in his works all the advances that existed on the geometry and arithmetic of his time.

“Elements” is his best known work and contains 465 propositions, 93 problems and 372 theorems in thirteen volumes. He also wrote other works related to thought, music, and optics.

According to investigations, the death of Euclides took place in the year 265 a. C.

Discoveries

In his life, Euclides made several important discoveries in number theory such as his well-known algorithm for calculating the greatest common divisor of two numbers ; in the field of geometry with its axioms and the set of books that make up the work entitled “Elements” .

Contributions

Within his work several contributions stand out that have been of great importance for the development of the study of geometry: These are: the “Elements” , the “Euclid’s Algorithm” , the ” Euclidean Geometry “ , the “Mathematics and Demonstration” and the Axiomatic Methods .

Elements

It is Euclid’s best-known contribution and is made up of 465 propositions , 93 problems and 372 theorems that collect the most important mathematical and geometric developments of his time. In this work, there are the 5 Euclidean postulates and the Euclidean algorithm.

Books I to VI develop themes of plane geometry ; Books VII to X deal with arithmetic topics by presenting the theory of numbers and irrational segments; books from XI to XIII explain spatial geometry .

Euclid’s algorithm

In this algorithm, Euclid describes the method to find the greatest common divisor between two numbers . This work has been of great importance for mathematics and has been applied in other fields such as economics.

Euclidean geometry

The contributions developed by Euclid in the field of geometry have dominated the study of this science for almost two millennia , especially in the areas of plane geometry and spatial geometry .

Euclidean geometry, in addition to being a valuable tool for deductive reasoning , has been used in other fields of knowledge such as physics , mathematics, astronomy, chemistry and different branches of engineering.

The demonstration

Euclid, like Archimedes and Apollonian,  perfected the process of mathematical proof , as a chained argument, so significantly that its use in modern mathematics is essential today.

Axiomatic methods

The axioms raised by Euclid in his work “Elements” pose a global perspective of the axiom that motivated the development of this fundamental area of ​​modern mathematics.

Euclid’s works

Euclid produced many treatises on geometry and other sciences . However, his best known work is called “Elements” and it is composed of 13 books that compile works by other authors and his and where the topics of plane or elemental geometry, number theorems and spatial geometry are touched. In addition to developing in the field of arithmetic and geometry, Euclides has a work entitled “Sophisms” and writings on topics of music and optics.

Euclid’s postulates

Euclid developed a set of axioms in the area of ​​geometry that he later called postulates. These are five and we will present them below:

• Postulate 1: ” Given two points, a line can be drawn that joins them.”
• Postulate 2: “Any segment can be continuously prolonged on an unlimited line in the same direction.”
• Postulate 3: “You can draw a center circle at any point and any radius.”
• Postulate 4: “All right angles are equal.”
• Postulate 5: “If a line, when cutting two others, forms the internal angles of the same side that are less than two straight lines, those two lines prolonged indefinitely intersect from the side with the angles that are less than two straight lines.” This axiom is also known as the axiom of parallels.

Phrases

Below are some of Euclid’s best-known phrases. These are:

• What is affirmed without proof, can be denied without proof
• The freedom is not an end, it is a means to develop our forces
• Reason is a means to the truth
• Success is not for what they think they can do something, but for those who do
• There is no royal road to Geometry