Euclid or Euclides was a Greek mathematician and geometer, considered one of the great mathematicians of antiquity and father of geometry. He was born in Alexandria in 435 b.C and would die in 265 b.C.. However, there is not much information about his life. The historians say that Euclid would begin his education in Athens, where he acquired his great knowledge of geometry, in the elaborate school of Plato. Later on, Euclid would become professor of his own school in Alexandria, which was the most important in the Hellenic world and in which he would reach the highest recognition as a teacher, in the reign Ptolemy I Sóter, who was the founder of the Ptolemaic dynasty that ruled Egypt and who seek Euclid to teach him and shorten the process to learn mathematics and geometry.
Euclid was the author of different works, such as “Elements”, which is a collection of works of other philosophers such as Hippocrates, and this work would challenge some of the most important literary works in the world, such as the Bible and Don Quixote. This work was made up of 13 books, of which the first 6 made reference to basic flat geometry concepts. From the seventh to the tenth book, Euclid deals with numerical issues such as divisibility, prime numbers, and radicals. In the last three books, he would include topics on the geometry of solids, polyhedra, and circumstantial spheres. Among the most important theorems of Euclid’s work are:
- The sum of the internal angles of a triangle, add up to 180 degrees.
- In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the adjacents, which refers to the Pythagorean theorem.
Besides this, Euclides formulated 5 postulates, which he used as a starting point to explain geometric and mathematical knowledge. These postulates are:
- A straight line segment can be drawn joining any two points.
- Any straight line segment can be extended indefinitely in a straight line.
- Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
- All right angles are congruent.
- If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate.
Euclid’s fifth postulate cannot be proven as a theorem, although this was attempted by many people. Euclid himself used only the first four postulates.
The geometrical principles of Euclid were important in areas such as physics, astronomy, chemistry, some engineering and worked as inspiration for the Ptolemaic theory of the Universe in the second century. His ideas also formed an abstraction of reality, because he made assumptions such as that a point has no size so it is assigned a dimension zero or equivalent to zero, a line is a set of points that has neither width nor thickness, only length and assigned a value equal to 1, a surface has no thickness and has dimension 2 equivalent in length and width; to conclude, he said that a solid body, like a cube, has dimension equivalent to 3, length, width, and height.
“Elements” has had more than a thousand editions since the first time it was published in the year 1482, so it is said that Euclid is one of the most read mathematics in history.