Hi creative bloggers! Today we are going to know the father of the geometry: Euclides of Alexandria.
Geometry was already being used by the Egyptians and Babylonians to solve everyday problems and for artistic creation. It was in Greece that geometry became a science structured around logical-deductive reasoning, initially to solve the three classical problems: the doubling of the cube, the squaring of the circle and the trisection of the angle (Cortés, 2012).
Geometry before Euclid evolved from a practical tool for survival into a philosophical system of absolute rigour. Its roots lie in the civilisations of Mesopotamia and Egypt, where it was a purely empirical discipline used by ‘rope-stretchers’ to demarcate land following the Nile’s floods and by architects to calculate the volumes of pyramids using approximate formulas. The great shift occurred in the 6th century BC when the Greeks, led by figures such as Thales of Miletus and Pythagoras, began to demand logical proofs rather than mere measurements, transforming geometry into a deductive science. As Plato’s Academy established geometry as the foundation of rational thought, mathematicians such as Eudoxus of Cnidus developed advanced methods for dealing with irrational numbers and curved areas.
Euclid of Alexandria was one of the first teachers at the University founded by Ptolemy. He was a learned and honourable man who gave credit where credit was due and taught in a kind manner. Once a student asked him if there was not a short and easy way to learn geometry, and he replied, ‘Oh, prince, there is no royal road to geometry.’ In his work comprising 13 books, which he called *Elements* and which offered a definitive treatment of two-dimensional (the plane) and three-dimensional (space) geometry.
Figure 1.
Euclid of Alexandria.
His main achievement was not merely the discovery of new theorems, but the formalisation of the axiomatic method: Euclid demonstrated that all geometric knowledge could be logically derived from just five basic postulates and a few common notions. In doing so, he established the standard of scientific rigour and logical proof that defines modern science. Euclid made fundamental contributions to number theory. He succeeded in proving the infinity of prime numbers and developed the algorithm that bears his name for calculating the greatest common divisor, a tool that remains essential in modern computing. Thus, before Euclid, mathematics was a collection of isolated results; from his work onwards, it gradually evolved into a supersystem of interrelated systems (Levi, 2026).
This fascinating video provides an overview of Euclid’s postulates, which began with very simple definitions (point and line) and five fundamental postulates. The video places particular emphasis on the fifth postulate—that of parallel lines—as it was the most controversial and eventually led to the emergence of non-Euclidean geometries. It concludes by emphasising that Euclid’s impact went beyond the drawing of figures: he taught us the scientific method, to think deductively; without his rigour, Newton’s physics or Einstein’s theory of relativity would not have been possible. It also points out that, although we now know that space can be curved, Euclidean geometry remains the perfect tool for our daily lives, from carpentry to urban architecture.
In essence, the video presents Euclid not only as a mathematician, but as the man who gave us a new way of observing and measuring the universe in an orderly manner.
References
Cortés López, R. (2012). Historia de la Geometría Euclidiana y sus aplicaciones para la enseñanza.
Levi, B. (2026). Leyendo a Euclides. Libros del Zorzal.
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