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'There is no royal road to geometry', was the honest view of Euclid - the Father of Geometry.

Debopriya Bose
Jan 28, 2019

Geometry has formed an integral part of human lives since ancient times. Earlier, geometry was used to survey and measure land. Throughout the history of mankind, many scholars have made their postulates and propounded theories, but what makes **Euclid of Alexandria** the *Father of Geometry* is his book *The Elements*.

Euclid probably belonged to a rich family, as he is believed to have attended Plato's school. After his schooling, he taught in Alexandria, where he wrote his book, *The Elements*. Not much can be said about Euclid's life, mainly because of the lack of general information from such ancient times and also because 'Euclid' was a common name during that era.

He is often misconceived as Euclid of *Megara*, a Socratic philosopher. But what sets the former apart from the latter is his book, The Elements. The contents of this book is referred to as Euclidean Geometry, and is taught in elementary and middle schools.

The postulates and theorems of the book also span various areas of algebra, trigonometry and advanced mathematics. Euclid based his geometry on a number of postulates and notions and derived many other theorems. The book begins with five postulates, the first of which states that if there are two points, a straight line can be drawn through them.

His book was first published towards the end of the 15th century and millions of copies have been sold since then. It remained a part of the school curriculum till 1901, but the geometry that was taught thereafter had its foundation in the teachings of the book.

Till the 19th century *Euclidean Geometry* was undisputed. However, with further study, drawbacks were found by more recent researchers, the most notable being in the 5th postulate. The 5th postulate states that there can be only one line passing through a point and parallel to another line.

However, according to hyperbolic geometry that was created by the 19th century mathematicians, there could be more than one line passing through a point and parallel to a given line. This loophole along with some other drawbacks, gave birth to Non-Euclidean Geometry.

Although *The Elements* remains his greatest accomplishment, Euclid has quite a few other works to his credit. One of them is *Data*, that is closely related to *The Elements*. His *Division of Figures* deals with dividing figures into equal parts or according to a given ratio.

In *Phenomena* Euclid has dealt with Spherical geometry. *Optics* is another notable work of Euclid. Lost works of Euclid include *Porisms* that probably deals with analytic geometry, *Surface Loci*, *Pseudaria* and *Conics.*

Euclidean geometry may not be able to describe physical space and there may also be loopholes in *The Elements*, but the fact still remains that Euclid's work influenced the development of the present day geometry and mathematics.