Euclid

As we were learning in class Euclidean spaces I decided to deepen on the figure of Euclid who I have been studying through all my student life. Euclid was a Greek Mathematician who lived between the 4^th century and 3^rd century BC. He is considered “The Father of Geometry”. Despite having lived such a long time ago his geometry is not at all old fashioned if not that it is still used nowadays as we can see. Another models have not been developed until the 19^th century what can give us an idea about his figure. 

His most famous book is called “Elements” where much of the knowledge he acquired is shown. He also based his work in another compositions when defining bodies but he also states some theorems very common nowadays. They are, for example, the sum of the interior angles of a triangle equals 180º. He assures lines have only one dimension, the length, planes two and so on. He created, that way, a system that by that time was enough to understand things.

However, Gauss and other mathematicians but also Einstein in his modern physics investigation needed something else so some statements from Euclid had to be changed. His research was limited in a way. We can see now that we call Euclidean spaces to the set of vectors where the scalar product is defined in it. It has to follow symmetry, lineality and positivity, otherwise it is not an Euclidean space.

All this knowledge can be applied to many different fields. As I was saying it has much to do with geometry, which is everywhere around us. I hope you find this post interesting and you keep up to date with my blog!