Greek Geometry

Geometry is one of the easiest of the early maths to be able to understand because it is the math of the physical world. Where geometry becomes difficult is the lack of formal logic education to help people build the world around them.

The start of geometry as a math was with the need to describe the physical world. Areas and volumes for different shapes began to be more than guesswork- this allowed for a more scientific basis of trade, commerce, and more.  Pythagoras, a man living in 530 BCE Greece was especially interested in 2dimensional triangles.

Pythagoras found some extremely useful patterns, especially right triangles. This is the most important thing in terms of our lives- right triangles are everywhere, especially in the buildings we live in. Without Pythagoras and his great contributions to making sense of such a common structure, we would struggle to make the buildings we do today, we wouldn’t have GPS, and we would not be able to have reliable bridges, and planes would take up way more time attempting to get somewhere than they do now! 

Euclid came next, and what he did was very important to philosophy and math. Euclid said that there are ‘axioms’, which are undeniable and unprovable things, and these axioms are the base of the world we live in. 

His first axiom is that between any two points there is exactly one line. 
Second axiom is that any ‘finite’ line, or a line that exists between two points, can be extended past those two points into the infinite line. 
Thirdly, a circle is defined by a center and the radius. 
Fourth, all right angles are equal to each other. 
Lastly, the fifth axiom: the parallel postulate, which says if there is a point p not on a line, then there is only one line through p that is parallel to the line. 

These five axioms go on to create all the rules of the world around us. When proving geometry, one must use these to build up more rules. Then those rules can be used further to prove more complicated structures and ideas. That is what formal geometry proofs do- prove, without a doubt, that if you start with one thing, you will end up certainly at another.

This type of knowledge makes humans able to create with speed and ferocity, and not get bogged down with guessing and checking constantly – or trial and error, which would lead to building collapses, cell phone outages, planes crashing into one another…. Which seems amusing until you realize that it isn’t temporary, it is destructive, and could happen to you. 

These are just the two ancient Greek geometricians that are most famous today. I’ll explore more geometry later!