How is Geometry today related to the history of it?

Answer 1

Any field of study today is essentially the sum of its entire history. Anything that has been examined in a given subject has either given rise to new information and theories, or disproved existing hypotheses. Many ancient and historical mathemeticians, including Pythagoras and Euler, obtained geometrical results that are well known today. Other, more complex theories are the result of recent work that is still part of the history of geometry, having taken past in the past.