Euclid aka. Euclid of Alexandria I believe to be so important because he is considered the “Father of Geometry.” I find Euclid interesting because we know so much because of him, yet we know very little about him. In fact, even his birth and death are estimations based off writings found from his time period. Euclid was believed to be a student of Plato, and is most famous for his work within geometry where he wrote 13 books known as, The Elements. These books are split up into the following topics:
Books one thru six discuss plane geometry
Books seven thru nine have to do with number theory
Book ten deals with Eudoxus’s theory of irrational numbers
Books eleven thru thirteen discusses solid geometry
Euclid was said to compile these Elements from a variety of men before him such as Hippocrates of Chios and Theudius.
I am most familiar with the 5 assumptions from Book I, that Euclid called postulates or axioms.
1. Given two points there is one straight line that joins them
2. A straight line segment can be prolonged indefinitely
3. A circle can be constructed when a point for its centre and a distance for its radius are given
4. All right angles are equal
If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if
5. produced indefinitely, meet on that side on which the angles are less than the two right angles.
These to me are some of the foundations for understanding geometry, specifically Euclidean geometry.