The Life of Euclid

I'm going to be talking about Euclid. He is the father of geometry as you can see on the poster. I'm going to be talking about N Elements, which is the most popular or best known book that he wrote. That's a little bit about him. He was probably born around 300 BC. Nobody really knows for sure, but that's kind of the consensus on when he was born. He was born in Greece. Nobody really knows when he died, but it's probably based around 300 BC sometime. His name translated means good glory. I think that's just an interest. He probably studied at Plato. He was educated and for much of his life he lived in Alexandria, Egypt. So that's just a little bit about him and about his book Elements. It is his most widely known book that he wrote. It's the origin of Euclidean geometry. It's comprised of 13 volumes. Volumes 1 through 6 are on plain geometry. Volumes 7 through 9 are number theory. Volume 10 is theory of irrational numbers. Volumes 11 through 13 are solid geometry. His book Elements kind of took different concepts that were floating out there about geometry and it just put it together and made it really concise and simple for people or more simple for people to understand what geometry really was. Euclid had five postulates. I'm going to talk about them. This first one he states that for every point P and for every point Q not equal to P there exists a unique line L that passes through P and Q. Now in the second postulate he states for every segment A and B for every segment CD there exists a unique point E such that B is between A and E and the segment CD is congruent to the segment BE. In his third postulate he states for every point O and every point A that is not equal to O there exists a circle with the center of O and a radius of OA. The fourth postulate simply states all right angles are congruent to each other. Now in his fifth postulate it's also known as the parallel postulate. It states two lines L and M are parallel if they do not intersect. No points lie on both of them. His fifth postulate is also known as the parallel postulate and it states two lines L and M are parallel if they do not intersect and no points lie on both of them. Euclid had some very famous ideas. Of course everyone knows about his mathematical textbook. It was used around the world until today and it's still used today. Some other lesser known things that are still very important that people might not know is a book called the Optica. You might wonder what that means but just think optic. It's like the camera we're using. It has to do with what you see in your eyes. He did a lot of visual stuff especially with things that are spherical in the shape of a sphere. I'm not going to go into a great deal of detail but basically he said that objects appear to be different sizes depending on the distance from the object to you. So for instance if I look up in the sky and I see a star the way you see it it looks really small but it's not that small and this seems like a very basic idea but I'll tell you why it's important for us to know this idea because just think if we didn't know this then I could just pick up like an apple or like say this blade of grass and say oh well I think that this thing is the same size as this tree way over here or if you see a tree closely you say this is a really big tree. I think that this tree that I see way over here must be really small. They're not great examples of course but just think the implications that it would have for us in all other areas such as outer space. Like if we're studying the planets and we think it's the same size as earth or one is smaller or vice versa then we're going to get things wrong and leading on from that from that people developed different ideas and basically how we use it today is in mirrors in our cars and trucks. So when we look in the mirrors in our cars and trucks it has that little message things may appear closer than they really are. So from Euclid's idea of optica in his book we know just basically that just because things are different distances away doesn't mean that they're the same size they can be bigger or smaller and we use that principle to help protect us in our cars and we can see people in our mirrors. What is mathematics? Euclid once proclaimed that a student should learn mathematics not for the sake of knowing it for the sake of learning. There's been stories about Euclid that some may not be true but they're believed that these are true stories that Ptolemy once took a class of geometry taught by Euclid. He asked him is there a short road to learning geometry and Euclid pronounced there's no road to learning geometry. In another story a student once asked what is the sake of learning what is the goal of learning geometry. He proclaimed give this man money for what he has learned is good and that student was dismissed from the university. These stories give insight to Euclid to how Euclid felt about mathematics. He loved the study of geometry and he would probably answer the question what is mathematics along the lines of mathematics is is which a privilege to study something we should study not simply because we can gain from it but because it's beautiful and creates order. He believed that math should be studied not necessarily for a gain but for the importance of learning for the sake of it.