MTH495

If I could meet any mathematician and chat over dinner, I would choose the one and only Euclid. I didn't think there would ever be a class where I would actually enjoy writing proofs, but Euclidean Geometry changed that for me. Through trying to learn more about Euclid, I found that there isn't a lot known about his early life - when or where he was born, his early childhood, his family life. He is commonly referred to as the "Father of Geometry", and he is said to have founded and taught at a school in Alexandria where he wrote his book The Elements, a book that is split into 13 separate books, each one focusing on a different topic in geometry. Alexandria is a town in Egypt that is currently the second largest city in Egypt, playing a major role in Egypt's economy. It lies on the coast of the Mediterranean Sea, and was said to be founded by Alexander the Great. In its early years, it was a very popular place for scholars to travel to, as it was one of the most...

I think so far this year, the most mindblowing thing that I have experienced in this class was Aristotle's wheel. There aren't too many things that I take home from my math classes and ask my roommates opinions, but this was one of those things. I became intrigued by this paradox because it simply had never crossed my mind. Walking to my car, I looked at every wheel/tire on a car that I passed. I just couldn't figure out how the heck that thing worked. So I took it to my trusty friend Wolfram Alpha and got some answers. The popular graphic of Aristotle's wheel seems as though it is illustrating that two circles with drastically different circumferences unroll themselves and end up having the same length. However, this is not the case. Aristotle's wheel is really illustrating one-to-one correspondence. The site that helped me grasp this concept stated the following "The cardinalities of points in a line segment of any length (even an infinite line, a plane...