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...

The book I chose to read for MTH495 was How to Bake Pi, by Eugenia Cheng. I chose this book, mainly because I love to cook and I felt that this book would make a lot of realistic life connections between math and cooking. This book was very easy to read, because it was broken up very nicely by topics and concepts and each chapter began with a recipe that was relevant to what would be covered in that chapter. I really enjoyed this book, but if I were to review it honestly, I wish that the coverage on some concepts was a little bit more detailed. There were some topics that were talked about several times throughout the book, and multiple examples were given. However, on some topics that I wasn't as familiar with, I felt as though the author didn't touch on them as heavily. I would have preferred a more consistent coverage of topics throughout the book, but the way it was written was still very fun to read. I think that having read this book, I am now more prepared to be an e...

What comes to mind when you hear the word infinity? Some might say forever, never ending, or a huge number that makes their head hurt just thinking about it. To me, infinity is so intriguing. I feel like every math course I've taken has had concrete answers to every problem we solve, every concept we engage in and every equation we analyze - except for the idea of infinity. There is nothing concrete about infinity. What really is infinity? Where does it start? Where does it end? Does infinity truly exist? Aristotle was the first mathematician to give a reasonable description of infinity in terms that are easily understandable to the general population. He divided infinity into two categories - potential infinities and actual infinities . Potential infinities  are like numbers. They go on and on forever with no exact ending point. For example, you could count numbers forever and ever, never reaching an end number. This infinity is one that Aristotle confidently believed in. An act...

Jennifer Nolan 0-th Blog MTH495 - Golden What is math? This answer will change dependent on who you ask, but since you've asked me, I will respond with my own opinion. Math is operations, math is numbers, math is shapes, math is patterns, and sometimes, math is hard. Math is all about applying the skills you've learned through your experiences with problem solving to come up with answers to specific questions. Math is all around us - it's in grocery stores, it's in finances, it's everywhere. People use math without even thinking that they are using math. If you are driving the speed limit on the freeway, how long will it take you to drive 70 miles? Some people might struggle with this question, making it more difficult than it needs to be. The answer is simple! If the speed limit is 70 mph, then you probably can drive 70 miles in about an hour. I'm sure people wouldn't think of miles per hour as a ratio, but it is. I told you, math is everywhere! ...