Why is Euclid important?
Euclid was a famous Greek mathematician known as the Father of Geometry. He wrote a textbook, Elements, which was considered one of the most important textbooks in the history of mathematics. In this textbook the principles of Euclidean Geometry were introduced from a small set of axioms. Euclid understood that building a logical geometry depends on the foundation, this began with Euclid's book. It has 23 definitions (some listed below), five unproved assumptions which Euclid called postulates (now known as axioms), and five further unproved assumptions that he called notions. He then goes on in the book proving elementary theorems about triangles and parallelograms and ends with The Pythagorean Theorem. Below are the basic definitions brought to us by Euclid that are used as the foundation of much of mathematics:
Definition 1. A point is that which has no part.
Definition 2. A line is breadthless length.
Definition 3. The ends of a line are points.
Definition 4. A straight line is a line which lies evenly with the points on itself.
Definition 5. A surface is that which has length and breadth only.
Definition 6. The edges of a surface are lines.
Establishing these terms was a major step in mathematics. Not much is known about Euclid's life except that he taught at Alexandria.
Below is a representation of Euclid's Windmill Proof which we saw in class.
Sources:
http://en.wikipedia.org/wiki/Euclid
http://www.britannica.com/EBchecked/topic/194880/Euclid
So what is math? Originally when I read this question I was going to respond by saying math is the study of different topics including calculus, algebra, trigonometry, and geometry. But those are just different subjects within the field of math.
I think math is a language in which people speak using numbers, formulas, critical thinking, and problem solving. Those are not the only components related to the language of math though, there are many different ones. I think critical thinking and problem solving are a big chunk of what math is. Math is interesting because whether you are aware of it or not, you use it every day. Math is used when you go shopping, when you cook, while playing sports, exercising, and in many other every day activities. Answering this question is not easy because people use math in many different ways.
Milestones in Math
1) The Pythagorean Theorem: I have always found this theorem to be a significant tool used to help us further our knowledge of trigonometry. It's main purpose to find an unknown in an equilateral triangle is just one of the many uses for this theorem but as we have learned one you can do that you are able to figure out angles and lengths in other shapes as well.
2) The Quadratic Formula: Since my very first algebra class I was asked to memorize the Quadratic Formula which has proved to be a very useful tool in algebraic problems. I would consider this one of my favorite tools in math because it is used quite often and once memorized is very helpful.
3) When it comes to calculus which has surprisingly become one of my favorite topics in math, you cannot forget to mention Sir Isaac Newton. He was largely influential in the history of mathematics for creating calculus. This was so important because it allowed us to take our calculations a step further. The study of calculus was such an advancement in the field.
4) Numbers & Counting: I guess none of this would be possible before the discovery of numbers and counting themselves. This would be considered the very center of all things math.
5) Proofs: As much as I hate to admit it, I think proof writing is a very big aspect of math. The ability to solve an equation is one thing, writing proofs uses your critical thinking. I have always been rather good at solving equations but the tough part for me is typically writing down the steps, theorems, and thought processes I used to arrive to an answer. It makes you question different things we learn in math and prove them to be true rather than just excepting an answer or rule because someone says so.
