1 224 224 Professor Roybal History of Mathematics 10/21/08 History of Mathematics Project 1
This is an example of corresponding angles. In the diagram, the two horizontal lines are parallel to each other, and are crossed by a sloping straight line, causing angles to be formed. (Everett)
A proof is how to do a problem a proof will walk you through each step and elaborates on how to do the step or how to solve the problem. A proof is made so that everyone can read it and understand how to do the problem. It makes it so that someone can pick up the proof and know how to go through the steps to solve it. This makes it so that through the years everyone can learn the way the problem was meant to be solved. Proof based mathematics compared to non-proof based mathematics allows the student to get a step-by-step learning if the problem. This also gives a student another
224 2 way of learning the math if they are not a certain type of a learner. With non-proof mathematics you just have one way of learning how to do the problem. However, some student cant understand a non-proof way a little more. An example of the difference between proof and non-proof mathematics is how Greek mathematics was helped by proofs because it allowed the mathematician to get their work out of their mind and on to something to help teach it to others. Once the work was out in writing and explanations, others could go over the work and revise it or add to it. Because of the proofs being recorded on how they did it and how they understood the problems it allowed the world across all centuries to observe the work and learn from it and develop our understandings of the problems as well as adding a new since of how to solve the problem or make it easer to understand. The Greek mathematicians were also hindered by the proofs because it caused for questioning of their beliefs on how to do the problem. For example, some of the proofs were written for the problem long after the original thinker had passed on. For a typical text, the earliest copy was probably written one thousand years or so after the text. (Emerson handout) This creates a major because problem we dont know how the original mathematician really solved the problem. Some of the proofs like Euclids could be questioned. Some of the proofs could be discredited for example Proposition I 47 is the Pythagorean theorem, with a proof universally credited to Euclid himself, and the final proposition, I 48, is the converse of the Pythagorean theorem. The material of this book was developed by the early Pythagoreans. (Eves) If these proofs went unpublished then the wrong person was given credit for achievement that had already been done. The problem that I did was 5.8 the proof is as followed:
224 3
224 4
224 5 The advantage of doing this problem with a proof is that it will help get real detail into the problem and understand it a little better. If you do this proof by intuition you might miss certain aspect of the problem causing you to do it all wrong. For example, you might get that the line would not be all three angles adding up to the line to equal the triangle. For a typical student there it would probably be better to solve the problem by the proof. The proof would make it easier to understand and would confuse the student less and help them really understand and take the concept in and learn how to solve the problem. However, there are o...