Here is a really nice and neat PDF website that shows Euclid's solution to Quadratic Equations.
I am really into this topic, to prove a numerical equation by using geometry ideas, even though it is really hard to come up with a solution. I guess one of the reasons that I like this it is because it is new to me, I mean I do not think I have ever seen this way of proofing things before (maybe I have, but this is the first time I am actually "learning" it). I am wondering if there is a "trick" to it, like basic steps or ideas when we try to prove something using geometry.
- Did you notice that this is a link to an on line version of a part of our text? You can read this material there.
- I actually have not read this part of the text yet, I usually read the text after the lecture, and that is why I always do research before we talk about in class. Thank you for letting me know.
After class I wanted to know more about how the babylonians did math and naturally googled it. I found this link which gives some background on the civilization and more importantly some key points about how they did math. The first page or so is probably the most valuable but it goes on to explain their use of fractions and square roots and gives some examples of problems that they were capable of solving.
With all of this talk about the notion of a system of equations, I decided to look at the history of the development of systems. I wanted to get an idea of how the techniques for solving such systems evolved over time. I also wanted to see how much about system solving mathematicians knew both before and after al-Kwarizmi's development of al-jabr and al-muqabala. I did some research and found a cool timeline application that I made online. Maybe some people can give me suggestions for how to edit it, or maybe the class can make a timelines that we can work on together to trace the events for the units we have been discussing in lecture.
You can find the timeline here
Rob's timeline was very informative, I especially appreciated the brief synopsis of the major contributions. It seems to be a useful tool that we can use for other topics for the course.