Monday, June 28, 2010
Mathematics in the Renaissance
We will now talk about the mathematical developments that took place in the 15th and 16th centuries in Europe. This period is generally referred as "Renaissance" which means "rebirth" (from the dark ages). There is a lot of incredibly beautiful mathematics which was developed during this period which initiated in Italy. Although there were many other developments during the Renaissance we will focus on the mathematical developments and look how they effected other fields of enquiry: art, music, navigation, physics and astronomy. Please post your comments here.
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After watching that video today in class I was really interested by the clips of monkeys remembering number order so I looked into it and found this website...
ReplyDeletehttp://www.spookyfilms.com/chimpmath.htm
Alex, that is a very interesting article. Thank you for sharing. It is indeed very interesting that monkeys can understand orderings and magnitude. What would be really cool is if these monkeys can be trained also to add and subtract numbers. To me that does not sound completely impossible.
ReplyDeleteAfter Mondays class, I was sitting down reading Katz when I thankfully stumbled upon perspective and the Renaissance. My roommate was next to me drawing an infinite train disappearing as far as the eye could see into the vantage point. I instantly got excited when I noticed that this is a derivation from Thales distance to a ship problem. Our eyes are separated from each other and the object creating a triangle. Since the distance between our eye is small we are left with being more accurate at smaller distances. Lets say an artist has no concept of trigonometry and geometry but, when drawing realistic pictures automatically draws like so. I believe we can argue that his brain "secretly" has an idea of how to "EYE BALL" the distance. The equation gives us an idea of how to draw. (for example, I have been drawing pictures of necklaces using what I know about inverse cosh)I couldn't even sleep thinking about how sports players like Michael Jordan or Peyton Manning can judge distances and excel in their appropriate sports by using this approximation. Note: I don't believe that sports players and artists can properly judge these distances by performing math but, to know how can give us a better understanding on how to make a better decision (whether it be probability in gambling or initial velocity throwing a basketball)
ReplyDeleteReading through renaissance history, it is almost clear in my mind that, the unease surrounding Mathematics is real. The reason I say that is because the development of Mathematics both in the east and the west and in the Renaissance period was developed as a necessity. The cubic equation was developed as a possible way to calculate interest over a period of 3years. Before the renaissance period the Greeks needed to calculate the distance of the enemy ships or the king needed to know if he had the right silver crown. So did the Indians wanted to build structures. For example unique fire alters shapes were associated with gifts from the God. Those who wish to destroy existing and future enemies would construct a fire alter in the form of a rhombus. Amazingly the theory or ritual is the origin of geometry. What I am insinuating is that mathematics could be much welcome if the goals are well articulated. Until university I had never known the real reason why mathematics and some of its very complex equations are been thought.
ReplyDeleteRegarding the video we watched yesterday… I always thought that mathematicians must have a call for Mathematics. They have to be born for that. It is really interesting that some of those people were struggling in Math while in school. How can this happen? Can anyone explain that?
ReplyDeleteMaria: Your question is very natural. As the saying goes "Mathematicians are not made. They are born". As you back in time, you will see fewer examples of mathematicians who struggled with Math while in school. This phenomena is completely unique to the 20th century way of education and research, I think.
ReplyDeleteIt seems very easy for anyone to become a mathematician in the current society. Such a thing was unthinkable in the past. Only the best and capable minds who had the drive and passion for math ended up being mathematicians. Such a thing is unfortunately not true any more. This is one of the reason why the overall quality of mathematics has gone down in the 20th century despite the enormous amount of math done in this century.
Remigius: I can summarise your comment in one sentence which I already mentioned in class:
ReplyDelete"NECESSITY IS THE MOTHER OF INVENTION"
This has been true throughout the history of mankind. Necessity is the driving force of invention.
In response to Maria and Dr. Chebolu, I believe a person is born into a certain skill set and can deviate up to their potential. One pursing the mastery of a subject that they may be weak in, will just have to try harder to reach that potential. Much like a Taylor series the further we travel the more accurate.
ReplyDeleteKevin: That is interesting. We shall discuss more about it in class today or tomorrow. There is a branch of geometry known as projective geometry which has its roots in the renaissance period. I will show some videos in class and you can appreciate the power of illusion which can only be explained in mathematical terms of projective geometry.
ReplyDeleteIn relation to the video we watched I found the people in the video to be very interesting; I mean there was a magician and someone that said that in school they were not really that good at math. This just shows that there is a variety of people that are mathematicians. I liked how one of the guys described a mathematician as someone who looks at things in a different way than the majority of people. I think this is a good description of mathematicians because I believe that they do think differently sometimes and that is what has led to some of the great discoveries and accomplishments of them. I thought it was interesting how they tied in real world examples when talking about synchronization of large systems and they showed how this is similar to flashing fireflies, cricket choruses, a beating heart, and a clapping audience. I think that real world examples are so important especially when it comes to teaching math. I also thought was interesting about the perfect shuffle and how that relates to computers being hooked together as well to other occupations.
ReplyDeleteanalex: I also thought it was intersting about the monkeys/chimps. I have seen such studies in some of my psychology courses and it is amazing how intelligent animals cane be!
To some degree I've got to agree with Bugs. There are some aspects of math that come more easily to me than others. I think it is how the brain is formed as to how we envision something. What makes a person a good athlete is not defined by their ball-handling skills but rather the extent of their ability to "see" the game...that is instinctive. I can practice my mathematical skills but that won't help me see processes and procedures.
ReplyDeleteAfter reading about mathematics in the Renaissance, I found it very interesting how important mathematics was to the development of other subjects such as art, navigation, and geography. When talking about the Renaissance in high school we always talked about how it was a very important time in the development of these subjects, but I don't ever recall being taught about how important mathematics was to the Renaissance. In particular I thought it was very clever how navigators not only discovered that the shortest route to another location was via the great circles of the globe, but also how they used time to determine longitude.
ReplyDeleteA quick little fact that I thought was interesting (and we didn’t go over in class) was how the current system of writing out the amount of money on a check comes from this time period because they were switching over from the bartering system to a money economy. It is crazy to think people were already worried about liars, people cheating them, and the greed people could have for money. It kind of can tie back to the idea how mathematicians started to become independent and hide their work from others. I feel money and power can sometimes bring out the worst of people and it is interesting to see how the systems change so did the intention of mathematicians.
ReplyDeleteThank you Jenny, for this interesting comment. It is impossible for me to cover everything in class because we are short on time. This is a rapid summer crash course on the vast history of mathematics. So it good that you and others are bringing here on the blog those topics not covered in class.
ReplyDeleteI know this course isn't strictly geared towards teaching mathematics, but I know most (if not all) of us are in or plan on going into the teaching field. I'm used to most of my classes discussing how we can use this information or that idea to help our students. While reading the chapters I've been trying to focus my thoughts on how I could incorporate this into a future lesson. 14.3.2 covers Blaise Pascal, Probability, and the Pascal Triangle. I found this particularly interesting and feel parts of it could be introduced in a high school classroom. I know I was taught the Pascal's Triangle as a cheat, but with this information I could be even more descriptive with what is really going on.
ReplyDelete-Ashley Runck
I definitely agree with you Ashley. Every reading assignment we have been given, I think of possible ways to apply the information to high school students. I think this class will help us answer the question, "Why do we have to learn this?" I know our fun talks concerning the Pythagorean theorem could be applied to high school students as well as the section you mentioned. If we give students a deeper understanding of what they are learning, they may understand better.
ReplyDeleteSide note: The video of the Vanishing head illusion didn't work for me at first. I had to use full screen if anyone else was having trouble.
In response to the previous two posts by Ashley and Michelle, I want to add that one of the main reasons why some students (at the high school level) find mathematics uninteresting (boring and dull) is because it is presented to them in an abstract manner without showing the relevance and connection to the real world. I bet that a student who hates geometry would instantly fall in love with it if you explain how you can use geometry to measure distances to the moon and the sun. The same comment applies without exception to all branches of mathematics.
ReplyDeleteGood point Michelle. For the vanishing head illusion to work it has to be in full screen mode.
ReplyDeleteAlso, if you are too close to your monitor it may not work, you have to be at a certain distance from your screen. So go back from the screen as much possible and gradually come close to the screen. At some intermediate point his head will appear to disappear. That point is called the "optical blind spot." With two eyes the blind spots cancel each other and everything would appear fine.
When it comes to what we were talking about yesterday with astronomy and people getting punished for having different beliefs from the church, I think that is really sad when they were actually correct. I cannot believe that Galileo was actually sentenced to home imprisonment and was actually correct and helped make some great discoveries. I wonder what he would have thought and the person that sentenced him to that would think now, after Galileo's thoughts were proven correct?
ReplyDelete