Tuesday, June 15, 2010
Greek Mathematics
We are currently talking about the Greek Mathematics. In my opinion this is the most fascinating part of Mathematics. Please feel free to share your thoughts and comments on the topics we are covering in class on this blog. Here you have 100% freedom of thought and speech. This blog is a forum for students in the class to share their ideas. You will get participation points for posting messages and replying to the posts. So welcome aboard to the fascinating journey of the history of Mathematics and post your ideas and comments as you read the book.
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I just started reading the Men of Mathematics on google books... It says pages 5 and 6 are omitted, is that just for me or is that like that for everyone?
ReplyDeleteI think one of the most fascinating things about the Greeks is that they were the first ones to pursue math for pure joy. Far too often, math gets a reputation of being boring, dull, or connected to science (as we read in the introduction of Men of Mathematics), but as we saw from the findings Thales had from measuring the heights of pyramids and finding the distance from shore to a boat, math can be quite interesting and fascinating at times. Back in the day, those problems Thales solved might have seemed terribly hard, but with the proper mathematical techniques it turned what some thought was an impossible problem into a fairly simple explanation. Also, one of the things I thought was very interesting but we did not discuss in class was how they built the tunnel thorough the mountain. I thought it was neat that they used their number system to track how far that had gone everyday as well was using flags to make sure they were going straight. It was those simple techniques that got them to construct the tunnel and it is interesting to think that those basic techniques they used are some of the same foundational ideas construction workers use this day. Finally, I thought it was very interesting that the banner to the entrance of Plato’s academy read “Let no one ignorant of geometry enter here”. Like I said in class, it is interesting to see how the focus of math in the school systems has change over time and how with new discoveries the focus is put on different topics.
ReplyDeleteAnalex: It happened for me too. It was some of the later pages as well.
ReplyDeleteJenny I totally agree with what you said. I'm going to be a teacher and so often kids complain and whine about doing math but in reality I think they also ask many of the same questions posed in mathematics. Perhaps if they were on the beach and actually measuring the distance to the boats using geometry they could spark and interest in mathematics, it may be an impossible task for the classroom but the concept should still be mentioned in class at least. I think if more history of mathematics (explaining why these things were developed and what questions they answered) along with real life examples, perhaps a new outlook would be taken towards mathematics.
ReplyDeleteAlso with the sign above Plato's academy, I think that a lot of times mathematics plays a role in different subjects (such as geometry and logic in philosophy) but people only recognize it when they see numbers. Perhaps if they understood math as more of an exercise of the mind rather than simply calculations they would appreciate it more.
I think the most impressive feature of Greek Mathematics is the number of centuries they were ahead of their time. Even by modern standards, the Greeks were very superior in their thoughts, ideas, and philosophy. No other civilization comes even close to the Greeks in this respect. The Golden age of Mathematics is the Greek era. Any comments?
ReplyDeleteI was skeptical about having to read Men of Mathematics, but before even getting very far into it I realized it would be worthwhile. From the very beginning it talks about changing what most authors call the preface to the introduction so that readers would not skip over it. Normally I would be a reader to skip over anything called the preface, but more likely to read an introduction.
ReplyDeleteI also like how in class we have been instructed by Sunil to skip what might seem too technical but to get the whole idea of the chapter. I see this mentioned in Men of Mathematics as well when it says, "skipping is not a vice... but a virtue of common sense." This doesn't strictly relate to Men of Mathematics or our class textbook, but all subjects and areas of life.
Reading chapter 3 was difficult for me. I found the material dry and dull but after today I feel better assured about the work of Euclid. The additional information given by Sunil helped me gain a better understanding of his 5 postulates and their role in Geometry and also allowed me to have a greater appreciation for his work, passion for math, and brilliant knowledge base. I remember Euclid's name being mentioned in my Euclidean Geometry class but I now know more of his life and journey to discover what he did. His book, Elements, is claimed to be the most important work in Science... not many people can say the same, this guy is pretty cool!
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ReplyDeleteI think the last sentence in the Introduction of God Created Integers is compelling ("The greatest wonder of the modern world is our own understanding" ). It can have different interpretations but I feel like it's saying our understanding and our knowledge is undefined. We can read scholarly journals, study books, or listen to lecturers but it is what we do with our understanding that is the unknown. The introduction explained the progression of Math and the impact previous Mathematicians had on ones that came after them. Without the understanding of the more recent Mathematicians when studying past Mathematicians like Euclid, Descartes, Newton and so many more... Math may not have evolved into what it is today. People can take what they have learned and turn it into something new.. maybe a new phenomenon, or people can take what they know and share it with others, or others can digest that understanding solely for their own personal gain. Putting a capacity on the amount of knowledge one can take in is impossible. People are learning new things everyday; we are continually being taught new things and understanding new concepts, and I think this process will continue to repeat itself until our time is up.
ReplyDeleteI would like to add something to what Christine wrote. It is true that the last sentence by Hawkings in his introduction to God Created the Integers is rather striking and compelling. I think it is also referring to the profound question of why this mode of sheer thinking should help us understand and unlock the deepest secrets of nature which have enabled mankind to attain heights which were unthinkable. Therefore there is no doubt that the biggest wonder of our modern world is our own understanding.
ReplyDeleteAlso the more we learn, the more we realise how little we know. There is no end to the process of learning and discovery. This reminds me of the famous proverb from Latin which says
ARS LONGA VITA BREVIS
which means "Art is long, life is short." In other words the life of a human is too short to master any form of art because any art, be it math, music or physics, in its totality is infinite.
Along with the previous two posts, I find it interesting in the into "Men of Mathematics" it goes on to say that most early discoveries in the field of mathematics have either been trivialized to the point of being included in elementary textbooks or lost in the shuffle of bigger discoveries. This is reiterated in the intro "God created the Integers" where credit is given to those who "paved the way". Without a base from which to work from, it is hard to know if you are moving forward or not. For those of us that are still students of mathematics (of which I hope we all are) or teachers of the discipline, rigor is still needed.
ReplyDeleteI agree with Jenny about how it was interesting that the Greeks were doing math for the pure joy of it. I know at my high school the majority of the students did not seem to like or understand math. I think that sharing some of the history behind it and some of the videos we have seen already in class might make them more interested in the subject. This will help them see that the stuff they are learning is important because it was discovered so long ago and is still a huge part of mathematics.
ReplyDeleteI thought that in the introduction of "Men of Mathematics" it was interesting how they described who some of the great mathematicans are or were. That they are not always professors and some did not even have an occupation.
I was impressed with the ideas and discoveries that were discussed in Chapter 4. I thought it was impressive and funny how he got the idea about the volume of the gold in the crown. I think that would be a good story of video to share with a high school class. I also thought the weapons of war that he created were creative and interesting.
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ReplyDeleteIt was very interesting to read about the death of Hypatia. I can’t believe they tied the knowledge of philosophy, mathematics, and astronomy into satanic work. What did everyone else think when they read this section? Also, did this happen to other men in mathematics at that same time as well?
ReplyDeleteYes, it happened to at least one man of the Greek era, although in a different form. It is a very sad story of the death of Archimedes. According to some popular accounts Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet the General but he declined, saying that he had to finish working on his circles on the soil. The soldier was enraged by this, and killed Archimedes with his sword.
ReplyDeleteAs E.T. Bell mentioned, no Roman lost his life because he was absorbed in the contemplation of a mathematical diagram!
(In relation to Jenny's comment) I think it is sad that Hypatia and Archimedes were both killed. I wonder what else would have been discovered if they had not been and how that would have changed the history of math. I found it interesting that there are not really any other records of Greek women being mathematicians before Hypatia.
ReplyDeleteI wasn't really sure what to read for "What is Mathematics?" so I read the part titled What is Mathematics? and the Introduction in Chapter One. I like the part that says"...it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science." This statement just shows how much work is behind the developments and discoveries in math throughout the years and how important they are. They build off each other to be able to discover new ideas and facts. I thought it was interesting that the Babylonians actually developed or discovered math first and what they discovered would now be considered elementary algebra, but the idea of math really did not emerge until Greeks. I wonder if this is because Greeks made so many developments in math; astronomy, axioms, number system, levers, deductive reasoning, and many other things. I thought it was interesting that the idea of axiomatic crystallization and systematic deduction acutally disappeared in the 17th and 18th centuries. The 19th century was a very important time in math because that is when there was the return of classical ideas and proofs as well as new advances. I wonder what would have happened though if those Greek mathematical developments did not disappear for those two centuries. In the introduction of chapter 1 it say that numbers is the basis for modern math. This is a statement that I would agree with because when people usually think about math it usually think of numbers as well as other things. Children in school would also think of numbers because that is the basis of math.
ReplyDeleteBy the way, I forgot to mention what the famous English Mathematician G. H. Hardy said about Greek Mathematics. He said, ``Greek mathematics is permanent, more permanent even than Greek literature. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.”
ReplyDeleteThus Mathematics has a sense of absolute permanence unlike languages and physical theories which eventually die.
Okay, here is my solution for Eratosthenes calculation of the circumference of the earth on any given day.
ReplyDeleteCirc = (360/(<FHE - <ABC))(arc distance of CE)
Where:
<FHE is the angle of the shadow created by the stick in the Southern city
<ABC is the angle of the shadow created by the stick in the Northern city
C is the Northern city
E is the Southern city
Good job David! That is exactly the solution I was looking for. You get extra credit for this.
ReplyDeleteI have been also interested in easier ways of doing Math operations without the use of calculator. For reference… I have never used a calculator while in school. I have completed my bachelor degree in Mathematics without a calculator – if you can believe that. So, during the weekend, I found myself searching the internet about Vedic Mathematics just to discover other ways of doing multiplications or other Math operations and also telling my friends and family what I learnt in my History of mathematics class… I really enjoyed it!
ReplyDeleteHere is another example:
32 x 38 = 1216
Both numbers here start with 3 and the last figures (2 and 8) add up to 10.
So we just multiply 3 by 4 (the next number up)
to get 12 for the first part of the answer.
And we multiply the last figures: 2 x 8 = 16 to
get the last part of the answer.
Can use the same one for: 24 x 26 =; 62 x 68 =; 17 x 13 =; 59 x 51 =
Isn’t that easy? I wish I can remember all these rules and use them in the future.