Heesung Yun EDCP442

 1. The subjects that were studied in the medieval universities were called liberal arts where liberal meant that they were for free men. As part of liberal "arts", it was surprising to see subjects such as grammar, arithmetic, geometry and astronomy which would be part of sciences to be considered to be arts.  2. The difference usages of the words logistic and logic: logistics meant practical and utilitarian usage of numbers and calculations and therefore were for children and slaves while logic meant liberal arts which corresponds to further study of numbers which were for the free men. 3. For Greeks, logistics was a study of dealing with sensible objects and doing computation, reckoning, the arithmetic of business while arithmetic was more advanced philosophical study of numbers that looked at the relations and nature of the numbers. This is quite contrasting to modern understanding of these words, as arithmetic often refers to brainless, repetitive calculations while logi...

 The film Dancing Euclidean Proofs  is a video that I would like to show to students in class in the future. I think that there is a common misconception that math is a rigid subject where there are very set tools, methods of solving and presenting understanding. I think that by showing this video to the students, they can learn that there are diverse ways to understand mathematical principles and there are no set ways that they have to show their understanding. Also as a person who majored in mathematics from the faculty of arts, I think that it would be a great opportunity for the students to see the artistic side of mathematics. However, I do not believe that the physically proofs activity would be very effective in the school settings because of several constraints that the students face. First, they have to understand the principles and theorems from reading the Euclid's Element which could be too difficult to them since they are not experienced with reading mathematical ...

 Most interesting fact that I observed from the presentations was frequency of appearances of familiar names in different presentations which shows the influence of these mathematicians across diverse fields of mathematics. For instance, ancient Greek mathematicians like Pythagoras, Archimedes and Euclid were mentioned multiple times in Dion, Yiru, Mike and Victor's presentations as well as my own. More over, modern mathematicians such as Descartes and Cardano were mentioned in Crystal, Ivan, and Dion's presentations. Another thing which I noticed is that most of the mathematicians were also vastly invested in philosophy. I knew that there were not much differentiating in mathematics and philosophy for the ancient Greeks as they viewed math as a way of epistemology, but I did not know that these commonalities continued until more modern times. During Emilie's presentation, she mentioned that Gauss wanted to be a philosopher until he was 19, and Descartes mentioned in Crysta...

 There were lots of cool facts that I learned from the presentations on Wednesday. One thing that I found most interesting is the fact that almost all mathematical discoveries were made across different regions at different times. Also it is very interesting to see that at times, mathematical knowledge that was lost in certain  regions were kept in different cultures which then gets reintroduced to the same region. In Yi Wei's presentation it was interesting to learn that Chinese first translated Euclid's work and had originally had the word rational numbers which was mistranslated to Japanese as reasonable numbers and came back to China as reasonable numbers instead of its original name. Besides the anecdotal things, I thought that the Indian mathematician in 1300 from Andrew's presentation being able to come up with a version of mean value theorem without any knowledge of Calculus was very impressive. 

 Although his work was first written and organized almost two millenniums ago, but schools have continued to teach it as one of the most basic and integral part of the curriculum. The article argues that Euclid's Elements is one of the best math textbook that exists and continue to will be in the future. I believe that this is due to the fact that it provides simple, understandable geometric features that can be extended and applied in more complex situations. In the Element, Euclid provides a propositions and gives instructions that are very easy for the reader to follow which makes it a good textbook. The beauty of his work lies in the fact that it is gives fairly simple and clear instructions of proof that are easy to be reenacted. Unfortunately I do not think that it is possible to postulate and define beauty from the standard of Euclidean geometry. There are other forms that are quite different from the work of Euclid that could also be considered beautiful. Euclid's work ...

What stuck out the most for me in the poem was capitalization of Beauty which normally is not. By capitalizing Beauty, I think that the author is putting two different meanings to the word. She first uses the word as its original meaning as most people understands, and secondly I think that she may be referring to herself. Throughout the poem, she claims that Euclid was the only person who had genuine understanding of beauty, which the second poem by David Kramer questions if she had read and seen other forms of art from different artists/writers. However, by referring to Beauty as a proper noun which also could mean herself, she is claiming that Euclid is the only artist who understood and believed in the definition of Beauty the same way that she does, not because she is ignorant of other forms of art. 

I think that it is very important to acknowledge non-European sources of mathematics since there are many benefits that can follow from studying mathematics from different cultures. By learning that there were different ways that the different civilizations used and proved same mathematical concepts, students can learn that there are several ways to approach a question. Often the creativity is ignored in math classes and students are asked to reiterate what they saw on the board, but by acknowledging different styles and approaches of different cultures, the students can naturally comprehend that mathematics is a creative process. Also, by studying mathematics from different cultures, students can be more appreciative of different cultures as they see that there were other cultures that were just as intellectually advanced as the western societies.   When I first learned that Pythagoras was not the first person to discover Pythagorean theorem, I was shocked and thought about th...