Tuesday, November 17, 2020

Reflection on Assignment 1

For this assignment, our group chose to work on discovering rules in multiplying and dividing by 6 in the sexagesimal system. We have talked about the sexagesimal system quite a lot in class, and our classmates also have some decent knowledge on how to work with numbers in the sexagesimal system with the multiplication tables. 

Clearly, talking about the multiplication part was not challenging in this assignment. The more difficult part was understanding and explaining division in the Babylonian system. Our group explained the concept of Babylonian exmaple with an example. We believed our explanation was clear and everyone understood how it worked. The most challenging part in this assignment was the modern way approach portion. It was not as simple as we have seen with the Babylonian system. The modern way approach actually involves more calculation and requires deeper knowledge in math to fully undesrtand the rules. Overall, I think this is a meaningful assigment for math teachers and I enjoyed working with my partners,Chloe and Yiwen. 

Friday, November 13, 2020

Blogging on Euclidean Proofs Dance

 The idea that mathematical proofs can be represented through dance has truly amazed me. I have to admit that I would not have came up with such a creative idea if I was asked to. The beauty of dancing surprisingly worked well with the Euclidean proofs. Using body and arms as the compass is very thoughtful. I also think that the choreographers chose to make the dance moves on sand is very ingenious. They are not only dancing, but they are also drawing out the Euclidean proofs with their bodies using sand as the paper. The fact that all their work "would eventually be erased by tide and wave" makes the whole scene very poetic. They are able to show the proofs through dance, but they don’t last forever. It makes me link to the idea that there is a time limit on beauty. The whole dance is in fact very aesthetic and enjoyable. 

Sunday, November 8, 2020

Blogging on Euclid Poems

 Background on Euclid of Alexandria 

Euclid is a Greek mathematicican who lived in Alexandria in Egypt around 300 BCE. 

He is also known as the Fathter of Geometry

He wrote "Stoicheion" or "Elements", which is the most important and successful mathematical textbook of all times. His work also include division of geometrical figures into into parts in given ratios, catoptrics (the mathematical theory of mirrors and reflection), and spherical astronomy (the determination of the location of objects on the “celestial sphere”), as well as important texts on optics and music.

information retrived from https://www.storyofmathematics.com/hellenistic_euclid.html


Euclid Alone Has Looked on Beauty Bare

by Edna St. Vincent Millay


Euclid alone has looked on Beauty bare.

Let all who prate of Beauty hold their peace,

And lay them prone upon the earth and cease

To ponder on themselves, the while they stare

At nothing, intricately drawn nowhere

In shapes of shifting lineage; let geese

Gabble and hiss, but heroes seek release

From dusty bondage into luminous air.


O blinding hour, O holy, terrible day,

When first the shaft into his vision shone

Of light anatomized! Euclid alone

Has looked on Beauty bare. Fortunate they

Who, though once only and then but far away,

Have heard her massive sandal set on stone






The Euclidean Domain

by David Kramer

…Euclid alone

Has looked on beauty bare. Fortunate they

Who, though once only and then but far away,

Have heard her massive sandal set on stone.

—Edna St. Vincent Millay, Sonnet



Euclid alone has looked on Beauty bare?

Has no one else of her seen hide or hair?

Nor heard her massive sandal set on stone?

Nor spoken with her on the telephone?



Proud poets, as you penned your paeans to Beauty,

Did you not think it was your bounden duty

(Though it were one that any might have loathed)

To tell that you have only seen her clothed?


And as you sang praise, Orpheus, of Eurydice,

Your mouth became the orifice of your idiocy!

For Beauty bare you never yet had seen,

’Twixt Hades’ depths and lofty Hippocrene.


O Beauty! Would you, for this mathematician,

Remove (if it would cause to give permission

To look on Beauty bare too great a scandal),

Once only, and then but far away, your sandal?


It appears that Millay has portrayed Euclid as the mathematical god who is above all mankind. Through this poem, Millay has applauded Euclid for his work and findings in mathematics.

In Millay' poem, Euclid is able to see the Beauty Bare in mathematics.

 Now, what exactly is Beauty Bare? 

Since Euclid has looked on Beauty Bare alone, it must be something or someone that could be observed and examined by. In relation to Euclid's work on mathematics, Beauty Bare could possibly be some mathematical related concepts or objects that might have given inspirations to Euclid while he looked on it alone. It is possible that Millay is trying to convey the message that Euclid was able to figure something out from looking at the Beauty Bare alone. 

The parody poem written by Kramer has challenged Millay's illustration on Euclid looking at Beauty bare alone. Kramer began by questioning the fact that Euclid was viewing the Beauty bare alone, and no one else has seen or heard about it. I begin to wonder if Kramer was questioning whether Euclid has done all the findings himself? Or he was just criticitizing the fact that Millay has blindly praised Euclid for doing the findings alone without knowing the legitimacy of his work. 

Anyhow, Euclid has contributed remarkbly to mathematics without doubts. 


Saturday, October 17, 2020

Blogging for Eye of Horus and Unit Fractions in Ancient Egypt

 


The most interesting finding is that people still use the Eye of Horus today. In Mediterranean countries, fishermen would paint this symbol on boats and vessels for protection. People would also make this symbol into jewelry to wear daily for protection against illness. It is also a symbol of power, knowledge and illusion. 



Chinese people dislike the number "4" because its articulation sounds very similar to "death" in Mandarin and Cantonese. In most buildings, floor and unit numbers do not have the number 4, so there are no 4th,14th,24th ..(so on) floors, and no unit numbers such as 104, 114, 204.. etc.  Contrarily, Chinese people favor the number 8 because it sounds very similar to "make a fortune" and "become rich". 

Constructing a magic square

 

Rule: each number from 1 to 9 is used once, and where all the rows, columns and diagonals add to 15 
I also tried to make a 3x3 magic square with different numbers, but I failed. 



Saturday, October 10, 2020

Oct13 Response to Was Pythagoras Chinese?

Does it make a difference to our students' learning if we acknowledge (or don't acknowledge) non-European sources of mathematics? Why, or how?


If we do or do not acknowledge the non-European sources of mathematics, for most of our students, I don’t think it will make a difference as long as they learn what they are suppose to learn as prescribed on the curriculum. I think it will only make a difference to those who are interested in knowing more about mathematic history. For example, if we acknowledge the Greek and Chinese sources of mathematics, students who are interested in the Chinese or Greek culture may be more attracted to the information presented. However, as teachers, it is worth noting other non-European sources of matematics so their students recognize that there are other people in the worlds who also contributed to the knowledge we are learning today. Nobody's contribution should not be ignored. 


What are your thoughts about the naming of the Pythagorean Theorem, and other named mathematical theorems and concepts (for example, Pascal's Triangle...check out its history.)


It is interesting to see that most mathematical theorems and concepts are named after the main contributor who discovered or proved the theorems in the Western culture. Whereas the Chiense had named their theorems and concepts differently.  For example, the Pythagorean Theorem is named Gougu Theorem in Chinese because ancient Chinese called the right triangle "gougu". I like the idea to have theorems and conpcets named after the contributors/founders because it show apprecitaion and acknowledgement to their hard work.

The method of False Position

 




course reflection

What fascinates me the most about this course is the range and depth of topics that we have covered. When I first saw the title of the cours...