Reflection on Assignment 1

 In our first assignment for this course, we talked about Babylonian arithmetic using base 60 sexagesimal system. We learned about the history and Babylonian way to multiply and divide in base 60 system as well as the modern way interpretations of multiply and divide in the sexagesimal system. Overall, I think the organization of our presentation was reasonable. We covered some basics at the beginning so that audience have good background for the later content. One thing we would consider to improve in the future is to include a slide for summary and wrapping up. We shouldn't have ended our presentation abruptly. We had rehearsed several times before the presentation to make sure we had good pacing. We didn't use much of materials from the media but we did have activities to engage the class with some interactions. I would say that we did a satisfactory job and we will take what we have learned for the betterment of our future studies. 

 

Number with personality

Ramanujan considered that each of the positive integers was one of his personal friends. According to Major’s paper, this type of individuals who have the tendency to put personal characteristics to numbers are thought of having Ordinal Linguistic Personification (OLP). Comparing numbers as his personal friends, Ramanujan associated not only the personalities to numbers, but also possibly ages, genders, looks, and etc. Since OLP is one type of synaesthesia, one can presume that Ramanujan can make connections between many different kinds of mental experience. 

I would consider introducing the concept of linking characteristics and numbers to students at lower grades. The reason is that I have seen young kids who are emotionally scared of mathematics. Some may call this the “math anxiety”. Asking students to give numbers personalities and characteristics might help them “dedemonize” math. For example, a student can think of himself as “Zero”. “One” is the guy living next door. “One” is a weird old man who only makes friends with people who are “primes” such as “Two”, “Three”, or “Five”. “Three”, “Four” and “Five” are living down the street and they formed a band called “P-Triple”. They are proud to be the band with the youngest average age. However, “Six”, “Eight”, and “Ten” are in another competing band called “Nobody is Odd”. The story can go on with more characters and more plots. The point is to make students more familiar with numbers and their properties. Also, some important attributes of math such as creativity and imaginations are promoted in this type of learning. 

As a math student, numbers always means more than just numbers to me. For example, I really like the number “seven”. For some reason, “seven” is disliked by many people. But to me, seven is an interesting number. It is single digit, prime, odd, and “hard to get along with”. However, it is not only a Mersenne prime, but also a double Mersenne prime. It has the highest probability of being rolled with two standard dice. It is, outside of three, the only other dimension that a vector cross product can be defined. And one thing everyone knows, we have seven days in a week!! So, to me, “seven” is like a low-key and odd person that is often underappreciated by the others. Many of my favorite people are like that. Hence, if I have to pick a favorite number, it will definitely be seven.

The dancing Euclidean proof

 1. “embodying mathematical concepts and relationships through dance and movement”

Dance and movement can be done by person(s) with or without an object such as a stick or an umbrella in an environment in which the action is possible. These actions can represent a mathematical or physical process such as drawing a line, a circle, marking a length on the line. Even the speed of a moving particle can be represented by adjusting the speed of the dancer movement. I see a lot of opportunities not fixed to euclidean proofs. For example, we can have two concentric circles with different diameters. Two dancers move along the circles at two different speeds such that they complete one round trip at the same time. The audience can clearly see that the dancer on the larger circle moves faster (greater linear speed) to keep the same angular speed as the other dancer on the smaller circle. 

2. “potential to make the beauty of Euclid’s proofs accessible to mainstream audiences”

Dancing and moving make people feel good, happy, and engaged. By allowing learners to participate or even watch others doing the dance we create a happy learning environment. This is a good benefit of dancing and movement whenever possible in helping people learn through doing something that makes them happy.

3. “Help students understand and appreciate the beauty of Euclid’s proofs in new multisensory, experiential ways”

 

By dancing to construct a mathematical process students are part of the construction tools and objects (pencil, divider, ruler, etc.). Before the dance, students need to plan each move and entire process - that gives the exterior point of view. During the process students manage the movement, direction, magnitude and speed. Therefore they get the whole interior view of the process. 

Explication and commentary on a poem about Euclid

 Poem 1: 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.

Speculation

Euclid alone saw the beauty of geometry (or geometry is the beauty) clearly (in his time). Euclid displayed the beauty he saw to the rest of the people. That made people who talked foolishly about the ‘geometry’ going silent. Geometry made people come face to face with the world they live in and not to be selfish in the old way in which they learned nothing. After passing through many different generations, many people still did not understand geometry. But those who understood geometry escaped from the dark world and came to the world in which they used geometry to build civilization and beauty.

The old days before the geometry were primitive and terrible. At the first opportunity of the beauty of geometry in details, Euclid was alone who saw it clearly.

When Euclid first understood the concept of geometry, it was him alone who saw the beauty in details and clear. The event that Euclid managed to compile a complete beauty of geometry happened once, but far away from our time. It was fortunate that people re-discovered the beauty. We have heard the great importance of geometry as a massive sandal set on stone more than 2000 years ago! (metaphor, according to wikipedia Eda was a feminist)

Poem 2: The Euclidean Domain

…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?

Speculation

Repeat the second part of the poem by Edna St. Vincent Millay.

Is it true Euclid alone saw the beauty of geometry bare (clearly, completely)?

Has no one else seen her (geometry) hiding or even just her hair? (metaphor)

Has no one heard of the importance of geometry? Has no one heard that geometry set her sandals on stone (and sent out the loud sound wave) more than 2000 years ago?  

Has no one worked with geometry? Has no one spoken to geometry on the phone?(Sarcasm)

You (Edna) were a proud poet. You wrote your poem of praise to geometry (beauty). Did you think that it was your burden (duty) to tell that you only saw the surface of the beauty of geometry? It looked like this is something anyone was unwilling to do.

(Edna might not be trained as mathematician according to wikipedia)

As you sang the praise (Edna’s poem) - at this point David used the comparison with Orpheus mourning, praising his late wife Eurydice (both from ancient Greek mythology) - your mouth became the pipe producing your idiocy (stupidity). Because, you have never seen the bare beauty of geometry. It was between the depths of the Hades (god of the dead) and self imposed inspiration.

O beauty (geometry), would you, for this mathematician (is it David?) remove the event that ‘Euclid or someone discovered you in whole’ (which is taken as the beauty set her sandal on stone with a loud sound) into our world more than 2000 years ago? Would you (beauty) please, for once, go back in time and did not set your sandals on stone? To look at that beauty could come with a great scandal.

Notes: According to wikipedia, Euclid presented the already discovered geometries into one single logically organized work. His contribution seems to be the organization including writing axioms, and putting proofs in the collection.