Hi ! I’m Hyun Yen. I heart Math 🙂

Thanks.

Science and Math
Science and Math World

(From 11/ 2013 to 11/2017): It has been 4 years since, I created my blog on Tumblr: Spring of Mathematics. I remember that: Geometry in daily life (Herb pot) is my first post on Tumblr.

Currently, I am also very happy for teaching mathematics and research. After a long time, I have been working with the lecture hall. My mathematical passion hasn’t diminished.

Thank you everyone and the Tumblr math community! I’ve learned so many things and had lots of fun. Thank you all 🙂

**Brachistochrone Problem & cycloid. **

GIF:Source is Vsauce / The Brachistochrone :https://www.youtube.com/watch?v=skvnj67YGmw.

**Which is the quickest path?** …. The cycloidis is the curve which yields the quickest descent.

Suppose there is an incline such as that shown in Figure 1. When a ball rolls from A to B, which curve yields the shortest duration? Let’s assume that we have three hypotheses: a straight line, a quadratic, and a cycloid. The shortest path from A to B is the straight line, so one might think that the straight path is the fastest, but in fact it is surprisingly slow. It’s better to select a path which has a downward drop in order to accelerate the ball in the first phase, so that it rolls quickly. The ball arrives earlier on the quadratic path than on the straight line path. However, increasing the degree of the function causes the ball to travel more slowly on the flat section.

It is said that Galileo (1564-1642) first presented this problem. It is also known that the cycloid is the curve which yields the quickest descent. This time I will discuss this problem, which may be handled under the field known as the calculus of variations, or variational calculus in physics, and introduce the charming nature of cycloid curves.

See more atThe Brachistochrone Curve: The Problem of Quickest Descent by Yutaka Nishiyama- PDF.

** (**Written by** poet ****Lilia Rose )**

*Shapes of the Past.Numbers of the PresentVariables of the Future.*

*Shapes are different for every little hand drawing them,every grown-up touching them.Sometimes they miss a point,only later to remember and disappoint,in finding it too late to mend,that broken shape.*

*Numbers are the same every time you see them,a constant in problems and mazes of wits.Yet, with 1 careless mistake,it changes, never to be fixed again,because you wrote in pen,with the confidence of a youth, the bane and talent of adolescence.*

*Variables change every time you try to simplify them.Yet they never change their appearance,staying the same throughout.Until that moment, reaching the last step,they just become additional numbers,that might be the right or wrong solution,later confirmed with substitution. *

Wow! 🙂

[https://soundcloud.com/huyn-n-y/shining-the-morning-cd1-morning]

♩ ♪ ♫..

♩ ♪ ♫

Mama loved Me to infinity ∞

**Infinity** …

… it’s not big …

… it’s not huge …

… it’s not tremendously large …

… it’s not extremely humongously enormous …

… it’s

…Endless!

**Infinity** has no end. Infinity is the idea of something that has no end.

to show that: The set T is uncountable. He assumes for contradiction that T was countable. Then (all) its elements could be written as an enumeration s1, s2, … , sn, … .

Applying the above theorem to this enumeration would produce a sequence s not belonging to the enumeration. This contradicts the assumption, so T must be uncountable.

**Calculus:**

**Geometry and topology: **Infinite-dimensional spaces are widely used in geometry and topology, particularly as classifying spaces, such as Eilenberg−MacLane spaces. Common examples are the infinite-dimensional complex projective space K(Z,2) and the infinite-dimensional real projective space K(Z/2Z,1).

**Complex analysis**: By stereographic projection, the complex plane can be “wrapped” onto a sphere, with the top point of the sphere corresponding to infinity. This is called the Riemann sphere.

In complex analysis the symbol {\displaystyle \infty } \infty , called “infinity”, denotes an unsigned infinite limit. {\displaystyle x\rightarrow \infty } x\rightarrow \infty means that the magnitude {\displaystyle |x|} |x| of x grows beyond any assigned value. A point labeled {\displaystyle \infty } \infty can be added to the complex plane as a topological space giving the one-point compactification of the complex plane. When this is done, the resulting space is a one-dimensional complex manifold, or Riemann surface, called the extended complex plane or the Riemann sphere

**Fractals: **The structure of a fractal object is reiterated in its magnifications. Fractals can be magnified indefinitely without losing their structure and becoming “smooth”; they have infinite perimeters—some with infinite, and others with finite surface areas. One such fractal curve with an infinite perimeter and finite surface area is the Koch snowflake. [ ]

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**SONG: A Mother’s dairy **

母の日記 (日本語の正式バージョン-

**Origin of song , is in Vietnamese : Nhật Kí Của Mẹ **

**) – Here is English sub – **

How many days I’ve been waiting for your coming to this world

Cherished inside me, was there a laughter of an infant forming up?

Suddenly I wake up, and then I see your tiny form like an angel

You burst into tears, my eyes are red, thank you for coming to me.

My lovely dear, do you know that I love love you so much.

Looking at you in a cradle/ Your wide eyes, oh honey./ Looking at your Dad, he’s happy

And his tears are coming out, you can see that he’s crying for you.

One day i wake up and i can hear your whistle to me : “Mama”

Your tiny lips suddenly sounded , this makes my heart jumping out.

This is the ground, this is the sky, this is the place you were born.

Then You toddle after your Dad, placing your first step in life.

My lovely dear, do you know/ I love you, love you so much

Keep walking, I am here, follow your every steps.

Tomorrow, when you grow up, life is not like you still hope.

Keep always standing up and moving on.

The first day to class, I go with you, you go after my back.

The cicadas in late summer, welcome you under sunshine…

Day after day, you love your school, and friends and your kind teachers

My lovely dear, be a good child, i am so happy inside.

Oh my honey , do you know I love you most in this life.

Many nights you stay awake, I feel so heart – rending.

Then every exam follows, your childhood passes quickly/ I hope you will success tomorrow

One day, I see you vague smile, a rose under the table

There is a name in your letter, this must be someone you love.

One day I see , you look so sad, the rose is still here for you, the leaves are green, the flower blooms, but I see your heart is blue.

Oh my dear, do you know, I love you love you so much./ The first love of your life, it’s not easy to forget.

And the moon will cover you, sunlight comes after the rain./ Someone will love you more than I do.

One day you grow up, you can decide, one day you have to leave me

On your firm feet, face to the world, you spread your wings with freedom

Day after day,night after night, I feel I miss you so much/ Miss your figure, miss your smiles, in every moment in life

My lovely dear, do you know that I love you most in this world./ Wherever you go to, be assured I am still glad.

Every letter with my love, I ask the clouds bring to you./ Wish you always be happy forever.

How many days I’ve been waiting for your coming back to me./ Inside my mind, the memories of your innocent childhood.

Suddenly wake up, then I see you still tiny as an angel/ My eyes are red from happy tears. Thank you for coming to me.