Visit my timeline of mathematics in Ancient China, Korea, and Japan. The chronology spans 3000 years (1350 BC – 1850 AD).
Author: giulienhwan
Favourite Instrumental Music of 2014
Here I share my favourite instrumental music of this year. This list is not ordered by preference, it is ranked from East to West. Hope you guys enjoy!
Yoshida brothers
Yuunagi
https://www.youtube.com/watch?v=FstLUoQKK0
Ibuki
https://www.youtube.com/watch?v=0p_yo_VGOSw
Fuyu no Sakura
https://www.youtube.com/watch?v=muqM4rV7ovM
Tabidachi
https://www.youtube.com/watch?v=9C1aBi0hbEA
Takeda no Komoriuta
https://www.youtube.com/watch?v=1TBe5o3Phpw
Sakamoto Ryuichi
Merry Christmas Mr. Lawrence
https://www.youtube.com/watch?v=kf0HYeQp760
Rain
https://www.youtube.com/watch?v=zzDRJ9yCe_Y
Energy Flow
https://www.youtube.com/watch?v=R17s8fCZ2AM
Chinese
Pipa Yu by Lin Hai
https://www.youtube.com/watch?v=sFe31JmxM
Yuan Ye Xian Zong by Chen Yue
https://www.youtube.com/watch?v=5qhNRmMilI
Some reconstructed Tang Dynasty performance by some Hokkien Nanguan Troupe
https://www.youtube.com/watch?v=hXjoJIv8sg
Hou Hua Yuan Xu Yu performed by the GangETsui (Hokkien Nanguan) troupe
https://www.youtube.com/watch?v=4Olt2yUqvI
Yao Zu Wu Qu performed by China Central Chinese Orchestra
https://www.youtube.com/watch?v=OxHNyZs1gvI
Uyghur
Gul Bagh
https://www.youtube.com/watch?v=igpNZ1kHgKI
Turkish (Apologies for any mistakes. I don’t speak Turkish.)
Keklik Dağlarda Şağılar
https://www.youtube.com/watch?v=tJFvb4dYDMw
Ömer Faruk Tekbilek
https://www.youtube.com/watch?v=f7EJbyPylKc
Hürremin Dansı
https://www.youtube.com/watch?v=SQmEf8Dtp1U
Alyazmalım
https://www.youtube.com/watch?v=jyZxwOU6Uk
David Byrne
Last Emperor Opening
https://www.youtube.com/watch?v=cXUMB19WkT8
Erik Satie
3 Gymnopédies, 6 Gnossiennes
Mathematical Investigations and Problems
The following files contain some of my mathematical investigations and problems that I created. Please notify me of any errors found in the comments section. I will then correct the files.
Favourite Quotes of 2014
What’s really wrong
The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.
–– Bertrand Russell (18721970)
I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.
–– Galileo Galilei (15641642)
If language is not correct, then what is said is not what is meant; if what is said is not what is meant, then what must be done remains undone; if this remains undone, morals and art will deteriorate; if justice goes astray, the people will stand about in helpless confusion. Hence there must be no arbitrariness in what is said. This matters above everything.
–– Confucius (551479 BCE)
Learning and Inspiration
Tell me and I forget, teach me and I may remember, involve me and I learn.
–– Benjamin Franklin (17061790)
Your beliefs become your thoughts,
Your thoughts become your words,
Your words become your actions,
Your actions become your habits,
Your habits become your values,
Your values become your destiny.
–– Mahatma Ghandi (1869 1948)
Happy ideas come unexpectedly, without effort, like an inspiration. So far as I am concerned, they have never come to me when my mind was fatigued, or when I was at my working table. They came particularly readily during the slow ascent of wooded hills on a sunny day.
–– Hermann von Helmholtz (18211894)
Clear Thinking
The wise man in charge of governing the empire should know the cause of disorder before he can put it in order. Unless he knows its cause, he cannot regulate it.
–– Mo Di (c. 470391 BCE)
Know thy enemy and know thyself, find naught in fear for 100 battles. Know thyself but not thy enemy, find level of loss and victory. Know thy enemy but not thyself, wallow in defeat every time.
–– Sun Wu (fl. 6th century BCE)
When torrential water tosses boulders, it is because of its momentum. When the strike of a hawk breaks the body of its prey, it is because of timing.
–– Sun Wu (fl. 6th century BCE)
Make everything as simple as possible, but not simpler.
–– Albert Einstein (18791955)
Do the right thing
To fight and conquer in all our battles is not supreme excellence; supreme excellence consists in breaking the enemy’s resistance without fighting.
–– Sun Wu (fl. 6th century BCE)
(i) Never use a metaphor, simile, or other figure of speech which you are used to seeing in print.
(ii) Never use a long word where a short one will do.
(iii) If it is possible to cut a word out, always cut it out.
(iv) Never use the passive where you can use the active.
(v) Never use a foreign phrase, a scientific word, or a jargon word if you can think of an everyday English equivalent.
(vi) Break any of these rules sooner than say anything outright barbarous.
–– George Orwell (19031950)
Advanced Guesstimation 1: The Temperature of Lightning
The Question
The temperature of lightning is hotter than the surface of the Sun, averaging 20000 K, and ranging from 15000 – 60000 degrees Fahrenheit (8600 – 33000 K), whereas the surface of the Sun is averages 5800 K. The temperature range of lightning is measured using spectroscopy, but is this is mathematically demonstrable? Here we will calculate the temperature of lightning using basic electromagnetic theory and the StefanBoltzmann Law. Hopefully the presented model will be accurate enough to produce accurate results.
Data
Altitude of storm clouds 
2000 – 16000 m (average 3000 m) 
Base area of storm clouds 
10^{8} m^{2} 
Voltage 
10^{7} – 10^{8} V 
Resistivity of air 
1.3 – 3.3 x 10^{16} Ω m 
Figure 2. Plasma storm on Earth
Proposition 1
Treating the Earth and cloud as a capacitor, the current of lightning can be estimated.
Treating the Earth and cloud as a parallel plate capacitor, the stored energy is equal to the product of its capacitance and voltage.
Here, h is the base altitude of the cloud in metres, and A is the area of the base of the cloud in square metres. The dielectric constant k of air is approximately one, so the stored energy is approximately
The average current is defined as passing charge density divided change of time.
Proposition 2
Treating the flash of lightning as radiation from heat, the temperature of lightning can be estimated.
Suppose the energy stored in an Earthcloud capacitor is suddenly released. The energy is transferred between the Earth and cloud through the atmospheric medium, which if assumed to be the path of least work, would discharge minimum quantities of stored energy. This being said, the particles of a path traced from the Earth to the storm cloud would ionize the atmospheric gas particles, producing plasma that will radiate light, which can be measured by spectroscopic instruments.
The power dissipated is , where i is the average current of the Earthcloud capacitor, is the resistivity of air, h is the base altitude of the storm cloud, and A is the base area of the storm cloud. Equating the power dissipated to StefanBoltzmann law, which relates power to temperature, we arrive at
where is the surface area of the body of ionized air. The emissivity of the atmosphere is approximately one. I will assume the body of ionized air to be contained in a cylindrical volume.
Interestingly, the temperature of lightning is independent on altitude. The main factor for storing all that energy is in the size of the cloud. Also, if the lightning spreads out over a larger cylindrical space, the temperature decreases.
Calculations
This figure is within the 8600K33000K temperature range!
My Favourite Instrumental Music of 2014
Here I share my favourite instrumental music of this year. This list is not ordered by preference, it is ranked from East to West. Hope you guys enjoy!
Yoshida brothers
Yuunagi
https://www.youtube.com/watch?v=FstLUoQKK0
Ibuki
https://www.youtube.com/watch?v=0p_yo_VGOSw
Fuyu no Sakura
https://www.youtube.com/watch?v=muqM4rV7ovM
Tabidachi
https://www.youtube.com/watch?v=9C1aBi0hbEA
Takeda no Komoriuta
https://www.youtube.com/watch?v=1TBe5o3Phpw
Sakamoto Ryuichi
Merry Christmas Mr. Lawrence
https://www.youtube.com/watch?v=kf0HYeQp760
Rain
https://www.youtube.com/watch?v=zzDRJ9yCe_Y
Energy Flow
https://www.youtube.com/watch?v=R17s8fCZ2AM
Chinese
Pipa Yu by Lin Hai
https://www.youtube.com/watch?v=sFe31JmxM
Yuan Ye Xian Zong by Chen Yue
https://www.youtube.com/watch?v=5qhNRmMilI
Some reconstructed Tang Dynasty performance by some Hokkien Nanguan Troupe
https://www.youtube.com/watch?v=hXjoJIv8sg
Hou Hua Yuan Xu Yu performed by the GangETsui (Hokkien Nanguan) troupe
https://www.youtube.com/watch?v=4Olt2yUqvI
Yao Zu Wu Qu performed by China Central Chinese Orchestra
https://www.youtube.com/watch?v=OxHNyZs1gvI
Uyghur
Gul Bagh
https://www.youtube.com/watch?v=igpNZ1kHgKI
Turkish (Apologies for any mistakes. I don’t speak Turkish.)
Keklik Dağlarda Şağılar
https://www.youtube.com/watch?v=tJFvb4dYDMw
Ömer Faruk Tekbilek
https://www.youtube.com/watch?v=f7EJbyPylKc
Hürremin Dansı
https://www.youtube.com/watch?v=SQmEf8Dtp1U
Alyazmalım
https://www.youtube.com/watch?v=jyZxwOU6Uk
David Byrne
Last Emperor Opening
https://www.youtube.com/watch?v=cXUMB19WkT8
Erik Satie
3 Gymnopédies, 6 Gnossiennes
Matching Curriculum with Proper Maths Education
Motto – Learn through investigation: investigate to learn
Reason for Change
Teaching mathematics with proper rigour is highly challenging in a large classroom setting. Schools and most institutions of education fail to achieve the imperatives of effective learning: maintaining student interest, good communication, cooperative learning, and most importantly, developing the sense of inquiry. The current teaching model for school mathematics is more like drilling maths into growing minds instead of growing up with maths in mind. It shouldn’t be that way; in fact, the latter road is much more rewarding –– it is efficient and enjoyable.
How To Solve It
I propose to develop a model for teaching mathematics at the high school level. This model encourages students to ask questions, engage in investigations and discussions, challenge networked peers with their problems, and develop three crucial types of thinking: critical, creative, and logical thinking. The central concept is to set up a classroom that grants people the freedom to investigate and share what they know. By doing so, the investigations and conversations will flourish, generating a productive and intellectually stimulating learning environment. I believe this can be achieved by the following strategies:
 Let the history of math introduce ideas and concepts. This elicits the feeling that mathematics is a culture, and vital to human civilization. It will also remind people of the impetus and purpose for investigating mathematical concepts.
 Use visuals as teaching tools. This method was widespread across many ancient civilizations, and it was extremely effective. People learn better with pictures and diagrams than words and equations. However, the equations must be introduced as a derived result to compactly express the maths. And that is all –– a useful, compact representation of the truth.
 Logical thinking and mathematical proof. There is nothing more vital to understanding mathematics than mathematical proof. Through reason and evidence, mathematical proofs secure its entire framework, making it both reliable and applicable.
 Learn how to apply maths to practical problem solving . Students should know that math is useful in making our world possible. So students should learn how to make mathematical models to solve actual reallife problems.
 Encourage students to discuss and create problems. When people discuss, learning will become more enjoyable, and the retention of knowledge more fruitful. When people create problems, more people will think and come up with solutions. This is how humanity makes progress.
 Do not give exams. Exams deter people from learning beyond the exam; instead, exams encourage people to study solution methods. Often times, when finding answers become more important than understanding the connections between subjects, knowledge will become secondary and eventually forgotten. Exams are a disaster for the retention of knowledge.
Curriculum
The original purpose of curriculums is to make sure every student learns what is considered important. Without curriculums, teachers are then left to their devices, often teaching less than what is expected out of their students. Hence, a general curriculum is still required regardless of the style of teaching.
I have devised a curriculum for each year into four modules: algebra, discrete math, geometry, and analysis. The idea is to introduce, on average, an equal amount of mathematical topics per module. I noticed that most modern curriculums waste too much time on solving algebraic equations, which (to great dismay) has been taught with limited relation to other forms of mathematics (i.e. geometry). As a result, geometry has been heavily deemphasized, and much of discrete maths is pushed into university.
Below are the allocated topics for grades 812. The number in parentheses next to each module is the order in which the modules should be taught. It is advised that math in grades 11 and 12 be optional, and be replaced for learning other skills related to practical problem solving and group learning. For students interested in pursuing higher mathematics and scientific careers, the combined grade 11 and 12 curriculum is nearly equivalent to first and second year undergraduate mathematics.
Grade 8
Algebra (1)

Discrete Maths (2)

Geometry (4)

Analysis (3)

Grade 9
Algebra (1)

Discrete Maths (4)

Geometry (2)

Analysis (3)

Grade 10
Algebra (4)

Discrete Math (3)

Geometry (1)

Analysis (2)

Grade 11
Algebra (2)

Discrete Math (4)

Geometry (1)

Analysis (3)

Grade 12
Algebra (2)

Discrete Math (4)

Geometry (1)

Analysis (3)

The Problems
But how can all this be done? Where do we find the expertise to train qualified teachers? Where can we find administrators who would be devoted enough to put forward such a standard? These pragmatic questions are valid, and they should be thoroughly addressed. However, to properly address such questions, this proposal should undergo much debate. Furthermore, we must always exploit the newest, most effective, and most creative teaching methods available.
Potential Solutions and Outcomes
There is a vast reservoir of information called the Internet, and this reservoir has its medicines and poisons. The reason why we should advocate communicative and investigative learning is because this form of learning exploits the limits of the Internet. Many problems can be solved via Mining the Net, but progress itself cannot last entirely upon knowing what is instantly searchable. That is why, through students challenging one another with problems, we can outlearn what the Internet can immediately provide. This way people will search for background information and existing strategies for problem solving, but not how posed problems are exactly solved. Through communication, teams of students may pitch together what they know to arrive at a unique solution method.
I also encourage math teachers to become learners as well. Get involved with the discussions students are making, and join them in their mathematical journeys.