Math & Physics Problems Wikia
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Math & Physics Problems Wikia

Stevenzheng Stevenzheng 27 August
1

Energy Extraction of Kerr Black Holes

T. Zheng

Department of Physics,

University of British Columbia

(Dated: December 5, 2016)


This paper covers two theoretical mechanisms that seeks to explain the possibility of extracting energy directly from Kerr black holes. This paper begins with a self-contained introduction to black holes, followed by a discussion on the space-time features of Kerr black holes. The unique space-time features of Kerr black holes will then be used to explain the two mechanisms for energy extraction: the Penrose process, and the Blandford-Znajek process.


The study of rotating astrophysical objects is an active area of research in general relativity. Rotating black holes (also known as Kerr black holes) provide much insight into the space-time physics of strong,…



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Stevenzheng Stevenzheng 26 August
0

Thermodynamics of Rotating Black Holes

By: Tao Steven Zheng (郑涛)In the past three decades, the thermodynamics of black holes has provided much insight into the fundamental nature of space-time, as well as the information theory of our universe. Black holes lack many physical features commonly associated with the thermodynamics of matter (i.e. stars). Unlike material objects, there are only three characteristics of a black hole: mass, angular momentum, and electric charge. In gravitational physics, this is known as the no-hair principle. Mass is intrinsic to all black holes. Electric charge is associated with the Reissner-Nordstrom and Kerr-Newman black holes. Angular momentum is associated with the Kerr and Kerr-Newman black holes. In this paper we will focus on the thermodynami…

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Stevenzheng Stevenzheng 26 August
0

GEN-IV Molten Salt Reactors



  • 1 A New Hope for the Future of Nuclear Energy
  • 2 Generation IV: The Nuclear Revolution
  • 3 GEN-IV Molten Salt Reactors
  • 4 Advantages of GEN-IV Molten Salt Reactors
  • 5 Disadvantages of GEN-IV Molten Salt Reactors
  • 6 Progress in GEN-IV molten salt reactor technology

'By: Tao Steven Zheng'Nuclear energy production in the 21st century has experienced a cold start. After the Fukushima Daiichi disaster of March 2011, confidence in nuclear energy slipped from an all-time high to a new low. Several European countries have turned away from nuclear energy, with France being the exception. However, as of 2016, there is a renewed interest of nuclear energy in developing countries across the globe. These industrializing economies have expressed greater optimism about ac…




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Stevenzheng Stevenzheng 10 May
0

Combinatorial Sets from East Asia

By: Tao Steven Zheng


This article introduces sets of abstract figures found in East Asia that are pictorial representations of combinatorics. These diagrams were probably conceived without the intent of being mathematical, but ended up being mathematical curiosities in modern times.


The 64 hexagrams of the I-Ching or Yijing (易經) is the foundation of an ancient Chinese form of divination that dates from the Western Zhou dynasty (c. 1050 - 771 BCE). Each of the 64 hexagrams is a combination of six bars. The solid bar represents yang (陽), the positive force. The broken bars represent yin (陰), the negative force. Interestingly, the sixty-four hexagrams can represent the set of binary numbers from 0 to 63.

The math behind the I-Ching hexagrams is simple. …



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Nickhf1 Nickhf1 10 January 2020
0

Test

The ubiquity of

Hey, it works. :) 

On a side note, I need a little bit of help for those that knows LaTeX. When on each line of code when you want to separated different sentences. The first word of the second sentence always is a few spaces further then the first word on the first sentence. Why's that? And how do I fix it? 

So for example: Similarly, we can...
                Thus, ...

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Stevenzheng Stevenzheng 17 February 2019
0

Chinese Derivation of Pythagorean Triples?

By: Tao Steven Zheng


In the Chinese mathematical text Jiuzhang Suanshu, we find an interesting problem that requires the Pythagorean triples formula to solve.

Chapter 9: Gougu Problem 14

今有二人同所立。甲行率七,乙行率三。乙東行。甲南行十步而邪東北與乙會。問甲乙行各幾何?

[There are two persons standing at the same location. Person A moves at a speed of 7. Person B moves at a speed of 3. Person B moves east. Person A first moves 10 bu south, then diagonally northeast until he meets person B once more. How far did each man travel?]

  • bu (步) literally means pace, a Chinese unit of length that measures roughly 1.6 meters long.

The units of the speed are not specified, but it is reasonable to assume that the speed is measured in bu per second, which measures 1.6 meters per second.

For calculati…


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Stevenzheng Stevenzheng 3 September 2018
0

Ancient Chinese Mathematics (1600 BC - 600 AD)

By: Tao Steven Zheng


  • 1 Note to the reader
  • 2 Section 1: Early Antiquity
    • 2.1 Mathematics of the Shang
    • 2.2 Mathematics of the Western Zhou
    • 2.3 Mathematics of the Eastern Zhou
  • 3 Section 2: The Early Imperial Age
    • 3.1 The Math-deprived Qin?
    • 3.2 Mathematics of the Han
  • 4 Section 3: Era of Disunity
    • 4.1 Liu Hui
    • 4.2 Sunzi Suanjing

This historical overview on the mathematics of ancient China includes the major developments of mathematical thought in ancient China from the Shang dynasty (1600 – 1046 BC) to the Northern and Southern dynasties (420 – 589 AD). The mathematical development from the Sui dynasty (589 – 618 AD) to the Qing dynasty (1644 – 1911 AD) would be considered Medieval Chinese mathematics, and will not be discussed in this article.


Much of Chinese mathematics…




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Stevenzheng Stevenzheng 3 September 2018
0

Timeline of Chinese Mathematics

]] 1811 – 1882 AD: Li Shanlan develops transcendental functions, infinite series, and combinatorics from ancient Chinese mathematics

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Stevenzheng Stevenzheng 3 September 2018
0

Mathematics from Far East Asia: An Interactive Timeline

By: Tao Steven Zheng

Click here to view the interactive timeline.

Enjoy this video of a Song dynasty mechanical clock tower!

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Stevenzheng Stevenzheng 3 September 2018
0

Intro to the Abacus

By: Tao Steven Zheng



There is a growing epidemic of dyscalculia among today’s youth. The over-reliance of electronic calculators has led many to add and subtract slowly, forget their multiplication table, and fail to search for divisible factors. The abacus is an ancient computation tool that can remedy this modern malaise. How? Well, the abacus is just a tool that speeds up computation, but the computation is still done by the human brain. It trains the brain to think faster and more strategically. It internalizes the decimal number system. It requires the user to memorize the multiplication table, and the factors of a given integer.

Abacuses have been invented by several cultures around the globe; at different times. Many early abacuses were …



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Stevenzheng Stevenzheng 3 September 2018
0

Zheng's Problem Solving Process


There are five steps to problem solving: 

1) understanding

2) organization

3) strategy

4) execution

5) reflection

Step 1: Picture the problem (Understanding)

Read the problem carefully to know what is known and what is not known. Understand the objective of the problem. Write down what is known and what needs to be solved. 

Step 2: Get organized (Organization)

Separate the relevant and irrelevant parts of the presented information, and eliminate the irrelevant information. Translate words into the mathematical language. Introduce variables for the unknown quantities discussed. Attempt to obtain more information from prior knowledge, or by dabbling with the information given in the problem. Make correct connections between the gathered information i…


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Stevenzheng Stevenzheng 3 September 2018
0

Math Book Reviews by Steven Zheng

  • 1 Elementary Number Theory in Nine Chapters (Second Ed.)
  • 2 Explorations in Geometry
  • 3 Ancient Puzzles: Classic Brainteasers and Other Timeless Mathematical Games of the Last 10 Centuries
  • 4 How to Solve It
  • 5 A History of Chinese Mathematics
  • 6 Janos Bolyai: Non-Euclidean Geometry and the Nature of Space

Author: James J. Tattersall

Rating: 10/10

This is an excellent (and readable) intro text to number theory with proofs to many important number-theoretic formulas and theorems. Aside from theory, there is also an emphasis on applications such as calendrics, representations, and cryptography. From front to back, there are many interesting historical notes that connect the subject to several cultures (including Chinese, Muslim and Indian). I highly recommend t…


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