Theory of Everything
Theory of Everything
M theory and dualities
The fine tuning problem and the hierarchy problem
Sum of all the natural numbers
Comments
Chemistry
History of chemistry up until the beginning of 20th century
The structure of atoms and the periodic table
Comments
Some basic mathematics and statistics, the first part
What is a vector?
Manifold
Comments
Basic high school physics without calculus, the first part
Newton’s first law
Newton’s second law
The free fall
Comments
Trigonometric Functions
What are trigonometric functions?
Polar coordinate and trigonometric functions defined over all values
Radian
Inverse trigonometric functions
Rotation in the Cartesian coordinate system
Addition and subtraction rules for trigonometric functions
What is Fourier series?
Comments
Historical Introduction to Quantum Mechanics, the first part
Light as waves
Blackbody radiation spectrum, the Planck relation and the photoelectric effect
Rydberg formula
Comments
Some prerequisites for "Astronomy"
How can we know what chemical elements are there in stars without going there?
Doppler effect: How can we know the speed of stars?
Conic sections
Curved space
Why do closer objects seem bigger?
Comments
Astronomy
The round Earth
The rotating Earth
Why do we have seasons?
The phases of the Moon
The solar eclipse and the lunar eclipse
The Solar System and the apparent motion of planets
Parallax: How do we determine distances to stars?
History of astronomy up until the mid 17th century
History of astronomy from the late 17th century until the early 20th century
History of astronomy from the early 20th century to the early 21st century
Evidences that the Earth is not flat, but round
Comments
Bosons and Fermions
Supersymmetry: an exposition for laymen
Bosons, Fermions, and Pauli’s exclusion principle
Pauli's exclusion principle, color charge of quarks, asymptotic freedom and confinement
Bosons, Fermions and the statistical properties of identical particles
Bosons Fermions in quantum mechanics picture
Comments
Black hole
Why time goes more slowly at a lower place and what a black hole is
Comments
Some basic mathematics and statistics, the second part
Area of a sphere by Archimedes' method
Cavalieri's principle and the volumes of cones and spheres
Area of a sphere
Comments
Newton’s Law of Universal Gravitation
The inverse square law and the 3-dimensional world
Newton's law of universal gravitation
Comments
Some basic mathematics and statistics, the third part
Logarithm
Expectation and Standard deviation
Asymptotic behavior of polynomials
Exponential function vs polynomial function
Pascal's triangle, Combination and the Taylor series for square root
Scalar field and vector field
Proof by induction
Equivalence relation
Pentagon, the Fibonacci sequence, and the golden ratio
Ellipse revisited
Comments
Energy and Entropy
The conservation of energy
Heat as a form of energy
Specific heat and latent heat
What is entropy? From a microscopic point of view
What is entropy? From a macroscopic point of view
Comments
Loop Quantum Gravity
Discrete area spectrum and the black hole entropy I: Loop quantum gravity and the Bekenstein-Hawking entropy
Discrete area spectrum and the black hole entropy II: Domagala-Lewandowski-Meissner formula
Discrete area spectrum and the black hole entropy III: Newer variables
Discrete area spectrum and the Hawking radiation spectrum I
Discrete area spectrum and the Hawking radiation spectrum II: Single unit area deduction
Discrete area spectrum and the Hawking radiation spectrum III: Maxwell-Boltzmann
Discrete area spectrum and the Hawking radiation spectrum IV: Single-partition black hole
Comments
Complex Numbers
Complex numbers
Complex conjugate
Complex numbers and the trigonometric functions
Fundamental theorem of algebra
Comments
Algebra
What is a group?
Cyclic group Cn
The symmetric group Sn and the alternating group An
Finite group
Lie group
Comments
Topology
Topology, the Euler characteristic, and the Gauss-Bonnet theorem
Moebius strip and Klein bottle
The Gauss-Bonnet theorem for triangle on a sphere
Algebraic Topology
Comments
Electricity and Magnetism, the first part
Electric charge and Coulomb force
Electroscope
Magnetic field
Electric current makes compass needle turn
Magnet exerts force on wire through which electric current passes
The force between two parallel wires through each of which electric current passes
Comments
Special Relativity
“Why” is the speed of light constant?
Time dilation in Einstein’s theory of special relativity
Electromagnetic forces and time dilation in special relativity
Lorentz-Fitzgerald contraction: Why is a moving object shortened?
Origin of the magnetic force from the perspective of special relativity
The relativity of simultaneity
Lorentz transformation
Lorentz transformation and Rotation, a comparison
Light cone
Comments
Paradoxes in Special Relativity
Twin paradox
Length contraction paradox
Ki yung’s misunderstanding
Comments
Electricity and Magnetism, the second part
Electric field
Gauss’s law
Why is the electric field inside spherical shell zero?
Gravitational field on the surface of the Earth
Magnetic monopole and Gauss’s law
Comments
Basic high school physics without calculus, the second part
Constant acceleration in 1-dimension
Projectile motion
Work and kinetic energy
Potential energy and conservation of energy
Momentum
Center of mass
Newton’s third law and conservation of momentum
Elastic collision in 1-dimension
Elastic collision in 1-dimension in center of mass frame
Elastic collision in 2-dimension
Normal force
Motions on an inclined plane
Centripetal force
Centrifugal force
Rotation
Newton’s law of universal gravitation and Kepler’s third law
Torque
Moment of inertia
Angular momentum
Hooke’s law and harmonic oscillator
Harmonic oscillator and circular motion
Electric potential
Comments
Electricity and Magnetism, the third part
Faraday’s law of induction
Faraday’s law of induction from the point of view of magnetic force on moving charge
Comments
Dimensional Analysis, the first part
The power of dimensional analysis
Natural units
Comments
CPT
The symmetry of physical laws: the CPT theorem for laymen
CP violation and the Nobel Prize for Physics 2008
Comments
Neutrino oscillation
Neutrino oscillation
Comments
Wave
Travelling wave
The Doppler effect
Standing wave
Huygens’ principle
Snell’s law
Young’s interference experiment
Interference from thin films
Comments
A Crash Course in Calculus, the first part
What is a limit?
What are continuous functions?
Intermediate value theorem
Derivatives, velocity, and acceleration
Addition, subtraction rules for differentiation and Leibniz’s rule
Derivatives of the polynomials
The sandwich theorem and the limit of sin theta/theta
Derivatives of the trigonometric functions
Velocity re-visited and extremum
The chain-rule
Quotient rule
L’H?pital’s rule
Exponential functions and natural logs
Differential and infinitesimal change
Implicit differentiation
Comments
Modified Newtonian Dynamics and Verlinde gravity
The expanding universe
Tully-Fisher relation, Modified Newtonian Dynamics, and Verlinde gravity
Comments
A Crash Course in Calculus, the second part
Revisiting the volume of cone
Motivating integration
Integration and the fundamental theorem of calculus
Taylor series
Euler’s formula and hyperbolic functions
Integration by parts
Even functions and odd functions
Integration by substitution
Comments
Applications of Calculus, the first part
Area inside a circle, surface area of a sphere and volume inside a sphere
The derivation of Snell’s law using calculus
Convexity, concavity and the point of inflection
Center of mass of a half-ball
Fourier transformations
Expectation values in quantum field theory (1)
Probability density function
Gaussian distribution
Gamma function
Comments
The products of vectors
The law of cosines
The dot product
The dot product and the law of cosines
The cross product
Comments
A Crash Course in Calculus, the third part
Partial derivatives and the chain-rule
Differential equations
Partial differential equations
Separation of variables method in partial differential equations
Multiple integrals
Comments
Some basic ideas in General Relativity
Equivalence principle
By how much does time go more slowly at a lower place?
Experiments to test equivalence principle
Comments
Mathematical Introduction to Physics
Newton’s first and second laws
Newton’s third law and the conservation of momentum with calculus
Kinetic energy and Potential energy in one dimension
Harmonic oscillator
Simple pendulum
Kinetic energy and Potential energy in three dimensions, Line Integrals and Gradient
Earth’s Gravity near its surface
Centripetal force revisited with calculus
Newton’s proof of Kepler’s second law
Kinetic energy, Potential energy and angular momentum in polar coordinate
Re-visiting angular momentum conservation in central force
Reduced mass
Moment of Inertia revisited
Rolling down on an inclined plane
A pencil rolling down on an inclined plane, an International Physics Olympiad problem
Equilibrium of forces
Reflection and transmission of travelling wave
Young’s interference experiment, revisited
Diffraction
Comments
Electrodynamics
Electric potential revisited
Lorentz force
Magnetic force on a current-carrying wire
Magnetic dipole
Electric dipole
Electron magnetic moment
Relativistically moving charges around a square loop, an International Physics Olympiad problem
Comments
Historical Introduction to Quantum Mechanics, the second part
Bohr model
De Broglie’s matter waves
Schrodinger equation
Tunneling
Infinite potential well
Stern-Gerlach experiment
Comments
Enumerative Geometry
Conic sections in Cartesian coordinate
What is enumerative geometry?
Conic sections in polar coordinate
Comments
Dimensional Analysis, the second part
The Planck length, the Planck time, the Planck mass and the fine structure constant
Comments
Review Articles
Introduction
High School Mathematics
For Laymen
For Mathematically Oriented
High School Students
For Physics Students
The Most Recommended Articles
한국어
Korean
For Korean Laymen
For Korean Students
About Me
Facebook
Quora
Popular Essays
Math and Physics
Moving Beyond the Korean System:
On Learning To Love Mathematics and Physics
Surprises in math, the reason why I study physics,
and a recommendation for "The Number Devil"
Is math and science homework mechanical drudgery?
The mathematical beauty of physics:
simplicity, consistency, and unity
English as a foreign language versus English as a
mother tongue: an analogy for the language of
mathematics and the language of physics
Physics solutions for mathematical problems
Are memorizing formulas well and good arithmetic
skills essential to become a good theoretical
physicist or a good mathematician?
Math
The imagination in mathematics:
"Desargues's theorem"
Why Math Education Matters
Mathematical maturity in
solving mathematics problems
The square root 2 as
irrational number
The prisoner's dilemma
Math History
The superiority of Hindu-Arabic numeral system
Fermat's Last Theorem
The power of negative number
Nightingale, the statistician
The calculation of pi, the first part
The calculation of pi, the second part
Why are there as many even
natural numbers as natural numbers?
How to turn a complicated multiplication into a simple addition
Pythagoras and the musical scale
Physics
Studying physics as resolving paradoxes
The similarity between painting and theoretical physics
Fermat’s principle and the consistency of physics
Did Einstein really prove that Newton was wrong?
The cosmological principle, and my view on philosophy
The case for string theory
Why are theories of crackpots, the self-claimed physicists
who lack proper physics education, wrong and useless?
About This Page
Found out the reasons for my physics website
Other Resources
Recommended Physics Books
Other Physics Resources
My Harvard Application Essay
My MIT Application Essay
Ein Monat wie im Traum (in German)
Feedback
Review Articles
Introduction
High School Mathematics
For Laymen
For Mathematically Oriented
High School Students
For Physics Students
The Most Recommended Articles
한국어
Korean
For Korean Laymen
For Korean Students
Comments:
In these articles, we calculate the area of sphere using two different methods.