Interesting Aspects of Mathematics 趣味数学 www.h2maths.site/ywhmaths.html

I hope that from this website, you will find Mathematics interesting and easy to learn!
Algebra	Analysis	Arithmetic	Combinatorics
Complex Numbers	Fractals	Games	Geometry
Graphs	Java	JavaScript	Mechanics
Number Theory	Puzzles	Python	Sequences
Statistics	Tessellation	Trigonometry	Archive of Comments

Algebra 代数
Permutation Groups Groups of Small Orders Sylow's Theorems	Rings and Fields Rings of Small Orders	Semigroups Semigroups of Small Orders

Analysis 微积分
Differential Operator	l'Hopital's Rule Remainder Term of Maclaurin Series Convergence Tests For Series	Integration by Substitution Line Integral Laplace Transform

Arithmetic 算术
Factorial Fraction	Fibonacci Numbers Fibonacci Identities	The 4 Fours Problem
Highest Common Factor The Lonely 8 Puzzle	Magic Squares Generating Order 4 Magic Squares	My Mechanical Calculator How to Add How to Subtract How to Multiply How to Divide
Number Bases	Pascal's Triangle Ramanujan Summation RMS-AM-GM-HM Inequality Cauchy-Schwarz Inequality	Roman Numerals The "Send More Money" Puzzle

Combinatorics 组合数学
Random Walk in 1 Dimension	Random Walk in 2 Dimensions	Circular Arrangement With Identical Objects
Distribution Problems	Kirkman's Schoolgirls Problem	Monty Hall Problem
Poker Hands	The Worst Postman Problem

Complex Numbers 复数
Arc	Application of de Moivre's Theorem	Functions of Complex Numbers

Fractals 分形
Blancmange Curve	Hilbert Curve	Levy C Curve
Sierpinski Curve	Sierpinski Triangle	Kock Snowflake
Self Similarity	Landscape	Trees

Games 游戏
Checkers	Chess Chess for Kids	Chinese Chess Chinese Chess (Slow)
Conway's Game of Life	Othello / Reversi	Tic Tac Toe
Wordle

Geometry 几何
Angle Properties of a Circle	Sum of Interior Angles of a Polygon	Arc Length
Exterior Angles of a Polygon	Langley's Adventitious Angle	Pick's Theorem
Triangle Triangle Rhyme	Johnson Solids	Proof that there are exactly 13 Archimedean Solids

Graphs 图
Construction of Conics	General Form of the Equation of Conics	Directrix, Eccentricity, Focus
Conics in Polar Coordinates	Reflective Property of Conics	Cycloid
Convergence of Fixed Point Iteration	Fourier Series	Graphs of y = |f(x)|, f(|x|), 1/f(x), √f(x)
Hyperbolic Functions	y = xp/q	Rational Functions

Graph Theory 图论
Complement of Graph	Minimum Spanning Tree	Graphs of Small Orders Trees of Small Orders

Java
If you wish to learn Java, install Java on your desktop/laptop and try out each of the applets below. Source codes are all provided.
How to Create a Java applet	How to Create an Android App
Animate	Buttons	Checkboxes
Conditions	Choices	Draw an Image
Loops	Click the Mouse	Drag the Mouse
Enter the Mouse	Move the Mouse	Press the Mouse
Operators	Radiobuttons	Rainbow
Random Shapes	Run a Thread	Scroll Bar
Scroll Bars in Colour	Shapes	Stars
Strings	Text Field and Text Area	Variables

JavaScript
On your laptop/desktop, you can right-click to view the javascript source codes.
Addition	Animation	Button
Checkbox	Date of Birth	Draw
Dropdown List	List Box	Password
Radio Button	Slider	Textbox
Touch	Hot Air Balloon	How to Write a JavaScript Programme LaTeX Commands

Mechanics 力学
Collision	Connected Particles	Elastic String
Linear Motion	Projectile	Vertical Spring

Number Theory 数论
Chinese Remainder Theorem Continued Fractions	Euclidean Algorithm	Fermat-Euler Theorem Highly Composite Numbers
Linear Congruence	Number Theoretic Functions	Pell's Equation
Prime Factorisation Prime Numbers	Quadratic Residues Summary of Quadratic Residues	Waring's Problem A Special Pandigital Number

Puzzles 益智游戏
Tower of Hanoi	Chinese Rings Puzzle	1x3x3 Floppy Cube
Gari Garikun Puzzle	2x2x2 Pocket Cube	2x2x3 Tower Cube
2x3x3 Rubik's Domino	Rubik's Cube	Octagon / Cylinder
Mirror Cube	Void Cube	Gear Cube
Gear Shift	Pyraminx	Dino Cube
Skewb	Back To Square One	Square Two
MasterBall	Rubik's Cheese	Sudoku Cube
4x4x4 Master Cube	5x5x5 Professor Cube	6x6x6 Cube
Megaminx	Who owns the Zebra? The Governor of Kgovjni Puzzle	The 12 coin Problem

Python
Install Python from https://www.python.org/downloads/ and open the following source codes:
Factorial	Lists	Loops
Operators	Prime Factorisation	Prime Numbers
Sets	Strings

Sequences and Series
Method Of Differences	Mathematical Induction Examples of Mathematical Induction

Statistics 统计学

Negative Binomial & Hypergeometric Distributions	Normal Approximation	Sampling Methods
Variance	2-Sample t Test Proofs of Distributions Samples	Hypothesis Tests Non-Parametric Tests Analysis of Variance
Here are some Microsoft Excel Simulations to run on your laptop/desktop: (Click each link and press F9 on your keyboard)
4D Lottery	Binomial approaches Poisson Binomial approaches Normal	Poisson approaches Normal

Tessellation 平面填充
17 Wallpaper Tessellations	Proof That There Are 17 Wallpaper Groups	Ambigrams

Trigonometry 三角学
Complementary & Supplementary Angles	R Formula	Sine Rule & Cosine Rule
Small Angles Special Angles	Trigonometric Equations	Trigonometric Equations (Graphical)
Trigonometric Functions Inverse Trigonometric Identities	Trigonometric Graphs	3D Trigonometry

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