My Java Applets Reference Links

Algebra

  1. Definition of sets
  2. Quadratic equations 1
  3. Quadratic equations 2
  4. Problem of quadratic functions (1)
  5. Problem of quadratic functions (2)
  6. Problem of quadratic functions (3)
  7. Problem of quadratic functions (4)
  8. Congruence of quadratic functions
  9. Minimum value of quadratic functions
  10. Interactive algebra
  11. Interest calculations

Coordinate geometry

  1. Cartesian coordinates
  2. Coordinate system
  3. Polar coordinates
  4. Oblique coordinates
  5. The slope of a straight line
  6. Spatial coordinates
  7. Straight lines in 3-space
  8. Recognizing functions 2 (functions containing negative powers)
  9. Recognizing graphs 2 (functions containing negative powers)
  10. Planes in 3-space
  11. Cycloids
  12. Logarithmetic spirals
  13. Equations of a straight line

Angle and parallel lines

  1. Sum of three angles
  2. Regular m/n-Polygon
  3. Sum of outer angles
  4. Polygon creater
  5. Problem about angles (1)
  6. Problem about angles (2)
  7. Angle trisector
  8. Sum of angles in a triangle
  9. Special lines and circles of a triangle

Congruent figures and triangles

  1. Finding angles (1)
  2. Finding angles (2)
  3. Congruent triangles (1)
  4. Congruent triangles (2)
  5. Congruent triangles (3)
  6. Congruent triangles (4)
  7. Sum of three segments
  8. Folding tape
  9. Two squares (1)
  10. Two squares (2)
  11. Two equilateral triangles (1)
  12. Two equilateral triangles (2)
  13. Congruent transformation

Quadrilaterals and conservation of area

  1. Horizontal machine
  2. Two tapes
  3. Problem about quadrilateral
  4. Problem about parallelogram
  5. Conservation of area
  6. Transformation of a triangle
  7. Dividing triangle
  8. Changing border line
  9. Transformation of a pentagon
  10. Dividing a quadrilateral

Similar figures

  1. Similar figure
  2. Pantagraph
  3. Height of the pole
  4. Shadow of a square
  5. Dividing a square
  6. Polya's problem
  7. Midpoint
  8. Parallel line and ratio
  9. Two squares

Circles

  1. Eye ball
  2. Three circles
  3. Application of alternate segment theorem
  4. Peaucellier apparatus
  5. Inner centre
  6. Inscribed quadrilateral
  7. Common tangents
  8. Two regular triangle and locus
  9. Problem of maximum angle (1)
  10. Problem of maximum angle (2)
  11. Problem of two circles (1)
  12. Problem of two circles (2)
  13. Problem of two circles (3)
  14. Problem of two circles (4)
  15. Ruler
  16. Simson's law
  17. Root x
  18. Salinon (salt-cellar)
  19. Inscribed angles
  20. Quoits
  21. Angles standing on the same arc
  22. A flashlight
  23. Circumcentre

Pythagorean theorem

  1. Pythagorean Theorem (1)
  2. Pythagorean Theorem (2)
  3. Pythagorean Theorem (3)
  4. Pythagorean Theorem (4)
  5. Pythagorean Theorem (5)
  6. Pythagorean Theorem (6)
  7. Pythagorean Theorem (7)
  8. Pythagorean Theorem (8)
  9. Pythagorean Theorem (9)
  10. Hyppocrates' lunar
  11. Minimum distance
  12. Shortest distance
  13. Quadrangular pyramid (1)
  14. Quadrangular pyramid (2)
  15. Origami
  16. Two poles
  17. Pythagoras tree (1)
  18. Pythagoras tree (2)
  19. Theorem by Pappus
  20. Pythagorean Theorem (10)

Miscellaneous (at secondary school level)

  1. Billiards
  2. Solid of Solomon
  3. Linear function
  4. Stairs
  5. Similar figures and ratio
  6. Figure and area
  7. Linear functions and graphs
  8. Figures and ratio of area
  9. Thermometer
  10. Linear function and graph
  11. Platonic solids
  12. Rotate-able icosahedron

Miscellaneous (Others)

  1. Linear transformation (lattice)
  2. Linear transformation (lines)
  3. Fractal
  4. Problem of absolute value
  5. Iterating f(x) = ax (1 - x)
  6. Feigenbaum plot (exhibition of chaotic behavior)
  7. Life game
  8. Life game (large)
  9. Sum of geometric series
  10. Parametric equations
  11. Problem of rectangle
  12. Rectangular and polar coordinates
  13. Autonomous system (linear, part I)
  14. Autonomous system (linear, part II)
  15. Simple graph
  16. Log clock
  17. log M + log N
  18. Snail shell
  19. Rotary curve
  20. Orthocentre and circumcentre
  21. Gauss's symbol
  22. The least-squares line
  23. Factorization of x^3 - y^3
  24. Slide rule
  25. Semicircle and arithmetic - geometric means
  26. Simple 3D graph z = f(x,y)
  27. Pascal's triangle
  28. Problem of ax^2 - (a^2 + a)x + a^2 < 0
  29. Maximum and minimum of function (1)
  30. Maximum and minimum of function (2)
  31. Multiple windows
  32. Mandelbrot explorer
  33. Stereograms

Trigonometry

  1. Sine function box
  2. Cosine function box
  3. Tangent function box
  4. The graph of y = sin x
  5. The graph of y = cos x
  6. Graph of y = sin ax
  7. Graph of y = A sin (Bx + C)
  8. Graph of y = sin x + cos x
  9. Fourier series
  10. sin t = a
  11. cos t = a
  12. sin(A + B)
  13. sin t > a (1)
  14. sin t > a (2)
  15. cos t > a (1)
  16. cos t > a (2)
  17. cosine engine
  18. a sin x + b cos x
  19. The law of cosines (1)
  20. The graph of y = tan t
  21. Law of sines
  22. Ferris wheel
  23. Six trigonometric functions
  24. Crane
  25. The law of cosines (2)
  26. Sine, cosine, tangent of an angle
  27. Definition of the trig functions
  28. Triangle and the law of sines
  29. The graphs of sin, cos and tan
  30. Recognizing functions 3 (sine and cosine functions)
  31. Recognizing graphs 3 (sine and cosine functions)
  32. Graphs of elementary trigonometric functions

Differential Calculus

  1. The derivative of the sine
  2. Average rate of change and derivatives
  3. Surfing (derivatives)
  4. Derivatives of cubic functions
  5. Rolle's Theorem and the Mean Value Theorem
  6. Secant line and tangent line
  7. One sided derivative
  8. L'Hopital's Rule
  9. Composite functions
  10. The chain rule
  11. The product rule
  12. Derivative of exponential functions
  13. Derivative of trigonometric functions
  14. Derivative of y = x^2
  15. Second derivative of trigonometric functions
  16. Second derivative of y = x^n
  17. Second derivative of exponential functions
  18. Problem of the number of tangent line (1)
  19. Problem of the number of tangent line (2)
  20. Derivative of exp(x)
  21. Derivative of log x
  22. Animated tangent line
  23. Animation of secant approaching tangent
  24. How to find a function's extremum
  25. First and second derivative
  26. On the definition of the derivative
  27. Derivative puzzle 1
  28. Derivative puzzle 2
  29. Derivative puzzle 3
  30. The big derivative puzzle
  31. xFunctions xPresso
  32. Some max-min problems
  33. Derivatives of a function
  34. Slope

Integral Calculus

  1. The rectangle approximation method
  2. The volume of a solid (1)
  3. The volume of a solid (2)
  4. The volume of a solid of revolution (1)
  5. The volume of a solid of revolution (2)
  6. The Fundamental Theorem of Calculus
  7. Problem of area
  8. Minimum value of the integral of a function
  9. Geometric meaning of integration of 1 / x
  10. Integration of exp(x)
  11. Intersecting cylinders
  12. Intuitively understanding the integral
  13. xFunctions xPresso
  14. Riemann Sums - Function integration
  15. Approximation by rectangles

Limit and Continuity + other topics in calculus

  1. lim sin x / x (x ->0)
  2. Visualization of limits
  3. Circle of curvature
  4. Cycloids
  5. The number e (1)
  6. The number e (2)
  7. Progression of differences
  8. Recursion formula (1)
  9. Recursion formula (2)
  10. Sum of arithmetic sequence
  11. The locus of a triangle
  12. 1 / f(x) generator
  13. A circle touching two circles
  14. Circle of curvature of ln x
  15. The involute of a circle
  16. Involute of y = cosh x
  17. f(x) + 1 / f(x) generator
  18. Autonomouse (parametric) system
  19. Property of cycloid
  20. Recursion formula (3)
  21. Drawing exponential curve
  22. Cross section of Gutter
  23. First-order differential equations
  24. Polar coordinates simple graph
  25. Simple graph (parametric functions)
  26. Differential equations (parameter)
  27. Graph of f(f(x)) = x and f(f(f(x))) = x
  28. Problem of maximum of area
  29. limit (exp(x) - 1) / x
  30. limit log(x + 1) / x
  31. Graph of exp(ax) and equiangle spiral
  32. Finding the value of root using Newton's Method
  33. Numerical computation of sequences
  34. Numerical computation of series
  35. What's a fault? A tale that makes you smile

Vector

  1. The area of a parallelogram (1)
  2. The area of a parallelogram (2)
  3. Inner products
  4. Division vector
  5. Vector and field (1)
  6. Vector and field (2)
  7. Line and dot product
  8. Ceva's Theorem
  9. Menelaus's Theorem
  10. Cramer's rule
  11. Distributive law for alternate product
  12. Circle of apolonius
  13. Commutative law for inner product
  14. Distributive law for inner product
  15. Unit vector
  16. Angle bisector
  17. Vector equation of line
  18. Vector equation of line in 3D
  19. Intersection point of vectors
  20. Vector and circle
  21. Vector cross product
  22. Introducing 3-vectors
  23. Introducing plane vectors

Linear Algebra

  1. Matrix operation
  2. Matrix multiplication
  3. Vector calculator
  4. Linear equations solver

Complex numbers

  1. Complex number (1)
  2. Complex number (2)
  3. Complex number (3)
  4. Complex number (4)
  5. Complex number (5)
  6. Complex-valued function
  7. i^(i^(i^i))
  8. 1 / z (z = a + bi)
  9. Conjugate complex number
  10. Meaning of multiplication of complex variables
  11. Integral of z
  12. Integral of z^n
  13. Integral of 1 / z^n
  14. Geometric meaning of multiplication of z and dz
  15. Integral of exp(z), cos z and sin z
  16. Geometric meaning of mulitplication of 1 / z and dz
  17. Meaning of division of complex variables
  18. Integration of parametric function
  19. Derivative of z^2
  20. Derivative of z^3
  21. Derivative of z^4
  22. Circle in complex plane
  23. (1+i*t/n)^n (n->infinity)

Conic sections

  1. Focus of parabola
  2. Ellipsograph
  3. Problem of hyperbola
  4. Drawing hyperbola
  5. Drawing parabola
  6. Reflective properties of ellipses
  7. Reflective properties of hyperbolas
  8. Two ellipses
  9. Trace of shadow
  10. Conic sections

Famous curves

Probability

  1. The let's make a deal applet
  2. Histogram applet
  3. Buffon's needle
  4. Kid's dice page
  5. Random numbers
  6. Coin tosses
  7. The cliff hanger
  8. Estimation of pi
  9. The birthday problem
  10. Webdice