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Example of Math Graphics 数学函数图

2.2. plane curve 2D

Content

Plot 制图

A simple straightforward way to run interactive mathematics in a web page is by mathHand.com.

plot(x), implicitplot(x=y), parametricplot(t,t), tangentplot(x), secantplot(x), polarplot(x), overlapplot(x)
制图, 隐函数制图, 参数制图, 切线制图, 割线制图, 极坐标制图, 重叠制图.

The plot( ) function plots a function, implicit function, parametric function, polar. The system auto plot when you enter formula.

    Interactive plot 互动制图

  1. plot 制图 The system auto plot when you hit the ENTER key, move mouse wheel on graph to zoom and move.
  2. important plane curves

    solve equation graphically

  3. input sin(x)-0.5=0, hit the ENTER key or click the plot button, then put mouse on cross between its curve and the x-axis to show the x-axis value for solution ,
    sin(x)-0.5=0
  4. plot sin(x) and x^2, put mouse on cross between two curves to show solution.
    sin(x) and x**2
  5. implicit plot

  6. implicit plot sin(x)=y to show a multivalue function,
    implicitplot( x=sin(y) )
  7. parametric plot

  8. parametric plot with default pararmter t
    x=sin(t),y=sin(4*t)
  9. polar plot

  10. polarplot( 2*sin(4*x) )
  11. polarplot( exp(cos(x))-2*cos(4*x)+sin(x/12)**5,x,0,50 ) butterfly

    dynamic plot

  12. tangent plot, by moving mouse on the curve to show tangent
    tangentplot( sin(x) )
  13. secant plot, by moving mouse on the curve to show secant
    secantplot( sin(x) )
  14. overlap plot

  15. overlap plot by clicking the overlap button or with overlapplot

    complex plot

    In order to plot complex function, you should convert it to complex by tocomplex(x) before plot. Use complex(x) to set variable for complex variable in real value, and Use complex(0,x) to set variable for complex variable in imag value. Get real part by re() and imag part by im(). e.g. convert log(x) to re(log(complex(x))).

  16. plot complex number with entering complex number in complex(1,1) format, e.g.
    complex(1,1)
  17. or convert 1-i to complex() with tocomplex( )
    tocmplex(1-i)

  18. plot complex function in real domain with complex2D( ), e.g.
    complex2D(sqrt(x))

  19. plot complex function in complex domain with complex3D( ), e.g.
    complex3D(sqrt(x)) for 20 graphes in one plot.

    More examples in complex function

    area plot with integral

  20. integral( ) plot the area under integral curve.
  21. Here are some particularly nice curve examples by plot function. you can put more plot together by the and. e.g.

  22. sin(x) and cos(x)
  23. line plot with vector(x,y) and complex(x,y), e.g. vector(1,2), complex(3,4)
  24. lines plot with length(x,x,x1,x2), e.g. length(x,x,1,2)
  25. curves plot with length(sin(x),x,x1,x2), e.g. length(sin(x),x,1,2)
  26. teliscope
  27. bridge
  28. target 靶 with circle( ) and polarplot( )
  29. butterfly 蝴蝶 with parametricplot( ) and polarplot( )
  30. complex2D(sqrt(x)) complex plot with complex2D( )
  31. trophy
  32. sin(x)-cos(y) net
    More examples in graph.

    Animation

    The plot( ) plots animation by adding the timer(x) into your formula.

    Geometry 几何

  33. Drawing

  34. 2 semicircle with radius 1, 半园
    semicircle(1) and -semicircle(1)
  35. integral area by integral( )
    integral(semicircle(2))

  36. circle with radius 2, 园
    circle(2)
  37. oval with x radius 2 and y radius 1, 椭园
    oval(2,1)
  38. tangent 切线 at x=0 by default,
    tangent( sin(x) as x=1 )

    Dynamic tangent 切线

  39. tangentplot( ) tangent 切线 at x=0 by default, then put mouse over curve to show a tangent line and equation,
    tangentplot( sin(x) )

    Dynamic secant 割线

  40. secantplot( ) secant at x=0 by default, then put mouse over curve to show a secant,
    secantplot( sin(x) )

    more examples on graph

    plane graph 平面图

  41. important plane curves

    plot2D

    plot2D a curve, derivative and integral curve in 2D and polar, and calculate expression at any x and y=0.
  42. plot2D(sin(x))

    the 3-dimensional object (x,y,t) in 2D plane

  43. plot2D the 3-dimensional object (x,y,t) in 2D plane, manually change the t value by a slider, or tick the auto t checkbox for auto change.
    plot2D(x*y-t-1)

    function plot with funplot

  44. funplot a curve, inverse curve in 2D, and calculate expression at any x and y=0.

    differentiate graphically with diff2D

  45. diff2D numericallyly and graphically differentiate a function on graph.
    diff2D(sin(x)) first order derivative

    semidifferentiate graphically with semid2D

  46. semid2D numerically and graphically semidifferentiate a function on graph.
    semid2D(sin(x)) half order derivative graph
    d(x=>sin(x),x,0.5) half order derivative

    differentiate graphically with d(x=>sin(x))

    d(x=>sin(x)) first order derivative graph
    d(x=>sin(x),x,2) second order derivative
    d(x=>sin(x),x,0.5) half order derivative

    integrate graphically with integrate2D

  47. integrate2D numerically and graphically integrate a function on graph. it convert the integrate( ) to the integrates(x=>sin(x)) for integral graph.
  48. integrate2D(sin(x))

    integrate graphically with integrates(x=>sin(x),x)

  49. integrates(x=>sin(x),x)

    plot2D 制图2D

    The plot2D( ) plots a list of data, function, implicit function, parametric function, piecewise function, polar plot, derivative, integral, etc.

    Here are some particularly nice examples by plot function

  50. plot2D(x)
  51. sin(x) and cos(x-phase)
  52. Bessel function of the first kind — the first five Bessel function of the first kind of real or complex order n of a real or complex number.
  53. Bessel functions of the first or second kind for both positive (blue) and negative (red) real order, and derivative.
  54. Watt Curve
  55. Tangent Cotangent
  56. Fourier Series

    plot2D or parametric3D

  57. slinky
  58. Cornu Spiral - the Fresnel cosine and sine integrals.
  59. Mystery Curve

    solve ODE graphically with odeplot

    solve y'=f(x,y) graphically

    Some differential equations cannot be solved symbolly, but can be solved graphically by a plot function odeplot( ).
    odeplot graphically solve Ordinary Differential Equation (ode). The odeplot( ) can be used to visualize individual functions, First and Second order Ordinary Differential Equation over the indicated domain. Input the right hand side of Ordinary Differential Equations, y"=f(x,y,z), where z for y', then click the y'= checkbox for first order differential_equation, or click the y"= checkbox for second order differential_equation by a differential equation y'=f(x,y) graphically.
  60. y' = cos(x)
  61. odeplot graphically solve Ordinary Differential Equation (ode). The odeplot( ) can be used to visualize individual functions, First and Second order Ordinary Differential Equation over the indicated domain. Input the right hand side of Ordinary Differential Equations, y"=f(x,y,z), where z for y', then click the y'= checkbox for first order differential_equation, or click the y"= checkbox for second order differential_equation, by default it is first order ODE.
  62. y''=y'-y for second order ODE

    Animation

    The plot2D( ) plots animation by clicking the animate checkbox and/or adding the timer(x) into your formula.
  63. Cornu Spiral - the Fresnel cosine and sine integrals. Animation

  64. flowering by polarplot( sin(4*x)*timer(6) )

  65. I love you by my heart. abs(x)^(2/3)+0.9*sqrt(3.3-x^2)*sin(pi*x*timer(30))
  66. A plane curve which is progressively drawn. (Cycloid)
  67. The Cycloid is the orbit of a point on a circle rolling along a straight line. Here you can see how this is done precisely, with multiple curve plotting.
  68. By the same principle, the astroid (cos^3(t),sin^3(t)) is the orbit of a point on a circle of radius 1/4 rolling inside a fixed circle of radius 1.
  69. We have also the astroid with 3 arcs.
  70. Zooming effect on the curve sin(1/x).
  71. A moving tangent along a plane parametric curve (cardioid).
  72. The moving tangent along the astroid has a special property: the segment of the tangent cut out by the coordinate axes is of constant length.
  73. How an ellipse is drawn by a point on a segment of fixed length with two extremities on the x and y axes respectively.
  74. An animation which illustrates the functions sin and cos as vertical and horizontal positions of a moving point on a circle.
  75. Rotating and growing trefoil.
  76. Cornu Spiral - the Fresnel cosine and sine integrals.
  77. choreographies
  78. coloring butterfly
  79. coloring square
  80. Unwrapping Circle
  81. Weierstrass

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Reference 参阅

  • example 例题
  • graph 制图
  • graphics 制图法
  • drawing 画画

    Credit

  • Paul Masson
  • Xiao Gang

    If you have good idea or example, please contact us, I might include it into this demo page, of course with credit to you, your name will be included here. 


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