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# Example of Math Graphics 数学函数图 制图法

## 1. plane curve in 2D

Content
1. plane curve in 2D
2. space curve in 3D
3. surface in 3D
4. surface in 4D = hypersurface

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

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))).

### plot 制图

plot(x), implicitplot(x=y), parametricplot(t,t), tangentplot(x), secantplot(x), polarplot(x), overlapplot(x)

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

Here are some particularly nice curve examples by plot function. you can put more plot together by the and. e.g. sin(x) and cos(x).

1. line plot with vector(x,y) and complex(x,y), e.g. vector(1,2), complex(3,4)
2. lines plot with length(x,x,x1,x2), e.g. length(x,x,1,2)
3. curves plot with length(sin(x),x,x1,x2), e.g. length(sin(x),x,1,2)
4. teliscope
5. bridge
6. target 靶 with circle( ) and polarplot( )
7. butterfly 蝴蝶 with parametricplot( ) and polarplot( )
8. complex plot with complex2D( ), e.g. complex2D(sqrt(x))
9. trophy
10. net with sin(x)-cos(y)
More examples in graph.

#### Animation

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

### 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

11. plot2D( )

12. sin(x) and cos(x-phase)

13. 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.

14. Bessel functions of the first or second kind for both positive (blue) and negative (red) real order, and derivative.

15. Cornu Spiral - the Fresnel cosine and sine integrals.

16. Mystery Curve

17. Watt Curve

18. Tangent Cotangent

19. Fourier Series

### solve ODE graphically with odeplot( )

#### solve dy/dx=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 dy/dx=f(x,y) graphically.
20. dy/dx = cos(x)

#### Animation

The plot2D( ) plots animation by clicking the animate checkbox and/or adding the timer(x) into your formula.
21. choreographies
22. butterfly
23. square
24. Unwrapping Circle
25. Weierstrass

• example 例题
• graph 制图
• graphics 制图法
• animation 动画

• Paul Masson
• Xiao Gang