Dear Firdous,

if you have 3 variables x,y,t, your graph will be 4d.

You could perhaps create several x-y graphs in discrete time intervals, and then stack them along a third (time) axis. Depending on what you want, the x-y graphs will either be 3D, or you could use different colours to mark the values of the dependent variable.

Dear All,

You have a graph of f(x,y,t)=z, which is 4d.

Dear Firdos,

Here is a simple explanation of the idea.

If an equation F(x1,x2,...xn) = 0 has a solution set, we need n-dimensional space to describe it.

we are familiar with a zero-dimensional set ( in general discrete points ),

One-Dimensional set (curves) measured by lengths, two-dimensional sets (surfaces) measured by areas, three- dimensional sets measured by volumes. For higher dimensions, we need advanced tools of differential geometry to study such sets ( under the name of manifolds ) and calculus of multi-variables. Our senses allowed us to imagine and sketch the graph of at most three-dimensional geometrical objects.

As an example : x2 + y2 =1 is a circle , one sketch the graph of the circle in the plane (xy-plane).

x2 + y2 + z2 =1 is a sphere , one sketch the graph of the sphere in the space (xyz-space), for higher dimensions we have

x2 + y2 + z2 + t2 =1 is a hypersphere.

What is the graph (image in our mind) of the hypersphere? Our senses failed to create a graphical image of this geometrical object. But we can see the projections (Shadows) of this object in lower dimensions.

For example the projection of the hypersphere in the xyz space, is a usual sphere, t= 0, we obtain x2 + y2 + z2 =1.

Kline bottle is a nice attempt to sketch a four-dimensional surface in a three-dimensional space. Just google ( Klein bottle) to see this amazing attempt.

Best regards

Dear Firdous Khan, Hi

I suggest Mathstudio.

This app may be interesting to you. This is a free application for android devices that is free and easy to download(1MB approximately) . I think this is the strongest software ever designed for Android. In the Mathstudio, you can enter you formula which is depend on time, as an example cos(x+y*T), and plot it. The result is similar to video file that change in any times.

Thanks to Viera Cernanova, Jan Foniok, Abedal Hamza, Issam Kaddoura and Meysam Ghahramani, I will try all your suggestions.