A brief introduction to Mathematica by Moretti C. PDF

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You can do this with the option BoxRatios. BoxRatios->{a,b,c} creates a plot whose relative dimensions are a in the x-direction, b in the y-direction, and c in the z-direction. Using BoxRatios->{1,1,3} creates a plot whose length in the z-direction is 3 times that of the xand y- directions. Using BoxRatios->{1,2,3} creates a plot whose length in the y-direction is twice that in the x-direction and whose length in the z-direction is three times than of the length in the x-direction. BoxRatios is literally a set of ratios - using BoxRatios->{1,2,1} will yield exactly the same results as using BoxRatios->{2,4,2} will, since the ratios x-to-z, y-to-z, and x-to-z are the same in each option.

You can immediately replot by using the command Show[%,AspectRatio->Automatic] as the next command after the original plot. You can alter as many of these options at once as you want (except for PlotPoints) by using Show[ ]. You can assign nicknames to plots just like you can numbers and functions. You could enter f=Plot[Sqrt[4-xˆ2],{x,-2,2}] and then use Show[f,AspectRatio->Automatic], for example. Show[ ] can be used to plot multiple curves on the same set of axes as well. If you let f=Plot[Sqrt[4-xˆ2],{x,-2,2}] and g=Plot[Sin[x],{x,-2,2}], then Show[f,g] will combine the plots into a single graph.

Plotting surfaces defined by parameterizations takes a lot of horsepower, so you may have to wait a few moments for the entire plot to be generated. If this is the case, you will see the phrase “Rendering” appear in the title bar of the Mathematica window. ParametricPlot3D[ ] uses many of the same options as Plot3D[ ] - Boxed, Axes, AxesLabel, BoxRatios, and especially PlotPoints and ViewPoint. Surfaces defined using parameters often change their height very rapidly, so it is fairly common to use the PlotPoints option to get a smoother picture of the surface (remember, as you increase the value of PlotPoints, it takes more time for the computer to get the plot).

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A brief introduction to Mathematica by Moretti C.

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