3D Graphs Compare To The 2D Graphs

Daniela Fuschetto
November 3, 2009
Math 213W

The three different graphs, whos 2D graphs will be compared to their 3d Graphs.

Plot[Tooltip[{Sin[x],(x^3)-5,(x^2)+2}],{x,-3,Pi},PlotRange->10]

Graph 1: 15Sin[x]

15Sin[x] in 2D

Plot[15Sin[x],{x,0,2Pi},PlotLabel->15Sin[x],LabelStyle->Directive[Bold]]

15Sin[x] in 3D with two parallel planes perpendicular to the graph 15Sin[x]

Manipulate[Plot3D[{15 Sin[a x], 400 y +z,400 y +(z-250) },{x,0,2Pi},{y,-5,5},PlotRange->20,ClippingStyle->cs,Filling->Bottom,FillingStyle->Opacity[.5]]
,{z,-2000,2000,500},{a,1,5},{cs,{None,Automatic}}]

15Sin[x] in 3D with two parallel planes at an angle to the graph 15Sin[x]

Manipulate[Plot3D[{15 Sin[x], 12.5y +z ,12.5y +(z-25)},{x,0,2Pi},{y,-5,5},PlotRange->20,ClippingStyle->cs,Filling->Bottom]
,{z,-50,50,5},{cs,{None,Automatic}}]

Graph 2: (x^2)+2

(x^2)+2 in 2D

Plot[(x^2)+2,{x,-3,3},PlotRange->{0,10},PlotLabel->(x^2)+2,LabelStyle->Directive[Bold]]

(x^2)+2 in 3D with two parallel planes perpendicular to the graph (x^2)+2

Manipulate[Plot3D[{a (x^2)+2, 100y +z,100y +(z-100) },{x,-3,3},{y,-5,5},PlotRange->{0,8},ClippingStyle->cs,Filling->Bottom,FillingStyle->Opacity[.5]],{z,-495,495},{a,1,10},{cs,{None,Automatic}}]

(x^2)+2 in 3D with two parallel planes at an angle to the graph (x^2)+2

Manipulate[Plot3D[{a (x^2)+2,4y +z, 4y +(z-10) },{x,-3,3},{y,-5,5},PlotRange->{0,8},ClippingStyle->cs,Filling->Bottom,FillingStyle->Opacity[.5]],{z,-12,12},{a,1,10},{cs,{None,Automatic}}]

Graph 3: (x^3)-5

(x^3)-5 in 2D

Plot[(x^3)-5,{x,-4,4},PlotRange->{-20,10},PlotLabel->(x^3)-5,LabelStyle->Directive[Bold]]

(x^3)-5 in 3D with two parallel planes perpendicular to the graph (x^3)-5

Manipulate[Plot3D[{a (x^3)-5, 400 y +z,400 y +(z-250) },{x,-4,4},{y,-5,5},PlotRange->{-20,10},ClippingStyle->cs,Filling->Bottom,FillingStyle->Opacity[.5]]
,{z,-2000,2000,500},{a,1,5},{cs,{None,Automatic}}]

(x^3)-5 in 3D with two parallel plances at an angle to the grapy (x^3)-5

Manipulate[Plot3D[{a (x^3)-5, 12.5 y +z,12.5 y +(z-25) },{x,-4,4},{y,-5,5},PlotRange->{-20,10},ClippingStyle->cs,Filling->Bottom,FillingStyle->Opacity[.5]]
,{z,-50,50,5},{a,1,5},{cs,{None,Automatic}}]

Explanation

When starting off I started with ploting the orginal 2D graphs and from there Iwent on to the more complicated asspects of the problem such as how to make the parallel lines move in sync, as well as 

	When taking the 3D graphs and comparing them to the two parallel plans perpendicular to the original 3D graph you notice these few things:
		
		~When taking the section(slice) of the 3D graph know matter where you take it from you will always just get a smaller scale of the orginal 3D graph of which the section(slice) is from.
		
		~When looking at the slice head on from the front you will see that not only does it look the the orginal 3D graph from the front but it is also is a match to the orginal 2D graph that you started with orginally .
		
	When taking the 3D graphs and compparing them to the two parallel plans at an angle to the original 3D graphs you notice these few things:		
		~When taking the section(slice) from the 3D graph you will not get a smaller scale of the orginal 3D graph you will come across a graph that is at an angle compared to the original.
		
		~But just like when looking at the section of the 3D graphs(that had the plans perpendicular) head on you will still see what will look like to be ther orginal 2D graph that you started off with.
		
	With the graph that shown above you can see how I came aross the above statements.  I gave three different examples to show how it wont matter which type of graph you take it will always work out in this way.