# How to plot a region bounded by three equations?

I'm very new to this website. I am having trouble plotting a 3 dimensional region bounded by these equations:

R = {y == x <= y == - x + 2 <= y == -Sqrt[1 - (x - 1)^2]}


The problem is that I know what command to use to do this, but it gives me a blank plot. If it helps my code is below, and I have Mathematica Version 7.0:

RegionPlot3D[
y == x <= y == - x + 2 <= y == -Sqrt[1 - (x - 1)^2],
{x, -10, 10}, {y, -10, 2}, {z, -10, 10}]


If someone could lead me to the right direction or tell me what is wrong, I would greatly appreciate it.

• What exactly are the three equations? It is not clear from the question.
– ciao
Apr 28, 2014 at 2:10
• Your equations are not stated properly... look at the help file for RegionPLot3D to get the form right. Also, your limits are not right because when Abs[x] is large, the Sqrt[ ] has complex values. Apr 28, 2014 at 2:47
• Could you help me figure out which equations go where and what limits should I use? My algebra is not too good, I am interested in seeing what the region looks like. I will appreciate any help anyone can give at this point. Apr 28, 2014 at 3:42

The region is defined in two dimensions. Insights from the 2D plot:

Plot[{x, 2 - x, -Sqrt[1 - (1 - x)^2], Sqrt[1 - (1 - x)^2]}, {x, -3,
3}, AspectRatio -> Automatic, ImageSize -> 200,
PlotStyle -> {Red, Red, Red, Black}]


The region of interest is bounded in red, Exploiting the coincidence of the intersection of the lines at (1,1), a point on the circle: the region can be plotted in 3D:

RegionPlot3D[
y <= x && y <= 2 - x && (x - 1)^2 + y^2 <= 1, {x, -3, 3}, {y, -3,
3}, {z, -3, 3}, PlotPoints -> 100]


I have changed the plot range just to make visualization 'nicer':

• Thank you so much for the visualization.. I had them written as inequalities but not in the form you have showed me here. I really appreciate your help, it is much much clearer. Thanks again, ubpdqn! Apr 28, 2014 at 19:35