1. The problem statement, all variables and given/known data What does the equation [tex]x^2 -2x + y^2 -2y + z^2 -2z + t^2 -2t + 4 = 0[/tex] represent in [tex]\Re^4[/tex]? What does it represent in [tex]\Re^5[/tex]? What does it represent in [tex]\Re^6[/tex]? 2. Relevant equations Complete the square. 3. The attempt at a solution After completing the square (letting 4 = 1 + 1 + 1 + 1), the equation becomes [tex](x-1)^2 + (y-1)^2 + (z-1)^2 + (t-1)^2 = 0[/tex] In [tex]\Re^4[/tex], the equation represents the coordinate (1,1,1,1). I have a hard time visualizing the cases for [tex]\Re^5[/tex] and [tex]\Re^6[/tex]. I figure that it should be easier to visualize knowing that in [tex]\Re^4[/tex], we have a fixed point. Of course I have deduced that we will get a line and a plane in [tex]\Re^5[/tex] and [tex]\Re^6[/tex], respectively, by looking at smaller cases. But what is the exact configuration and how do I see it?