0

I have a parallelogram in $\mathbb{R}^3$ with the vertices $(0,0,0),(1,1,-1), (1,1,1), (2,2,0)$. How would I find the parameterization of this? Thanks!

hoya2021
  • 101
  • What have you done? – amsmath Apr 19 '19 at 23:37
  • I don't quite understand how parameterization works, so I have nothing so far – hoya2021 Apr 19 '19 at 23:40
  • So, I guess you should read first what a parametrization is and look at some examples. – amsmath Apr 19 '19 at 23:43
  • Think of it as finding a system of coordinates for points in the parallelogram. Try it in two dimensions first to get some ideas. – amd Apr 19 '19 at 23:43
  • Here is the parametrization of rectangle, this might help. – ersh Apr 20 '19 at 00:00
  • 1
    @amsmath It seems OP already knows the definition of parametrization and some examples. Actually, it is is not straightforward to parametrize parallelogram. See the example of rectangle above. – ersh Apr 20 '19 at 00:05
  • 1
    @ersh What you refer to is a parametrization of the boundary. I am sure OP wants a parametrization of the whole figure. – amsmath Apr 20 '19 at 00:14
  • I understand the main idea of parameterization and why it is useful. I have never seen how to parameterize a non-smooth object and I can't find any good examples that explain how to do this in the 3rd dimension – hoya2021 Apr 20 '19 at 00:44
  • Trying a different tack, can you find a parameterization of the unit square in $\mathbb R^2$? Having done that, can you think of a simple way to map the unit square onto a parallelogram? – amd Apr 20 '19 at 00:58

0 Answers0