distance measurement by Cartesian method and Cartesian product on multi dimensional spatial dataset

Hi, I want to find k-dist plot for a data. I used euclidean distance but It didn't find true values. So I searched and found that , Cartesian method can be used for distance measurement to drawing to k-dist plot. And Someone says this, ‘k’ as variable one by using algorithmic average determination and distance measurement by Cartesian method and Cartesian product on multi dimensional spatial dataset.

How can I estimate k-dist using algorithmic average determination and distance measurement by Cartesian method and Cartesian product ? How can I find distance measurement by Cartesian ? What is the differences between Cartesian distance and euclidean distance in mathematical way ?