Is there a set procedure that allows us to extend a mathematical proof in geometry to $n$ dimension or is there a limitation?

Question

Is there a set procedure that allows us to extend a mathematical proof in geometry to $n$ dimension or is there a limitation?

By my Question, I meant that can we take a geometrical proof that applies for a space with $3$ dimensions and extend it for a space of any dimension through a set procedure that's easy to follow such that the person who goes through the procedure won't be credited for proving it for $n$ dimension, because it's as rudimentary as $2+2$? What are the things that prevent it from being true? I am thinking that it's not true, because a theorem that holds for a space with $3$ dimensions does not hold for a $1$ dimensional line or a $2$ dimensional plane.

score 1 · Answer 1 · answered Aug 03 '20 at 05:10

1

No, not in general. In geometry, a four-dimensional space is in a certain sense special, see e.g. Why is four dimensions more difficult? or What makes four dimensions special?

answered Aug 03 '20 at 05:10

Randy Marsh

2,857

Is there a set procedure that allows us to extend a mathematical proof in geometry to $n$ dimension or is there a limitation?

1 Answers1