Timeline for Early examples of problems that are easier in high dimension
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2018 at 15:25 | vote | accept | Kostya_I | ||
| Apr 29, 2016 at 16:24 | comment | added | Kostya_I | If you put the question as "whether the Desargues theorem is valid in any projective space as defined axiomatically", then, of course, I agree. But, I believe, this view has little to do with how Desargues seen his result - he just proved the theorem for "the plane" that is obviously embeddable to "space". | |
| Apr 29, 2016 at 13:50 | comment | added | Francesco Polizzi | "but here the 3D result does readily imply the 2D one" Yes, but only for some projective planes, namely the ones where you can perform this lifting construction to the $3$-space. In fact, Desargues theorem is valid in all projective spaces of dimension $\geq 3$, but there are some non-desarguesian projective planes. So the case of dimension $2$ is really the tricky part here. Is not this precisely an example of what you are looking for? | |
| Apr 29, 2016 at 12:43 | comment | added | Kostya_I | a nice answer, but here the 3D result does readily imply the 2D one (and, I believe, wasn't published earlier, am I right?), so it is not quite what I meant. | |
| Apr 29, 2016 at 11:49 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |