Timeline for Who invented projective space $\mathbb{P}^n$?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2023 at 19:50 | comment | added | Ryan Budney | I'm not sure if you will be able to get a fully satisfying answer, other than a long list of answers that address aspects of your question. This is a little bit like saying who invented spheres or Euclidean space. Maybe it's showing my bias that most geometric things are "found" not "invented", which I suppose is a bit contrary to most foundational perspectives on mathematics today. | |
| Nov 29, 2023 at 17:06 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title, while this is on the front page
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| Apr 19, 2013 at 20:02 | answer | added | Peter Michor | timeline score: 5 | |
| S Apr 4, 2013 at 22:38 | vote | accept | Maxim Leyenson | ||
| Apr 4, 2013 at 22:37 | vote | accept | Maxim Leyenson | ||
| S Apr 4, 2013 at 22:38 | |||||
| Apr 4, 2013 at 15:24 | comment | added | Lennart Meier | In particular, $\mathbb{A}^n$ for $n>3$ was not so usual at all in the early days of geometry. So, perhaps, $\mathbb{P}^n$ for arbitrary $n$ was invented by Grassmann? | |
| Apr 4, 2013 at 7:28 | answer | added | Mikhail Katz | timeline score: 11 | |
| Apr 3, 2013 at 19:08 | comment | added | Michael Joyce | The idea of the projective plane is at least implicit in the work of the ancient Greek Pappus. It's not clear to me that one can say when projective space was developed. Anyway, it's still an interesting question, but I think it might be helpful to indicate exactly which aspect of projective space you are interested in. (I realize your second question does that, but I didn't know how to interpret your first question. Are you specifically interested in when people understood the generalization to $n$-dimensional space, or the first incarnations when $n = 2, 3$?) | |
| Apr 3, 2013 at 17:37 | comment | added | Maxim Leyenson | Michael, the current version of the Wikipedia page on Projective geometry does not answer these questions, I checked before posting... | |
| Apr 3, 2013 at 17:36 | vote | accept | Maxim Leyenson | ||
| Apr 4, 2013 at 22:37 | |||||
| Apr 3, 2013 at 15:15 | comment | added | Maxim Leyenson | Francesko, thank you. Very helpful. Interestingly, the article says that "Möbius' original formulation of homogeneous coordinates specified the position of a point as the center of mass (or barycenter) of a system of three point masses placed at the vertices of a fixed triangle". -- I.e., his goal was different rather than the completion of $\mathbb{A}^n$! | |
| Apr 3, 2013 at 14:59 | answer | added | Leo Alonso | timeline score: 28 | |
| Apr 3, 2013 at 14:48 | history | edited | Maxim Leyenson | CC BY-SA 3.0 |
linking to Wikipedia
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| Apr 3, 2013 at 14:48 | comment | added | Francesco Polizzi | I do not know. Anyway, it seems that homogeneous coordinates were introduced by Moebius en.wikipedia.org/wiki/Homogeneous_coordinates | |
| Apr 3, 2013 at 14:46 | comment | added | Michael Joyce | Start here? en.wikipedia.org/wiki/Projective_geometry | |
| Apr 3, 2013 at 14:42 | history | asked | Maxim Leyenson | CC BY-SA 3.0 |