Timeline for Where does the generic triangle live?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Dec 4, 2009 at 2:22 | comment | added | some guy on the street | Uniqueness is for pointed triangles; draw a bunch of pictures that look like perspective sketches of an infinite chequerboard; the Pappus' Theorem axiom gives that the proper diagonals are indeed lines; and then we can do a bisection search, finishing by continuity/completeness. | |
| Dec 4, 2009 at 1:54 | comment | added | some guy on the street | eep! not unique... many perspective shifts possible. | |
| Dec 3, 2009 at 23:07 | comment | added | some guy on the street | Alternatively; (spurred on by Tom's answer below), by the generic $T$ triangle let us mean the complete convex space generated by three points $A,B,C$, and satisfying Pappus' theorem in the most suitable sense. Then for any $\alpha,\beta,\gamma$ not colinear in any projective, affine, or hyperbolic space $X$, there exists a unique convex map from $T$ to $X$ mapping $A$ to $\alpha$, $b$ to $\beta$ and $c$ to $\gamma$. | |
| Dec 2, 2009 at 19:12 | history | answered | some guy on the street | CC BY-SA 2.5 |