Timeline for Two queries on triangles, the sides of which have rational lengths
Current License: CC BY-SA 4.0
5 events
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| May 5, 2022 at 17:41 | comment | added | LSpice | @ChrisWuthrich's answer alluded to above. Name of @NoamD.Elkies's slides: On the areas of rational triangles; or, how did Euler (and how can we) solve $x y z(x + y + z) = a$?. | |
| Jul 4, 2019 at 16:42 | comment | added | Noam D. Elkies | I was going to mention that soon . . . The $pqr(p+q+r)$ equation comes directly from Heron's formula: let $(p,q,r) = (s-a,s-b,s-c)$. For most $a$, there are only finitely many smooth rational curves on the surface $pqr(p+q+r)=a$ that are defined over the rationals, so Euler had to go further than that. But when $a=A^2$ it's a bit easier. | |
| Jul 4, 2019 at 16:40 | history | edited | R.P. | CC BY-SA 4.0 |
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| Jul 4, 2019 at 16:24 | history | edited | R.P. | CC BY-SA 4.0 |
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| Jul 4, 2019 at 16:07 | history | answered | R.P. | CC BY-SA 4.0 |