Timeline for Impossible Heronian Triangles (Ratio of 2 Sides)
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 27, 2012 at 13:57 | vote | accept | bobuhito | ||
| Jan 24, 2012 at 10:11 | vote | accept | bobuhito | ||
| Jan 25, 2012 at 10:03 | |||||
| Jan 21, 2012 at 23:47 | comment | added | Noam D. Elkies | This works; still, it's easier to get from "Heronian triangle with side-lengths $a,ra,b$" to "rational point on $y^2 = x(x-1)(x-r^2)$" using Heron's formula than using the formulas for $\sin A$ and $\cos A$ (granted that these formulas are one approach to Heron's formula too). | |
| Jan 21, 2012 at 18:48 | comment | added | bobuhito | Thanks! But, can you elaborate on "Testing gives the rank equal to 0"? My impression is that there is no general way to determine the rank but sometimes "infinite descent" luckily shows it's zero. So, if you need to be specific, can you show why 1/3 gives zero, and what the rank of a more random ratio like 6/17 is? | |
| Jan 20, 2012 at 20:48 | history | answered | Allan MacLeod | CC BY-SA 3.0 |