Timeline for What exactly does this diagram of Omar Khayyam represent?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 21 at 0:12 | answer | added | Amir Asghari | timeline score: 8 | |
| Sep 26, 2013 at 7:33 | comment | added | Marty | ...An approximation to the solution of this equation is not difficult to find, but Khayyam also generates a direct geometric solution: he uses the numbers in the equation to determine intersecting curves of two conic sections (a circle and a hyperbola), and demonstrates that the solution $x$ is equal to the length of a particular line segment in the diagram." (plato.stanford.edu/entries/umar-khayyam/#SolCubEqu) | |
| Sep 26, 2013 at 7:33 | comment | added | Marty | The Stanford Encyclopedia of Philosophy discusses this document further: "Khayyam seems to have been attracted to cubic equations originally through his consideration of the following geometric problem: in a quadrant of a circle, drop a perpendicular from some point on the circumference to one of the radii so that the ratio of the perpendicular to the radius is equal to the ratio of the two parts of the radius on which the perpendicular falls. In a short, untitled treatise, Khayyam leads us from one case of this problem to the equation $x^3 + 200x = 20x^2 + 2000$... | |
| Sep 26, 2013 at 7:32 | comment | added | Marty | Brin's answer below seems to be the best reference, judging from MathSciNet reviews. The translation of Al-Khayyam into French by Rashed and Vahabzadeh seems to be a scholarly critical edition... | |
| Sep 25, 2013 at 11:00 | answer | added | Matt Brin | timeline score: 7 | |
| Sep 24, 2013 at 14:19 | answer | added | Hicham | timeline score: 8 | |
| Sep 24, 2013 at 2:18 | comment | added | The Masked Avenger | I've asked someone from Syria who knows modern Arabic. He says it is a little challenging to read, that a ratio is involved, and that he might be able to say more tomorrow. My inference is that to compute the ratio of the two parts of the divided vertical radius in the top picture, a similar quantity involving the ratio of some areas in the bottom picture must be calculated. But I don't really know. | |
| Sep 24, 2013 at 2:08 | history | edited | Kim Morrison | CC BY-SA 3.0 |
added 40 characters in body
|
| Sep 23, 2013 at 22:09 | answer | added | Mohammad Farajzadeh-Tehrani | timeline score: 16 | |
| Sep 23, 2013 at 21:58 | history | asked | Frank Thorne | CC BY-SA 3.0 |