Timeline for computability and geometry
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jul 6, 2010 at 0:02 | comment | added | Joel David Hamkins | Peter, it doesn't matter that Tarski's theorem allows for greater expressibility, since his decision algorithm works even for the weaker cases. For example, it seems to me that for any fixed number $k$, the relation "$z$ is consructible by ruler-and-compass from $w$, $x$ and $y$ in $k$ steps or less" is expressible in the language of real-closed fields. So Tarski's theorem provides a decision procedure for all such statements. One could easily also allow more complex construction methods, as long as they were algebraic. What does not seem to be expressible are questions that quantify over $k$. | |
| Jul 5, 2010 at 22:33 | comment | added | Will Jagy | Given this answer, I can recommend "Old and New Results in the Foundations of Elementary Plane Euclidean and Non-Euclidean Geometries" by Marvin Jay Greenberg, the M.A.A.'s American Mathematical Monthly, March 2010, vol. 117, no. 3, pages 198-219; especially references to works of one Victor Pambuccian. If people cannot find it I have a pdf. I know from my own work that one can prove something is constructible with compass and straightedge while having no clue of how to go about it in practice. | |
| Jul 5, 2010 at 22:22 | history | edited | Will Jagy | CC BY-SA 2.5 |
lanagle to langle
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| Jul 5, 2010 at 22:13 | comment | added | Peter Shor | Tarski's theorem doesn't address ruler and compass constructability, if that was the original question, since it allows for more general algebraic equations. | |
| Jul 5, 2010 at 21:28 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |