Timeline for Characterization of angles trisectable with straightedge and compass
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2023 at 21:42 | comment | added | Fedor Petrov | Why is not the following a way of trisecting $\theta=\pi/2$: 1)verify that $\theta=\angle ABC$ equals $\pi/2$ by comparing the foot of the perpendicular from $A$ to $BC$ and $B$; 2) construct $\pi/6$? | |
| Feb 2, 2014 at 17:46 | vote | accept | Manfred Weis | ||
| Jan 30, 2014 at 8:06 | comment | added | Manfred Weis | @WillJagy, regarding my 'elaboration' on auto-trisecting angles, do you see any flaws in my argumentation? Does your statement also hold, if it is known, that the unknown angle is trisectable? If your argument were true in that case, then an infinite number of constructions would be necessary to be able to trisect all trisectable angles; again, am I right with my argument? I agree however that it is impossible to detect non-trisectability of an angle in a finite number of steps. | |
| Jan 29, 2014 at 19:37 | comment | added | Will Jagy | @ManfredWeis, it was not so much the lack of precision that I was trying to get across, it was the idea that an unknown angle cannot be correctly identified by a finite number of compass-straightedge operations; if unknown it remains unknown forever. | |
| Jan 29, 2014 at 7:49 | comment | added | Manfred Weis | it is more a philosophical problem whether an angle or a circle drawn on paper actually are mathematical angles or circles. The problem of trisecting an angle can also be interpreted as a practical one, where imprecision plays a role. | |
| Jan 27, 2014 at 19:15 | comment | added | Will Jagy | @ACL, my picture of being given an angle is, essentially, a pair of rays on a piece of paper, with no method for deciding the angle measure to arbitrary accuracy. | |
| Jan 27, 2014 at 17:23 | comment | added | ACL | @Will Jagy: I do not agree. If you are given an angle $\theta$, you know enough about it to be able to compute the minimal polynomial of $\cos(\theta/3))$ over some field containing $\cos(\theta)$. According to what this polynomial is (essentially, degree $1$ or $2$, vs. degree $3$), you will say how to perform the construction, or know it cannot be constructed. | |
| Jan 23, 2014 at 5:28 | comment | added | Manfred Weis | oops, of course I meant "to trisect an angle" and not to "triangulate an angle" | |
| Jan 22, 2014 at 19:33 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Jan 22, 2014 at 5:18 | comment | added | Manfred Weis | your last sentence is a very good point; constructing a trisection must not make use of values, I want however a characterization of the values, whose knowledge allows one to triangulate an angle with such a known value. There are other issues related to my question, which I will address in an edit. | |
| Jan 22, 2014 at 0:43 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Jan 20, 2014 at 5:27 | history | answered | Will Jagy | CC BY-SA 3.0 |