Timeline for A metric geometry problem which calculates the limitation of human eyes
Current License: CC BY-SA 4.0
31 events
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| Mar 15, 2023 at 15:35 | history | edited | Veronica Phan | CC BY-SA 4.0 |
new update
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| Jul 17, 2022 at 14:32 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 15, 2022 at 13:38 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 11, 2022 at 3:06 | comment | added | Gerry Myerson | Version 13 of this question. | |
| Jul 11, 2022 at 1:20 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 10, 2022 at 2:42 | comment | added | Veronica Phan | @WlodAA X is just an arbitrary point on M, usually a point that we have in mind where it is such as centroid, incenter, orthocenter,... of triangle. | |
| Jul 10, 2022 at 2:37 | comment | added | Veronica Phan | @MattF. I've fixed axiom 6 above, $a$ here work for all such ratios. | |
| Jul 10, 2022 at 2:36 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 10, 2022 at 1:09 | comment | added | Wlod AA | I've meant the 2nd (long) paragraph: "Let a Euclidean [...] we ask Bob to find a unique point 𝑋 on 𝑀 [...] when find 𝑋." ----- I don't see what that "X" is doing here or anything about "X". | |
| Jul 9, 2022 at 17:30 | comment | added | user44143 | I still don’t understand 2). Obviously for every positive ratio $XY/X’Y$ there is some $a>1$ with $1/a<XY/X’Y<a$. Do you mean that there is one $a$ that works for all such ratios? Or that each $Y$ has one $a_Y$ that works for all choices of $X$ and $X’$? | |
| Jul 9, 2022 at 13:07 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 9, 2022 at 12:25 | comment | added | Veronica Phan | @MattF. I've fixed 1), thank you. 2)It mean there exist real number a>1 such that 1/a<XY/X'Y<a. I wrote like that for simplified. | |
| Jul 9, 2022 at 12:21 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 9, 2022 at 11:04 | comment | added | user44143 | My difficulty with the English is in two places: 1) “Find C such that that AC/AB” — should this end with “=x”? 2) The phrase in axiom 6 and its later translation, “XY/X’Y and X’Y/XY is bound” — does that mean that these are bounded, and if so by what, or that they are bounds for something else? | |
| Jul 9, 2022 at 6:06 | comment | added | Veronica Phan | @WlodAA which paragraph? | |
| Jul 9, 2022 at 1:30 | comment | added | Wlod AA | I simply don't understand the first paragraph. And it's not about English, your English seems fine to me. That X makes no sense to me. | |
| Jul 9, 2022 at 0:46 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 6, 2022 at 8:46 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 6, 2022 at 8:41 | comment | added | Veronica Phan | @TimCarson Your assumption is not likely happen. We expected that the error set is "nice", like it have smooth boundary, and it hard for the intersection of finite "nice" set is again "nice". Moreover, in the simplest non-trivial case I explaint above, your assumption mean that at least one equality happen in inequation 4 or 5. Assume that $f^+(y)=\frac{f^-(xy)}{f^-(x)}$ (#). From the last condition, it seems like the limit of $\frac{x}{f^-(x)}$ when $x$ approach $0$ exist and not $0$, then by taking $x$ approach $0$ in (#) we have $f^+(y)=y$, that mean we have trivial solution. | |
| Jul 5, 2022 at 11:33 | comment | added | Tim Carson | I havent fully thought this out but this may be a route to improving the definitions in particular (7). Instead of assigning error to points, start by assigning errors to particular constructions. So write axioms for starting from $F$ and then accumulating error during a particular construction of a constructible point $X$. So for each construction you have an error set. Then you can consider the intersections over all error sets for all constructions of a particular point. Maybe you can show that this intersection is actually the intersection over a finite number of algorithms. | |
| Jul 5, 2022 at 7:16 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 4, 2022 at 2:40 | comment | added | Veronica Phan | @MattF. Sorry for my bad English and thank you to read my question. I think all question I asked is important. Of course the ultimate goal is solving the general problem, but i think its hard to answer here. | |
| Jul 4, 2022 at 1:25 | comment | added | user44143 | I think I would like this question if it were written in more standard English, and if the main question were more clearly identified. | |
| Jul 3, 2022 at 23:57 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 3, 2022 at 12:38 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 3, 2022 at 2:33 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 3, 2022 at 1:36 | comment | added | Veronica Phan | @GerryMyerson en.wikipedia.org/wiki/Centroid | |
| Jul 3, 2022 at 1:34 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 3, 2022 at 0:12 | comment | added | Gerry Myerson | "For example, give a triangle $ABC$ and ask Bob find its center $G$..." There are over 50,000 triangle centers (en.wikipedia.org/wiki/Encyclopedia_of_Triangle_Centers). Which one do you mean? | |
| Jul 2, 2022 at 15:43 | history | edited | YCor | CC BY-SA 4.0 |
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| Jul 2, 2022 at 12:57 | history | asked | Veronica Phan | CC BY-SA 4.0 |