Timeline for Arcular triangle inequality
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2023 at 15:12 | comment | added | domotorp | Indeed, thank you! Let me confess something. I knew a proof for the case when the arcs bend as in your solution, but it was a tedious computation, see page 17 here: doi.org/10.1007/BF02187821 Your solution is much nicer. | |
| Oct 18, 2023 at 15:09 | vote | accept | domotorp | ||
| Oct 18, 2023 at 14:41 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
added 86 characters in body
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| Oct 18, 2023 at 14:38 | comment | added | Anton Petrunin | @domotorp I will fix it, thank you. If arcs can bend the other way, then the statement does not hold. Take $c$ on the arc $ab$ closer to $a$; choose arcs $ac$ that are tangent to the line segment $ab$ and let $bc$ be subarc of $ab$. | |
| Oct 18, 2023 at 14:24 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
added 54 characters in body
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| Oct 18, 2023 at 8:14 | comment | added | domotorp | I assume you mean that first you assume that the arcs are tangent, then claim that equality holds if $c\in [a,b]$. Does your solution also work if one or both of the arcs $ac$ and $cb$ bend the other way? | |
| Oct 18, 2023 at 4:58 | history | answered | Anton Petrunin | CC BY-SA 4.0 |