Timeline for Conjecture: Given any five points, we can always draw a pair of non-intersecting circles whose diameter endpoints are four of those points
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2023 at 15:19 | comment | added | Peter Mueller | I got the first one from a numerical optimization and then rationalizing. The second one from a direct search of integer points $(-a,0), (0,b), (0,-c), (0,d), (e,f)$ where $a,b,c,d$ are positive, $|a-b|<6$, $|c-d|<6$ and $|e|,|f| < a/5$. | |
| Dec 2, 2023 at 15:04 | comment | added | Martin M. W. | @PeterMueller, that's elegant! Did you get those coordinates via numerical optimization, or is there a simpler logic to where they came from? | |
| Dec 2, 2023 at 15:02 | comment | added | Peter Mueller | ... and another one is $(-236, 0)$, $(236, 0)$, $(0, -235)$, $(0, 237)$, $(22, 1)$. | |
| Dec 2, 2023 at 8:57 | comment | added | Peter Mueller | One can even choose $2$ points on the $x$-axis and $2$ points on the $y$-axis. An example in particularly small numbers is $(-330, 0)$, $(330, 0)$, $(0, -333)$, $(0, 329)$, $(26, 25)$. | |
| Nov 29, 2023 at 14:38 | comment | added | Iosif Pinelis | @Dan : Thank you for your response. | |
| Nov 29, 2023 at 4:26 | comment | added | Dan | It shows a random pairing, not necessarily the "best". You can change the values of $A,B,C,\dots$, copying and pasting from the coordinates, to test the pairings. | |
| Nov 29, 2023 at 4:16 | comment | added | Iosif Pinelis | @Dan : Unfortunately, I am not familiar with desmos. Does the current picture there show the "best" (but still insufficient) choice of the pair of circles? | |
| Nov 29, 2023 at 4:03 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 29, 2023 at 4:00 | comment | added | Dan | Bravo! Here is the desmos graph I used to check all fifteen cases. | |
| Nov 29, 2023 at 3:58 | comment | added | Iosif Pinelis | @Dan : I have addressed your comments. | |
| Nov 29, 2023 at 3:54 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 29, 2023 at 3:30 | vote | accept | Dan | ||
| Nov 29, 2023 at 2:56 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |