Timeline for Sufficient coordinate-free condition for points being co-spheric
Current License: CC BY-SA 4.0
12 events
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| Feb 15, 2021 at 15:48 | history | edited | Manfred Weis | CC BY-SA 4.0 |
added a visualisation of @fedja's counter example
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| Feb 15, 2021 at 14:42 | history | edited | Manfred Weis |
added the counterexamples tag
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| Feb 15, 2021 at 14:40 | comment | added | Manfred Weis | @fedja you are of course right; sorry for my mental blockage. | |
| Feb 15, 2021 at 13:53 | comment | added | fedja | @ManfredWeis How is it different? The arc corresponding to the inscribed angle of 120 degrees on the triangle side has the same radius as that for 60 degrees because 120+60=180. Am I misinterpreting your definition of "circumscribed" :-) | |
| Feb 15, 2021 at 4:06 | history | edited | Manfred Weis | CC BY-SA 4.0 |
made more explicit that the simplices must have maximal dimension
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| Feb 15, 2021 at 3:48 | comment | added | Manfred Weis | @fedja in your example there are four simplices of which the three that contain the centerpoint have equal radius of circum circle, but the equilateral triangle's radius is different or did I miss the point? Maybe I have to edit my question. | |
| Feb 14, 2021 at 20:30 | comment | added | fedja | Three vertices of an equilateral triangle on the plane together with its center give a sure counterexample but I wouldn't call this one "exotic" :-). It looks like the statement may, indeed, hold if the points are sufficiently many though... | |
| Feb 14, 2021 at 13:50 | history | edited | gmvh |
Added top-level tag
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| Feb 14, 2021 at 13:13 | comment | added | Liviu Nicolaescu | Take four noncoplanar points of your group. They determine a sphere who's radius and center can be determined geometrically. Think of one of these points asthe North Pole of the sphere and consider the stereographic projection onto the tangent plane to the South pole. You are now left to decide if the projection of the remaining remaining points are coplanar. That is an easier proposition. | |
| Feb 14, 2021 at 10:15 | comment | added | Manfred Weis | @JeanMarieBecker I use corners to hint the geometric interpretation whereas I tend to reserve vertex for graph theoretic interpretations. In geometry vertices need not be corners; e.g. the vertex of a parabola as depicted here | |
| Feb 14, 2021 at 9:46 | comment | added | Jean Marie Becker | A tiny point of vocabulary : corners -> vertices | |
| Feb 14, 2021 at 9:35 | history | asked | Manfred Weis | CC BY-SA 4.0 |