Timeline for Writing the plane as {(x,y,z): x+y+z=0} [closed]
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 4, 2022 at 8:02 | history | closed |
Gro-Tsen Alexandre Eremenko abx Leo Alonso Neil Strickland |
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| Apr 27, 2022 at 14:32 | comment | added | James Propp | @Sam Hopkins: I like your last point. I'm going to call it the "zero-sum barycentric coordinate representation" unless someone can suggest a term that's already in the literature. | |
| Apr 27, 2022 at 0:59 | comment | added | Sam Hopkins | Alternatively, it really is barycentric coordinates with respect to the equilateral triangle which has vertices $(1,-1,0)$, $(0,1,-1)$, and $(-1,0,1)$. | |
| Apr 27, 2022 at 0:49 | comment | added | Sam Hopkins | @JamesPropp: The only difference is $x+y+z=1$ versus $x+y+z=0$ but that just amounts to subtracting $\frac{1}{3}$ from each coordinate. | |
| Apr 27, 2022 at 0:41 | comment | added | James Propp | @Sam Hopkins: I agree that the barycentric coordinates representation is similar, but it's not exactly the same thing. (Note that the Wikipedia article says "Every point has barycentric coordinates, and their sum is not zero.") | |
| Apr 26, 2022 at 23:09 | comment | added | Sam Hopkins | @LSpice: "Standard representation" is also a standard name- see groupprops.subwiki.org/wiki/Standard_representation or en.wikipedia.org/wiki/…. | |
| Apr 26, 2022 at 22:34 | comment | added | LSpice | Buckminster Fuller spent a long time promoting an approach to geometry based on this idea under the name synergetics. \\ By the way, speaking of names, I think the standard irreducible representation of $S_3$ is more commonly called its reflection representation. | |
| Apr 26, 2022 at 20:41 | review | Close votes | |||
| May 4, 2022 at 8:02 | |||||
| Apr 26, 2022 at 20:01 | comment | added | Sam Hopkins | I think "barycentric coordinates" is one term that is used for essentially this system, especially in e.g. computer graphics. See for instance en.wikipedia.org/wiki/…. | |
| Apr 26, 2022 at 19:59 | history | asked | James Propp | CC BY-SA 4.0 |