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The Maximum number of pentagons which can be selected from a dodecahedron with no elements (points, lines) shared is 3. 4 identical copies of such a set will make the dodecahedron. What is the maximum number of dodecahedra sharing no elements can be selected from the 120 cell and can X copies of that maximum set make the entire 120 cell? Naraht ( talk) 02:09, 7 November 2021 (UTC)
Talking with @SaulSchleimer: I was wrong, there is a configuration with 24 non-touching dodecahedra, and five copies of it do make up the whole 120-cell. On layers going out, we have 1, 8, 6, 8, 1 dodecahedra.Double sharp ( talk) 20:06, 9 November 2021 (UTC) —That's Henry Segerman saying that, not me, lest anyone be misled. I offered the question to Henry because I thought he might know. — Tamfang ( talk) 23:15, 9 November 2021 (UTC)
If x, y, and z are positive integers and z is a function of x and y, z(x,y) = (y^2-3y)/2+x+1, given z, what are x and y? (Actually, if you have y, x is trivial to get.) Bubba73 You talkin' to me? 02:32, 7 November 2021 (UTC)
If you have three variables that sum to some constant, , then you only have two degrees of freedom. So while you could plot them in a cube, you can also plot all three on a ternary diagram. Since the value of each variable can be read off a ternary diagram as proportional to the distance from each corner, and humans are pretty good at judging relative and absolute linear distances, and the internet is still mostly 2-D, this works well.
I need to present some data with three variables and two degrees of freedom in the form , with variables that multiply to a constant. Does anyone have any good suggestions for how to do this? I mean, something more like a ternary diagram than a contour plot. Ideally, I'd like to be able to join such diagrams along the axes, as ternary diagrams are joined in a piper plot (yes, a contour plot would do that, for two axes, but it's harder to read).
As a simple example for illustrative purposes, suppose I had the masses and maximum accellerations of a Saturn V rocket, the QEII, an ice yacht, the latest Tesla, the latest Hummer, and Usain Bolt. I probably do, this is Wikipedia. And knowing that F = ma, I wanted to plot all three variables for all of these on a ternary-like plot.
I actually want to plot some data over some equations, comparing the datasets and the fit of the data. I have several equations of form , sharing some variables. HLHJ ( talk) 15:56, 7 November 2021 (UTC)
Mathematics desk | ||
---|---|---|
< November 6 | << Oct | November | Dec >> | November 8 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
The Maximum number of pentagons which can be selected from a dodecahedron with no elements (points, lines) shared is 3. 4 identical copies of such a set will make the dodecahedron. What is the maximum number of dodecahedra sharing no elements can be selected from the 120 cell and can X copies of that maximum set make the entire 120 cell? Naraht ( talk) 02:09, 7 November 2021 (UTC)
Talking with @SaulSchleimer: I was wrong, there is a configuration with 24 non-touching dodecahedra, and five copies of it do make up the whole 120-cell. On layers going out, we have 1, 8, 6, 8, 1 dodecahedra.Double sharp ( talk) 20:06, 9 November 2021 (UTC) —That's Henry Segerman saying that, not me, lest anyone be misled. I offered the question to Henry because I thought he might know. — Tamfang ( talk) 23:15, 9 November 2021 (UTC)
If x, y, and z are positive integers and z is a function of x and y, z(x,y) = (y^2-3y)/2+x+1, given z, what are x and y? (Actually, if you have y, x is trivial to get.) Bubba73 You talkin' to me? 02:32, 7 November 2021 (UTC)
If you have three variables that sum to some constant, , then you only have two degrees of freedom. So while you could plot them in a cube, you can also plot all three on a ternary diagram. Since the value of each variable can be read off a ternary diagram as proportional to the distance from each corner, and humans are pretty good at judging relative and absolute linear distances, and the internet is still mostly 2-D, this works well.
I need to present some data with three variables and two degrees of freedom in the form , with variables that multiply to a constant. Does anyone have any good suggestions for how to do this? I mean, something more like a ternary diagram than a contour plot. Ideally, I'd like to be able to join such diagrams along the axes, as ternary diagrams are joined in a piper plot (yes, a contour plot would do that, for two axes, but it's harder to read).
As a simple example for illustrative purposes, suppose I had the masses and maximum accellerations of a Saturn V rocket, the QEII, an ice yacht, the latest Tesla, the latest Hummer, and Usain Bolt. I probably do, this is Wikipedia. And knowing that F = ma, I wanted to plot all three variables for all of these on a ternary-like plot.
I actually want to plot some data over some equations, comparing the datasets and the fit of the data. I have several equations of form , sharing some variables. HLHJ ( talk) 15:56, 7 November 2021 (UTC)