I was looking at the work @Pezevenk was doing with lower and upper bounds, and thought that could be used to make the 3d plot more meaningful. His inequalities say that we can iterate the lower and upper bounds with
U_(n+1)=4-1/(1+2*U_n)
L_(n+1)=4-1/(1+2*L_n)-1/L_n
which gives 3.6003 < c/(a+b) < 3.8861
Plotting this value instead of the actual pineapple value effectively exaggerates the deviations from a perfect plane. Now the points are on some kind of a curved 2d surface.
I thought it was interesting that the values only covered about a tenth of the allowed range. The real solution from google is very close to halfway between the bounds, so I would guess that someone could find tighter bounds (no idea how).
I'm not sure what to do with the small pineapple group, since the bounds don't apply to them. Although I suspect that this group might just be some of the same solutions with their variables swapped around.
I also added color to the 2d plots to show which combinations were closer to being solutions than others. I tried plotting the error as the Z-axis, and it just comes out as a cloud of gas. The only time I could see any noticeable pattern was the 2d patterns that you see when looking along the Z-axis
I really couldn't say. You'd probably need someone at least a little familiar with the analytical way of solving it. I looked at the explanation, and I have no idea how that stuff works.
I was looking at the work @Pezevenk was doing with lower and upper bounds, and thought that could be used to make the 3d plot more meaningful. His inequalities say that we can iterate the lower and upper bounds with
U_(n+1)=4-1/(1+2*U_n)
L_(n+1)=4-1/(1+2*L_n)-1/L_n
which gives 3.6003 < c/(a+b) < 3.8861
Plotting this value instead of the actual pineapple value effectively exaggerates the deviations from a perfect plane. Now the points are on some kind of a curved 2d surface.
I thought it was interesting that the values only covered about a tenth of the allowed range. The real solution from google is very close to halfway between the bounds, so I would guess that someone could find tighter bounds (no idea how).
I'm not sure what to do with the small pineapple group, since the bounds don't apply to them. Although I suspect that this group might just be some of the same solutions with their variables swapped around.
I also added color to the 2d plots to show which combinations were closer to being solutions than others. I tried plotting the error as the Z-axis, and it just comes out as a cloud of gas. The only time I could see any noticeable pattern was the 2d patterns that you see when looking along the Z-axis
Plots
What causes those wave patterns? I took some calculus freshman year, so this is entirely out of my wheelhouse
I really couldn't say. You'd probably need someone at least a little familiar with the analytical way of solving it. I looked at the explanation, and I have no idea how that stuff works.
Until then, pretty shapes!
This is dope. Perhaps I will try to figure out better bounds.