
Title text: If you can't get your graphing tool to do the shading, just add some clip art of cosmologists discussing the unusual curvature of space in the area.
I'm trying to imagine what would it look like when the percentage doesn't add up to 100.
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Tigerlion wrote:Well, I imagine as the game progresses, various people will be getting moody.
BoomFrog wrote:I still have no idea what town moody really looks like.
moody7277 wrote:I think it's like with triangles; pie charts add up to more than 100% on positively curved surfaces, exactly 100% on flat ones, and less than 100% on negatively curved surfaces.
FTFY Sum of internal boundary angles add up to>180° (or pi rads), but length of boundary (tending to circumference) is shorter than the 2.pi.r of a flat plan and areas likewise lower (whichever is the surrogate to percentage). Each centre-point still has a full 360° around it, but have only five 60°-worth elements and insist on making them adjoin around, you're starting to construct a dodecahedral corner.Heimhenge wrote:That was my first thought too ... graph it on a sphere if they add up tomoreless than 100%.
moody7277 wrote:I think it's like with triangles; pie charts add up to more than 100% on positively curved surfaces, exactly 100% on flat ones, and less than 100% on negatively curved surfaces.
Soupspoon wrote:FTFY Sum of internal boundary angles add up to>180° (or pi rads), but length of boundary (tending to circumference) is shorter than the 2.pi.r of a flat plan and areas likewise lower (whichever is the surrogate to percentage). Each centre-point still has a full 360° around it, but have only five 60°-worth elements and insist on making them adjoin around, you're starting to construct a dodecahedral corner.Heimhenge wrote:That was my first thought too ... graph it on a sphere if they add up tomoreless than 100%.
The other curvature handles more, 'rucking up' as per the comic, until you stretch it out into a hyperbolic plane of some kind.
Heimhenge wrote:
Now that you mention it, yeah I guess it depends on what geometric entity represents percentage. I was thinking "area" since circumference arc lengths and vertex angles would be meaningless. There might be some other measure that works ... maybe sum of the interior angles, or something like the Gaussian curvature. But I think area is the most intuitive, since on a normal flat pie chart area maps to percentage.
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