This isn't homework, just something I'm working on to pass the time, and I've hit a dead end. What I'm trying to think of is 4 two-dimensional shapes on the surface of a sphere that each share the exact same amount of their perimeter with EVERY other shape. Eg, if shape #1 shares 5 units along it's borders with shape #2, it also shares 5 units with #3 and #4, #2 shares 5 units with #3 and #4, and so on. I just can't seem to get it. Was about to give up, and then I remembered /sci/ and I thought anon might have some insight somewhere in his collective.
Name:
Anonymous2007-06-01 3:54 ID:gCVUrWyI
ive just drawn something on a plane i think fits your description, ill describe it in 4 colors.
start with a horizontal purple bar
at the left side of the purple bar, draw a vertical red bar, making your first perimeter contact. you should have a reflected "L" shape now
between the draw a bent blue bar starting on the right side of the red bar, extending horizontally then going down vertically to end at the purple bar. you should now have something like a rotated "d"
above this bunch of shapes, draw a horizontal green bar not touching anything. from the green bar, extend down 3 green bars, one touching only red, one touching only blue, one touching only purple. it should look something like a merged rotated "E" and "d"