Originally posted by aginisaginis asked:
why do you say that?
Originally posted by FabianFnasif your cube is is a cube of length one anchored at (0,0,0) and (1,1,1)
"given a cube can you take a cross-section that is a regular pentagon."
"No, but a hexagon."
"No", because a cross-section cannot give a pentagon.
"but a hexagon." because there is a hexagon to be found if you make a cross-section in the right way.
"why do you say that?"
And I answer:
That's why I said that.
Am I wrong?
Originally posted by aginisA hexagon, i knew, a pentagon I didn't know.
if your cube is is a cube of length one anchored at (0,0,0) and (1,1,1)
then the cross-section formed by the plane passing through (0,0.5,1) (0.5, 1, 1) and (1,0,0) will be a pentagon, therefore your solution is incorrect.
(although i agree that the cross-section defined by (0,0.5,1) (0.5, 1, 1) and (1,0.5,0) is a regular hexagon)
please note that i as ...[text shortened]... olygon is both equiangular and equilateral).
Originally posted by FabianFnasBut FabianFnas -- the example aginis gives is not a regular pentagon.
A hexagon, i knew, a pentagon I didn't know.
I have to get home and try myself, cutting a cheese or turnip or something.
Very fascinating, indeed...
Originally posted by SPMarsA regular pentagon, isn't that a polygon with 5 edges equal in length, and 5 angles equal in degrees?
But FabianFnas -- the example aginis gives is not a regular pentagon.
Doesn't aginis want a regular pentagon?
I would guess it's not possible to slice out a regular pentagon, but have no proof.
Of course the regular hexagon is easy -- you just slice perpendicular through the midpoint of a line joining opposite vertices.
Originally posted by FabianFnascut as if you want to make a regular hexagon but tilt the plane up so that it misses the bottom of the cube.
A regular pentagon, isn't that a polygon with 5 edges equal in length, and 5 angles equal in degrees?
I've tried to cut the d*rn cheese to get a pentagon but have not succeeded.
I'm about to think that it is impossible to cut a pentagon out of a cube.
A hexagon on the other hand ... easy.
I like cheese, especially the holes.