# the pentagon?

aginis
Posers and Puzzles 06 Jul '06 01:59
1. 06 Jul '06 01:59
given a cube can you take a cross-section that is a regular pentagon.
2. 06 Jul '06 07:261 edit
No, but a hexagon.
3. 06 Jul '06 08:43
Originally posted by FabianFnas
No, but a hexagon.
why do you say that?
4. 06 Jul '06 10:37
Originally posted by aginis
why do you say that?
"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?"

That's why I said that.

Am I wrong?
5. 06 Jul '06 11:041 edit
Originally posted by FabianFnas
"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?"

That's why I said that.

Am I wrong?
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)

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular and equilateral).

http://mathworld.wolfram.com/RegularPolygon.html
6. 06 Jul '06 11:43
Originally posted by aginis
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).

http://mathworld.wolfram.com/RegularPolygon.html
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...
7. 06 Jul '06 16:41
Originally posted by FabianFnas
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...
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.
8. 06 Jul '06 17:37
Originally posted by SPMars
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.
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.
9. 06 Jul '06 18:141 edit
Originally posted by FabianFnas
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.
cut as if you want to make a regular hexagon but tilt the plane up so that it misses the bottom of the cube.

i like cheese too especially the cheese
ðŸ˜›
10. 06 Jul '06 19:52
Originally posted by aginis
i like cheese too especially the cheese
ðŸ˜›
Cheese or chess - almost the same.ðŸ˜•