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Posers and Puzzles

Posers and Puzzles

  1. 06 Jul '06 01:59
    given a cube can you take a cross-section that is a regular pentagon.
  2. 06 Jul '06 07:26 / 1 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?
    aginis asked:
    "given a cube can you take a cross-section that is a regular pentagon."

    I answered:
    "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.

    You asked:
    "why do you say that?"

    And I answer:
    That's why I said that.

    Am I wrong?
  5. 06 Jul '06 11:04 / 1 edit
    Originally posted by FabianFnas
    aginis asked:
    "given a cube can you take a cross-section that is a regular pentagon."

    I answered:
    "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.

    You asked:
    "why do you say that?"

    And I answer:
    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)

    please note that i asked for a REGULAR pentagon

    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 18:14 / 1 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
  10. 06 Jul '06 19:52
    Originally posted by aginis
    i like cheese too especially the cheese
    Cheese or chess - almost the same.