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Posers and Puzzles

Posers and Puzzles

  1. Subscriber joe shmo On Vacation
    Strange Egg
    30 Jan '18 19:00 / 1 edit
    What is ( appx. - 4 significant figures ) the radius of a planet from which you could begin at the North Pole, walk 1 mile South. Then 1 mile ( East or West ) completing a full circle, and 1 mile North again to return to the pole?

    I figured I'd continue on with my oversight from the other puzzle.
  2. Standard member HandyAndy
    Non sum qualis eram
    30 Jan '18 22:59
    Originally posted by @joe-shmo
    What is ( appx. - 4 significant figures ) the radius of a planet from which you could begin at the North Pole, walk 1 mile South. Then 1 mile ( East or West ) completing a full circle, and 1 mile North again to return to the pole?

    I figured I'd continue on with my oversight from the other puzzle.
    The radius of the circle you walk is one mile (the distance from the pole to the circle).
    The circumference of the same circle is one mile.
    How is that possible? Are we on the flat surface of a spherical planet?
  3. Subscriber joe shmo On Vacation
    Strange Egg
    31 Jan '18 00:18 / 1 edit
    Originally posted by @handyandy
    The radius of the circle you walk is one mile (the distance from the pole to the circle).
    The circumference of the same circle is one mile.
    How is that possible? Are we on the flat surface of a spherical planet?
    "The radius of the circle you walk is one mile (the distance from the pole to the circle)."

    No, the radius of the 1 mile arc you walk in the southerly direction is unknown ( its the radius of the sphere). When you get to that latitude on the sphere you walk west (or east) a full circle that has a circumference of 1 mile.

    "Are we on the flat surface of a spherical planet?" We are not, no tricks of wording. Its a math problem.
  4. 31 Jan '18 00:53 / 1 edit
    Originally posted by @joe-shmo
    "The radius of the circle you walk is one mile (the distance from the pole to the circle)."

    No, the radius of the 1 mile arc you walk in the southerly direction is unknown ( its the radius of the sphere). When you get to that latitude on the sphere you walk west (or east) a full circle that has a circumference of 1 mile.

    "Are we on the flat surface of a spherical planet?" We are not, no tricks of wording. Its a math problem.
    Do I understand the poser correctly?

    The wording (“THE radius” ) implies that we are walking on the surface of a sphere whose radius, or distance from the center to any point on the surface, is the same at all points on the surface.

    You walk for one mile from a pole along any one longitude line, to a point where it intersects a certain latitude line. The latitude line is therefor one mile from the pole (as the crow walks) and is given as one mile in circumference (same crow).

    What is the radius of the sphere?

    Is this correct?
  5. Subscriber joe shmo On Vacation
    Strange Egg
    31 Jan '18 01:06
    Originally posted by @js357
    Do I understand the poser correctly?

    The wording (“THE radius” ) implies that we are walking on the surface of a sphere whose radius, or distance from the center to any point on the surface, is the same at all points on the surface.

    You walk for one mile from a pole along any one longitude line, to a point where it intersects a certain latitude line. T ...[text shortened]... one mile in circumference (same crow).

    What is the radius of the sphere?

    Is this correct?
    Yeah, I believe you have the proper setup.
  6. Standard member HandyAndy
    Non sum qualis eram
    31 Jan '18 01:23
    Originally posted by @joe-shmo
    "The radius of the circle you walk is one mile (the distance from the pole to the circle)."

    No, the radius of the 1 mile arc you walk in the southerly direction is unknown ( its the radius of the sphere). When you get to that latitude on the sphere you walk west (or east) a full circle that has a circumference of 1 mile.

    "Are we on the flat surface of a spherical planet?" We are not, no tricks of wording. Its a math problem.
    Do we agree that the radius of a one-mile circle is 0.159 miles on a flat surface?
  7. Subscriber joe shmo On Vacation
    Strange Egg
    31 Jan '18 01:26
    Originally posted by @handyandy
    Do we agree that the radius of a one-mile circle is 0.159 miles on a flat surface?
    Sure.
  8. Standard member HandyAndy
    Non sum qualis eram
    31 Jan '18 01:31
    Originally posted by @joe-shmo
    Sure.
    And what we're looking for is the radius of the entire planet.
  9. Subscriber joe shmo On Vacation
    Strange Egg
    31 Jan '18 01:42
    Originally posted by @handyandy
    And what we're looking for is the radius of the entire planet.
    Yes sir.
  10. Standard member HandyAndy
    Non sum qualis eram
    31 Jan '18 03:51
    Originally posted by @joe-shmo
    Yes sir.
    Just an observation: It's a really small planet.
  11. Subscriber joe shmo On Vacation
    Strange Egg
    31 Jan '18 04:05 / 1 edit
    Originally posted by @handyandy
    Just an observation: It's a really small planet.
    Quite small indeed! More like an astriod.
  12. Standard member HandyAndy
    Non sum qualis eram
    31 Jan '18 22:32 / 1 edit
    Originally posted by @joe-shmo
    Quite small indeed! More like an astriod.
    To determine the planet's radius, do we first calculate the relationship between the one-mile
    arc from point A to point B and the shorter (0.159 mile) chord linking point A and point B?
  13. Subscriber joe shmo On Vacation
    Strange Egg
    31 Jan '18 23:51 / 3 edits
    Originally posted by @handyandy
    To determine the planet's radius, do we first calculate the relationship between the one-mile
    arc from point A to point B and the shorter (0.159 mile) chord linking point A and point B?
    No, and FYI your figure of a chord length ( 0.159mi) between A and B must be incorrect because you cannot find the chord without knowing the radius in this case ( we do not know the angle subtended by the 1 mile arc - that is to say "explicitly" ) Hint: We can know the angle implicitly as a function of the radius.
  14. Standard member HandyAndy
    Non sum qualis eram
    01 Feb '18 01:57
    Originally posted by @joe-shmo
    No, and FYI your figure of a chord length ( 0.159mi) between A and B must be incorrect because you cannot find the chord without knowing the radius in this case ( we do not know the angle subtended by the 1 mile arc - that is to say "explicitly" ) Hint: We can know the angle implicitly as a function of the radius.
    I believe 0.159 mile is the radius of a circle having a circumference of one mile, but apparently that's a non-starter.

    We need a mathematician.
  15. Subscriber joe shmo On Vacation
    Strange Egg
    01 Feb '18 02:47
    Originally posted by @handyandy
    I believe 0.159 mile is the radius of a circle having a circumference of one mile, but apparently that's a non-starter.

    We need a mathematician.
    There used to be many posters in this forum that had mathematical backgrounds maybe 8-10 years ago. Now, they seem to have found greener pastures ( perhaps the debates forum - ) If you have little to no math background this will probably be difficult. I guess the pre requisites to this problem are algebra, and trigonometry (calculus - if you wish to get fancy finding the zero of the function).