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Posers and Puzzles

Posers and Puzzles

  1. Donation Acolyte
    Now With Added BA
    03 Oct '03 15:55
    Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

    (Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC )
  2. Donation richjohnson
    TANSTAAFL
    03 Oct '03 19:33
    Originally posted by Acolyte
    Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

    (Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC )
    The way you've described it, the first circle would just touch the sides of the square, leaving no room for a second circle between it and the square. Perhaps you could rephrase your question?
  3. 03 Oct '03 20:14
    Originally posted by Acolyte
    Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

    (Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC )

    1:2
  4. Donation Acolyte
    Now With Added BA
    03 Oct '03 20:40
    Originally posted by richjohnson
    The way you've described it, the first circle would just touch the sides of the square, leaving no room for a second circle between it and the square. Perhaps you could rephrase your question?
    Look at my avatar: the second circle has to fit in the grey area.
  5. Donation Acolyte
    Now With Added BA
    03 Oct '03 20:42
    Originally posted by ivanhoe

    1:2
    Nope.
  6. Standard member Phlabibit
    Mystic Meg
    03 Oct '03 22:14
    Originally posted by Acolyte
    Nope.
    Just by eye I would say 1/16? I am at home, had I seen this at work I would have used my CAD to figure it out... as I have done with RC Math Quizes....

    I will know some time this weekend if I am wrong.... and post the proper answer.

    Phla-
  7. Standard member royalchicken
    CHAOS GHOST!!!
    04 Oct '03 20:37
    Originally posted by Acolyte
    Look at my avatar: the second circle has to fit in the grey area.
    I won't say anything answerwise, but this is a puzzle only a inscribed biscuiteer could invent . I've had a good deal of trouble puzzling you too--else I'd post something in here.
  8. Standard member Phlabibit
    Mystic Meg
    06 Oct '03 17:26
    1 : 5.88

    or

    .17
  9. 06 Oct '03 18:49
    Originally posted by Phlabibit
    1 : 5.88

    or

    .17
    Thats almost, but not quite right. Not much more than pythagoras is needed I think...
  10. Standard member royalchicken
    CHAOS GHOST!!!
    06 Oct '03 18:54
    Phlabby, you've gone and rounded :'(.

    Acolyte, you've demanded an answer that is cumbersome with just ASCII, so now Phlabby was forced to round his answer. Shame on you .

  11. Standard member TheMaster37
    Kupikupopo!
    12 Oct '03 19:08
    Originally posted by Acolyte
    Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

    (Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC )
    Square with sides 2, so the biggest circle in it has radius 1. On the diagonal of the square there is exactly sqrt(2)-1 left in the top left corner. The bit is the diagonal of a smaller square, with sides...sqrt(3/2 - sqrt(2)). So the cicle in there would have radius 1/2*sqrt(3/2 - sqrt(2)), wich is then the ratio of them.

    Wich is also sqrt(2) / sqrt(3 - 2*sqrt(2)) : 1

    I think...
  12. Standard member Fiathahel
    Artist in Drawing
    13 Oct '03 14:36
    Originally posted by TheMaster37
    Square with sides 2, so the biggest circle in it has radius 1. On the diagonal of the square there is exactly sqrt(2)-1 left in the top left corner. The bit is the diagonal of a smaller square, with sides...sqrt(3/2 - sqrt(2)). So the cicle in there would have radius 1/2*sqrt(3/2 - sqrt(2)), wich is then the ratio of them.

    Wich is also sqrt(2) / sqrt(3 - 2*sqrt(2)) : 1

    I think...
    Hmm, I don't see what you're doing, but ....

    The answer is:

    sqrt(2)-1 : sqrt(2)+1

    Perhaps you might think now: WHY? so I'll give you my reasoning.

    The ratio of the radii equals the ratio of the (2*radius+distance from circle to corner of the smallest square around the circle)s. These lengths are easy to compute. The numbers in the answer are those lengths if you start with a square with sides 2.
  13. Standard member Phlabibit
    Mystic Meg
    13 Oct '03 16:42
    Originally posted by Fiathahel
    Hmm, I don't see what you're doing, but ....

    The answer is:

    sqrt(2)-1 : sqrt(2)+1

    Perhaps you might think now: WHY? so I'll give you my reasoning.

    The ratio of the radii equals the ratio of the (2*radius+distance from circle to corner of the smallest square around the circle)s. These lengths are easy to compute. The numbers in the answer are those lengths if you start with a square with sides 2.
    That small circle won't fit inside the square if you use the distance from the circle to the corner as the diameter.....

    P
  14. Donation Acolyte
    Now With Added BA
    13 Oct '03 17:03
    Phlabibit and Fiathahel's answers sound about right, but I'm not sure about the reasoning. Could you elaborate?
  15. Standard member royalchicken
    CHAOS GHOST!!!
    13 Oct '03 17:35 / 1 edit
    Fiathahel's answer is the same as 3-2sqrt(2), or about 0.17, which is what I got. They can explain themselves though