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Figure Eights (Posted on 2005-02-15) Difficulty: 5 of 5
Suppose that I drew an infinite number of disjoint closed curves in the plane (such as circles, squares, etc.). Suppose that I then tell you that there is one curve for each positive real number.

You would not have too much trouble believing my assertions at this point. For example, I could have drawn all circles with center at the origin. They are all disjoint, and for each positive real number x, there is a corresponding circle - namely, the circle of radius x.

But suppose that I also tell you that all the curves I drew were figure eights. Can you believe my assertions now?

(A figure eight is a curve in the plane obtained from the basic "8" shape by any combination of translation, rotation, expansion, or shrinking.)

See The Solution Submitted by David Shin    
Rating: 4.2000 (5 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
What am I missing?Harry2010-07-24 20:52:05
Some Thoughtsfull area fractal - but still countable number of curvesronen2005-02-24 15:04:04
re: solution - the number of curves must be countable(?)David Shin2005-02-23 07:19:29
Some Thoughtssolution - the number of curves must be countable(?)ronen2005-02-22 21:40:31
re: A thoughtDavid Shin2005-02-22 03:17:33
Some ThoughtsA thoughtowl2005-02-21 04:50:08
Some Thoughtsre(11): I think it's... - ElaborationTristan2005-02-19 17:28:58
re(10): I think it's... - ElaborationDavid Shin2005-02-19 15:28:11
re(9): I think it's... - ElaborationTristan2005-02-19 15:10:04
re(8): I think it's... - ElaborationDavid Shin2005-02-19 04:36:45
re(7): I think it's... - ElaborationTristan2005-02-19 03:22:30
re(6): I think it's... - ElaborationDavid Shin2005-02-18 22:40:33
re(5): I think it's...David Shin2005-02-18 00:14:05
re(4): I think it's...Tristan2005-02-17 23:42:23
re(3): I think it's...David Shin2005-02-17 19:31:39
QuestionNo SubjectVee-Liem Veefessional2005-02-17 05:05:51
re(4): still thinking / cardinalityLarry2005-02-17 04:42:35
Some Thoughtsre(2): I think it's...Tristan2005-02-17 03:15:00
re: I think it's...Avin2005-02-16 13:30:14
re: This may work!Charlie2005-02-16 13:27:11
This may work!np_rt2005-02-16 08:38:55
re(3): still thinkingDavid Shin2005-02-16 06:49:44
re(2): still thinkingLarry2005-02-16 03:56:09
re: still thinkingCharlie2005-02-16 03:31:26
re: I think it's...David Shin2005-02-16 01:08:36
SolutionI think it's...Tristan2005-02-15 23:56:25
still thinkingLarry2005-02-15 21:50:40
re(3): additional thoughtsGamer2005-02-15 20:51:33
re(2): additional thoughtsSteve Herman2005-02-15 20:08:30
Hints/TipsTipsDavid Shin2005-02-15 19:59:16
re: additional thoughtsCharlie2005-02-15 19:04:45
re: additional thoughtsSteve Herman2005-02-15 17:41:01
additional thoughtsLarry2005-02-15 16:52:06
thoughts and cheatsJer2005-02-15 16:43:39
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