Bob and the Septagon
In his seldomused blog, Brian Lauber does some musing over mathematics and philosophy. First, he admits that there are certain things one cannot do in Euclidean geometry using a straight edge and a compass. For example, you cannot construct a sevensided polygon and you cannot trisect angles.
Then Lauber poses an interesting twist: "Suppose there is an omnipotent being named Bob with the ability to do anything. You tell this being to construct a 7sided figure using only the rules of Euclidean construction. After a cloud of magic, Bob hands you the figure and poofs off into a wisp of smoke."
Wait a sec? Did Bob, being omnipotent, overcome the impossible? Did Bob resort to cheating? Or, did Bob use an infinite number of steps (another nono)? This last case bothered Lauber...
He posed a new "provenimpossible" problem to omnipotent Bob: You have a rod with 5 flexible hinges:
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Now bend it at the hinges to form a tetrahedron.
Again, Bob accomplishes the task and vanishes. But, since this task has a finite number of moves, you have eliminated Bob's use of an infinite number of moves. So....
No conlcusion here...just food for Euclidean thinkers who believe in omnipotent Bobs!
