Thread: Circles part 2
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Old 2004-12-18, 08:52   #3
cheesehead
 
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"Richard B. Woods"
Aug 2002
Wisconsin USA

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Quote:
Originally Posted by mfgoode
The 1st 5 terms are in G.P but from the 6th T6 =31 and not 32 as expected.
But that expectation of 32 is based on an assumption that powers of 2 are involved, just because the first few terms of the sequence are equal to powers of 2.

That assumption would probably not survive a thoughtful comparison of diagrams with n points and the connecting diagonals, for n= 2, 3, 4, 5, ... One would soon note, for example, that
each time a point is added, one more region bordering the circle is created.
There are [b]n[/b] such regions between the circle and the inscribed [b]n[/b]-sided polygon.
When one subtracts [b]n[/b] from T[b]n[/b], one is left with the number of regions inside the polygon.
But soon that doesn't jibe with a 2^([b]n[/b]-1) assumption ...


This would lead to one of your three ways of representing Tn, I suppose.

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P.S. Why does the spoiler tag interfere with word-wrapping when I don't explicitly include line breaks? Or is that just on my browser?

Last fiddled with by cheesehead on 2004-12-18 at 09:04
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