Table1SC.mw
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interface( rtablesize=20 ): |
Warning, the name changecoords has been redefined
Shrinking Circle Problem
Numerical Evaluation of Analytic Formula for R
in the Original Shrinking Circle Problem
Douglas B. Meade
9 February 2007
Derivation of Formula for Location of R
Auxiliary Procedure (MakeTable)
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rlist := [ 1, 0.5, 0.1, 0.05, 0.01, 0.005, 0.001, 0.0005, 0.0001, 0.00005, 0.00001 ]: |
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rlist2 := [ seq( 10.^(-j), j=0..15 ) ]: |
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dlist := [12,10,8,6,4]: |
Here is Table 1.
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MakeTable( 1,0, rlist, dlist ); |
The effect of a vertical offset in the center of the fixed circle (b<>0) can be explored:
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MakeTable( 1, -1, rlist, dlist ); |
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MakeTable( 1, -0.1, rlist, dlist ); |
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MakeTable( 1, -0.01, rlist, dlist ); |
And, here is a single table of values allows us to see now even a very small vertical offset in the fixed circle changes the value of the limit
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blist := [0, seq( -10.^(-j), j=[1,2,4,6,8,10] ) ]: |
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Matrix( 1, 1+3, [ nprintf(""), seq( nprintf("b=%07.1e",b), b=blist[1..3] ) ] ), |
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Matrix( [ MakeTable( 1, blist[1], rlist2, [20] ), seq( Column( MakeTable( 1, b, rlist2, [20] ), 2 ), b=blist[2..3] ) ] ) |
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Matrix( 1, 1+1+2, [ nprintf(""), seq( nprintf("b=%07.1e",b), b=[blist[1],blist[4..5][]] ) ] ), |
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Matrix( [ MakeTable( 1, blist[1], rlist2, [20] ), seq( Column( MakeTable( 1, b, rlist2, [20] ), 2 ), b=blist[4..5] ) ] ) |
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Matrix( 1, 1+1+2, [ nprintf(""), seq( nprintf("b=%07.1e",b), b=[blist[1],blist[6..7][]] ) ] ), |
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Matrix( [ MakeTable( 1, blist[1], rlist2, [20] ), seq( Column( MakeTable( 1, b, rlist2, [20] ), 2 ), b=blist[6..7] ) ] ) |