Editing Talk:2435: Geothmetic Meandian
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R(n) = max(n)-min(n)<br> | R(n) = max(n)-min(n)<br> | ||
CASE 1: max(n)=ave(n), THEN max(n+1)=median(n+1)=geomean(n) AND min(n+1)=geomean(n+1)<br> | CASE 1: max(n)=ave(n), THEN max(n+1)=median(n+1)=geomean(n) AND min(n+1)=geomean(n+1)<br> | ||
− | In this case max(n+1) is fixed to a previous value, | + | In this case max(n+1) is fixed to a previous value, geomean(n) and min(n+1) takes on the new geomean(n+1) which is guaranteed to reduce the range R(n) as min(n) < geomean(n+1) < max(n). It also implies case 2 must be invoked at n+1, because min(n+1)=geomean(n+1)<br> |
CASE 2: min(n)=geomean(n), THEN max(n+1)=ave(n+1) AND min(n+1)=median(n+1)=ave(n)<br> | CASE 2: min(n)=geomean(n), THEN max(n+1)=ave(n+1) AND min(n+1)=median(n+1)=ave(n)<br> | ||
− | In this case min(n+1) is fixed to a previous value, | + | In this case min(n+1) is fixed to a previous value, ave(n) and max(n+1) takes on the new ave(n+1) which is guaranteed to reduce the range R(n) as min(n) < ave(n+1) < max(n). It also implies case 1 must be invoked at n+1, because max(n+1)=ave(n+1)<br> |
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Each case forces the range to be reduced while also forcing the alternate case on the next iteration.<br> | Each case forces the range to be reduced while also forcing the alternate case on the next iteration.<br> |