Editing 2435: Geothmetic Meandian
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* Cueball offers to split the difference by averaging the rates €5:$6 and €6:$7 yielding a rate of €71:$84 (about 0.84524€/$ or 1.18310$/€). | * Cueball offers to split the difference by averaging the rates €5:$6 and €6:$7 yielding a rate of €71:$84 (about 0.84524€/$ or 1.18310$/€). | ||
* Megan offers to split the difference by averaging the rates $6:€5 and $7:€6 yielding a rate of €60:$71 (about 0.84507€/$ or 1.18333$/€). | * Megan offers to split the difference by averaging the rates $6:€5 and $7:€6 yielding a rate of €60:$71 (about 0.84507€/$ or 1.18333$/€). | ||
− | In one direction (€/$), Cueball is using the arithmetic mean but Megan is using the | + | In one direction (€/$), Cueball is using the arithmetic mean but Megan is using the geometric mean while in the other direction ($/€), Megan is using the arithmetic mean but Cueball is using the geometric mean. This creates two new exchange rates which are closer than the orginal rates, but the new rates are still different for each other. Megan and Cueball can then iterate this process and the rates will converge to the geometric mean of the original rates, namely: |
* sqrt((5/6)*(6/7)) = sqrt(5/7) = 0.84515€/$ or | * sqrt((5/6)*(6/7)) = sqrt(5/7) = 0.84515€/$ or | ||
* sqrt((6/5)*(7/6)) = sqrt(7/5) = 1.18322$/€. | * sqrt((6/5)*(7/6)) = sqrt(7/5) = 1.18322$/€. |