3 ms·
I found the thing about iteration quite strange. To iterate, we need to know if our mediant is larger or smaller than the true value. How do we know that? Ed
by geysersam 4y ago
I found the thing about iteration quite strange.
To iterate, we need to know if our mediant is larger or smaller than the true value.
How do we know that?
Edit: elsewhere in the thread someone explained that the purpose of iterating is to find an approximation with small denominator.
- madcaptenor 4y agoe isn't the best example for this, because you would need a good decimal expansion. But say we're trying to approximate sqrt(2) by this method. Say we've already established that it's in the interval [7/5, 10/7]. We can verify because 7^2 < 2*5^2 and 10^2 > 2*7^2. Then the mediant is 17/12, and since 17^2 = 289 > 288 = 2*12^2, we know 17/12 > sqrt(2). So [7/5, 17/12] is a smaller interval containing sqrt(2). Repeating this, [24/17, 17/12] is even better, and so on.