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Authored by: Anonymous on Tuesday, March 19 2013 @ 03:31 PM EDT |
I keep coming up with 1:
1.414213562.... (from my calculator)
1.41421356
1.4142136
1.414214
1.41421
1.4142
1.414
1.41
1.4
1
Perhaps I did not understand.
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Authored by: Anonymous on Tuesday, March 19 2013 @ 03:41 PM EDT |
The square root function is monotonic and smooth.
Therefore because 2 is between 1 and 4, the sqrt(2) is between sqrt(1) = 1 and
sqrt(4) = 2.
Therefore because 2 is between 1681/841 and 289/144 and , the sqrt(2) is between
sqrt(1681/841) = 41/29 and sqrt(289/144) = 17/12.
Now 41/29 < sqrt(2). So we can approximate sqrt(2) by rounding up 41/29 and
we do ourselves a favor because dividing by 29 is hard. Examining the
possibilities, we see that only 3/2 = 15/10 and 7/5 = 14/10 are reasonable
contenders, but 7/5 is rounding down. So we select 3/2, which is almost as good
as not having to divide at all.
So since not dividing is of common benefit to all we round 3/2 up to 2 and for
the good of the children establish that sqrt(2) = 2.
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Authored by: Anonymous on Tuesday, March 19 2013 @ 04:14 PM EDT |
RAS [ Reply to This | Parent | # ]
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