For fun I found the continued fraction expression
of the ratio of these two big integers:
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 1, 3, 12, 5, 1, 2, 1, 19,
3, 3, 3, 1, 1, 3, 2, 2, 3, 1, 5, 1, 4, 28, 2, 1, 3, 1, 2,
2, 1, 1, 1, 1, 10, 4, 1, 5, 6, 13, 1, 1, 2, 23, 1, 3, 16,
1, 29, 14, 4, 1, 3, 2.
It agrees with sqrt(2) for 70 steps.
On 2015-7-12 23:54, David Goldberg wrote:
This is in SageMath Version 6.6, Release Date: 2015-04-14 running on a
MacBook. The following lines print 'equal', even though m and m1 do not
appear equal to me!
m=540579833922455191419978421211010409605356811833049025*sqrt(1/2)
m1=382247666339265723780973363167714496025733124557617743
if m == m1:
print "equal"
--
*\\* Anton Sherwood *\\* www.bendwavy.org
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