Discussion:
Does anyone recognize this real number?
(too old to reply)
Stush
2004-10-26 20:23:50 UTC
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2.41421356237... or its reciprocal 0.414213562373

(Last digit might have been rounded.)

Thanks!
Dennis May
2004-10-26 20:28:38 UTC
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Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!
Looks like sqrt(2)+1 and its reciprocal sqrt(2)-1.
Zdislav V. Kovarik
2004-10-26 21:04:46 UTC
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Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!
Call the first number x, then the second number is 1/x,
as you said, and look at x - 1/x. Which positive x will fit the arising
equation?

(Others, I am sure, will do the algebra for you. Oh well..)

Cheers, ZVK(Slavek).
JEMebius
2004-10-26 22:32:49 UTC
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x - 1/x = 2 --> x^2 - 2x - 1 = 0 --> x = 1 + sqrt(2) or x = 1 -
sqrt(2); x = 1 + sqrt(2) fits your question.

Please read in any high school algebra textbook how to solve quatratic
equations.

HTH: Johan E. Mebius

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Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!
Oscar Lanzi III
2004-10-26 23:42:07 UTC
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The number minus its reciprocal is 2. Thus 1/x = x-2. Clear fractions
and solve for the positive root of the resulting quadratic equation.

--OL
Richard Henry
2004-10-27 04:39:50 UTC
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Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!
2+n = 1/n?

I always liked 1+n = 1/n, which is very close to the ratio between miles and
kilometers.
Stush
2004-10-27 13:09:02 UTC
Permalink
Post by Stush
2.41421356237... or its reciprocal 0.414213562373
(Last digit might have been rounded.)
Thanks!
sqrt(2) + 1 = 2.41421356237...

lim n->infinity P(n+1)/P(n) = sqrt(2) + 1
where P(n) is the nth Pell number.

Though I assume this result is well known.

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