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Sequence of the Day

A060294: Decimal expansion of Buffon’s constant .

0.63661977236758...
Buffon’s needle problem:
Theorem (Buffon’s needle problem, problem first posed in 1733, solved in 1777). (GeorgesLouis Leclerc, Comte de Buffon)
The probability that a needle of length will randomly land on a line, given a floor with equally spaced parallel lines at a distance apart, is .
Proof. (assuming that the angle and the position of the fallen needle are independently and uniformly random)
If the needle always fell perpendicular (angle radians) to the parallel lines, we would have . So we have

P (l, d ) = sin θ ⋅ ⋅ P⟂(l, d ) = ⋅ = ⋅ . 
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On this day...

 June 22, 1850 Count Libri is convicted in France in absentia of stealing valuable books on scientific and mathematical topics.
 June 22, 1925 Felix Klein dies in Göttingen.
 June 22, 1993 At Cambridge, Andrew Wiles gives the second of three lectures about Fermat's last theorem.
Sequences in the News
 Feb 01 2018 Alphabet announced a $8,589,869,056 = $A000396(6) stock buyback.
 Jan 03 2018 Largest known term of A000043 announced: 77232917.
 Nov 18 2016 PrimeGrid proves that 10223 is not a Sierpinski number, since 10223 × 2 31172165 + 1 is prime. So no changes to A076336 for now.
 Sep 14 2016 Tom Greer discovers the twin primes 2996863034895 × 2 1290000 ± 1 using PrimeGrid, TwinGen and LLR.
 Jan 19 2016 Largest known term of A000043 announced: 274207281, also discovered by Curtis Cooper.
 Mar 02 2014 Fredrik Johansson announces a computation of the partition number p(10 20) ≈ 1.8381765 × 10 11140086259, the largest known term of A000041.
 Dec 06 2013 Microsoft launches a challenge to find large nonMersenne primes, A138837.


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