Two Plus Two Newer Archives Maths: why does 987654321 / 123456789 = 8.000000073
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#11
11-19-2007, 05:10 AM
 Dan. Senior Member Join Date: Aug 2005 Location: The European Phenom Posts: 3,836
Re: NUMBER OF THE BEAST

[ QUOTE ]
I have worse news, sir. Try adding the numbers in ROULETTE.

1+2+3+4+...+35+36

Scary.

[/ QUOTE ]

*GASP!*
#12
11-19-2007, 06:10 AM
 jessica1994 Senior Member Join Date: Oct 2007 Posts: 482
Re: NUMBER OF THE BEAST

987654321/123456789 = 8.0000000729000006633900060368490...

which is very nearly 8, except for the isolated 729, 66339, 6036849 ... Now, 729 = 9^3. This isn't a coincidence, as we will see.

Explanation:
Using our prime factor finder program or built-in function, we find that:

729 = 9^3 = 9^3 * 91^0
66339 = 9^3 * 91 = 9^3 * 91^1
6036849 = 9^3 * 91^2 = 9^3 * 91^2

so we can conjecture that:

987654321/123456789 = 8 + 9^3*1E-10*SUM[N=0,N=INFINITE,(91*1E-10)^N]

where the sum goes from N=0 to N=infinite. This can be proved very easily using the well-known summation formula for geometric progressions, as this happens to be one.
#13
11-22-2007, 05:42 AM
 john kane Senior Member Join Date: Dec 2004 Posts: 2,829
Re: NUMBER OF THE BEAST

thanks for all the replies and apologies for not replying sooner. the link above has certainly helped me see there is an actual pattern, rather than it being an eerie one-off.

thanks and gl.
#14
11-22-2007, 01:17 PM
 Duke Senior Member Join Date: Sep 2002 Location: SW US Posts: 5,853
Re: Maths: why does 987654321 / 123456789 = 8.000000073

[ QUOTE ]
I'd rather someone tell my why cubes add up to squares. Using geomety, not algebra.

[/ QUOTE ]

I'm not convinced that they do.
#15
11-22-2007, 05:15 PM
 pzhon Senior Member Join Date: Mar 2004 Posts: 4,515
Re: Maths: why does 987654321 / 123456789 = 8.000000073

[ QUOTE ]
I'd rather someone tell my why cubes add up to squares. Using geomety, not algebra.

[/ QUOTE ]
(1+2+...+n)^2 = 1^3 + 2^3 + .. + n^3.

Proof without Words: Sum of Cubes
Alan L. Fry
Mathematics Magazine, Vol. 58, No. 1 (Jan., 1985), p. 11

I don't have that in front of me, but typically these proofs are inductive. You find some way to illustrate why n^3 = (1+2+...+n)^2-(1+2+...+(n-1))^2. If you fit the smaller square inside the larger, the remainder is an L shape, the intersection of two strips that are n x (1+2+..+n), or a strip that is n x (1+2+...+n) plus a strip that is n x (1+2+...+(n-1)). Break the strips into subrectangles indicated by the sum and pair n x k and n x (n-k), forming n pairs (pair n x n with n x 0) fitting into nxn squares.
#16
11-22-2007, 05:19 PM
 MelchyBeau Senior Member Join Date: Sep 2004 Location: Shaping the minds of young people everywhere Posts: 2,151
Re: Maths: why does 987654321 / 123456789 = 8.000000073

[ QUOTE ]
[ QUOTE ]
I'd rather someone tell my why cubes add up to squares. Using geomety, not algebra.

[/ QUOTE ]

I'm not convinced that they do.

[/ QUOTE ]

#17
11-25-2007, 02:32 PM
 CORed Senior Member Join Date: Sep 2002 Posts: 4,798
Re: Maths: why does 987654321 / 123456789 = 8.000000073

[ QUOTE ]
Uhm.. Because 123456789 * 8 is almost equal to 987654321? Not trying to sound smug but that's all there is to it I think [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

123456789 * 8 = 987654312, to be exact.
#18
11-28-2007, 02:27 AM
 GoodCallYouWin Senior Member Join Date: Nov 2006 Posts: 1,070
Re: Maths: why does 987654321 / 123456789 = 8.000000073

Someone is clearly trying to send us messages through the fabric of spacetime itself.

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